nested_blockmodel.py

#! /usr/bin/env python
# -*- coding: utf-8 -*-
#
# graph_tool -- a general graph manipulation python module
#
# Copyright (C) 2006-2019 Tiago de Paula Peixoto <tiago@skewed.de>
#
# 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

from .. import _degree, _prop, Graph, GraphView, conv_pickle_state
from . blockmodel import *
from . blockmodel import _bm_test
from . overlap_blockmodel import *
from . layered_blockmodel import *

from numpy import *
import numpy
import copy

class NestedBlockState(object):
    r"""The nested stochastic block model state of a given graph.

    Parameters
    ----------
    g : :class:`~graph_tool.Graph`
        Graph to be modeled.
    bs : ``list`` of :class:`~graph_tool.VertexPropertyMap` or :class:`numpy.ndarray`
        Hierarchical node partition.
    base_type : ``type`` (optional, default: :class:`~graph_tool.inference.blockmodel.BlockState`)
        State type for lowermost level
        (e.g. :class:`~graph_tool.inference.blockmodel.BlockState`,
        :class:`~graph_tool.inference.overlap_blockmodel.OverlapBlockState` or
        :class:`~graph_tool.inference.layered_blockmodel.LayeredBlockState`)
    hstate_args : ``dict`` (optional, default: `{}`)
        Keyword arguments to be passed to the constructor of the higher-level
        states.
    hentropy_args : ``dict`` (optional, default: `{}`)
        Keyword arguments to be passed to the ``entropy()`` method of the
        higher-level states.
    sampling : ``bool`` (optional, default: ``True``)
        If ``True``, the state will be properly prepared for MCMC sampling (as
        opposed to minimization).
    state_args : ``dict`` (optional, default: ``{}``)
        Keyword arguments to be passed to base type constructor.
    **kwargs :  keyword arguments
        Keyword arguments to be passed to base type constructor. The
        ``state_args`` parameter overrides this.
    """

    def __init__(self, g, bs, base_type=BlockState, state_args={},
                 hstate_args={}, hentropy_args={}, sampling=True, **kwargs):
        self.g = g
        self.base_type = base_type
        if base_type is LayeredBlockState:
            self.Lrecdx = []
        else:
            self.Lrecdx = libcore.Vector_double()
        self.state_args = dict(kwargs, **state_args)
        self.state_args["Lrecdx"] = self.Lrecdx
        if "rec_params" not in self.state_args:
            recs = self.state_args.get("recs", None)
            if recs is not None:
                self.state_args["rec_params"] = ["microcanonical"] * len(recs)
        self.hstate_args = dict(dict(deg_corr=False, vweight="nonempty"),
                                **hstate_args)
        self.hstate_args["Lrecdx"] = self.Lrecdx
        self.sampling = sampling
        if sampling:
            self.hstate_args = dict(self.hstate_args, copy_bg=False)
        self.hentropy_args = dict(hentropy_args,
                                  adjacency=True,
                                  dense=True,
                                  multigraph=True,
                                  dl=True,
                                  partition_dl=True,
                                  degree_dl=True,
                                  degree_dl_kind="distributed",
                                  edges_dl=False,
                                  exact=True,
                                  recs=True,
                                  recs_dl=False,
                                  beta_dl=1.)
        self.levels = [base_type(g, b=bs[0], **self.state_args)]
        for i, b in enumerate(bs[1:]):
            state = self.levels[-1]
            args = self.hstate_args
            if i == len(bs[1:]) - 1:
                args = dict(args, clabel=None, pclabel=None)
            bstate = state.get_block_state(b=b, **args)
            self.levels.append(bstate)

        self._regen_Lrecdx()

        if self.sampling:
            self._couple_levels(self.hentropy_args, None)

        if _bm_test():
            self._consistency_check()

    def _regen_Lrecdx(self, lstate=None):
        if lstate is None:
            levels = self.levels
            Lrecdx = self.Lrecdx
        else:
            levels = [s for s in self.levels]
            l, s = lstate
            levels[l] = s
            s = s.get_block_state(**dict(self.hstate_args,
                                         b=s.get_bclabel(),
                                         copy_bg=False))
            if l < len(levels) - 1:
                levels[l+1] = s
            else:
                levels.append(s)
            if self.base_type is LayeredBlockState:
                Lrecdx = [x.copy() for x in self.Lrecdx]
            else:
                Lrecdx = self.Lrecdx.copy()

        if self.base_type is not LayeredBlockState:
            Lrecdx.a = 0
            Lrecdx[0] = len([s for s in levels if s._state.get_B_E_D() > 0])
            for s in levels:
                Lrecdx.a[1:] += s.recdx.a * s._state.get_B_E_D()
                s.epsilon.a = levels[0].epsilon.a
            for s in levels:
                s.Lrecdx.a = Lrecdx.a
        else:
            Lrecdx[0].a = 0
            Lrecdx[0][0] = len([s for s in levels if s._state.get_B_E_D() > 0])
            for j in range(levels[0].C):
                Lrecdx[j+1].a = 0
                Lrecdx[j+1][0] = len([s for s in levels if s._state.get_layer(j).get_B_E_D() > 0])
            for s in levels:
                Lrecdx[0].a[1:] += s.recdx.a * s._state.get_B_E_D()
                s.epsilon.a = levels[0].epsilon.a
                for j in range(levels[0].C):
                    Lrecdx[j+1].a[1:] += s.layer_states[j].recdx.a * s._state.get_layer(j).get_B_E_D()
                    s.layer_states[j].epsilon.a = levels[0].epsilon.a

            for s in self.levels:
                for x, y in zip(s.Lrecdx, Lrecdx):
                    x.a = y.a

        if lstate is not None:
            return Lrecdx


    def _regen_levels(self):
        for l in range(1, len(self.levels)):
            state = self.levels[l]
            nstate = self.levels[l-1].get_block_state(b=state.b,
                                                      **self.hstate_args)
            self.levels[l] = nstate
        self._regen_Lrecdx()

    def __repr__(self):
        return "<NestedBlockState object, with base %s, and %d levels of sizes %s at 0x%x>" % \
            (repr(self.levels[0]), len(self.levels),
             str([(s.get_N(), s.get_nonempty_B()) for s in self.levels]), id(self))

    def __copy__(self):
        return self.copy()

    def __deepcopy__(self, memo):
        g = copy.deepcopy(self.g, memo)
        return self.copy(g=g)

    def copy(self, g=None, bs=None, state_args=None, hstate_args=None,
             hentropy_args=None, sampling=None, **kwargs):
        r"""Copies the block state. The parameters override the state properties,
        and have the same meaning as in the constructor."""
        bs = self.get_bs() if bs is None else bs
        return NestedBlockState(self.g if g is None else g, bs,
                                base_type=type(self.levels[0]),
                                state_args=self.state_args if state_args is None else state_args,
                                hstate_args=self.hstate_args if hstate_args is None else hstate_args,
                                hentropy_args=self.hentropy_args if hentropy_args is None else hentropy_args,
                                sampling=self.sampling if sampling is None else sampling,
                                **kwargs)

    def __getstate__(self):
        state = dict(g=self.g, bs=self.get_bs(), base_type=type(self.levels[0]),
                     hstate_args=self.hstate_args,
                     hentropy_args=self.hentropy_args, sampling=self.sampling,
                     state_args=self.state_args)
        return state

    def __setstate__(self, state):
        conv_pickle_state(state)
        if "kwargs" in state: # backwards compatibility
            state["state_args"] = state["kwargs"]
            del  state["kwargs"]
        self.__init__(**state)

    def get_bs(self):
        """Get hierarchy levels as a list of :class:`numpy.ndarray` objects with the
        group memberships at each level.
        """
        return [s.b.fa for s in self.levels]

    def get_state(self):
        """Alias to :meth:`~NestedBlockState.get_bs`."""
        return self.get_bs()

    def set_state(self, bs):
        r"""Sets the internal nested partition of the state."""
        for i in range(len(bs)):
            self.levels[i].set_state(bs[i])

    def get_levels(self):
        """Get hierarchy levels as a list of :class:`~graph_tool.inference.blockmodel.BlockState`
        instances."""
        return self.levels

    def project_partition(self, j, l):
        """Project partition of level ``j`` onto level ``l``, and return it."""
        b = self.levels[l].b.copy()
        for i in range(l + 1, j + 1):
            clabel = self.levels[i].b.copy()
            pmap(b, clabel)
        return b

    def propagate_clabel(self, l):
        """Project base clabel to level ``l``."""
        clabel = self.levels[0].clabel.copy()
        for j in range(l):
            bg = self.levels[j].bg
            bclabel = bg.new_vertex_property("int")
            reverse_map(self.levels[j].b, bclabel)
            pmap(bclabel, clabel)
            clabel = bclabel
        return clabel

    def get_clabel(self, l):
        """Get clabel for level ``l``."""
        clabel = self.propagate_clabel(l)
        if l < len(self.levels) - 1:
            b = self.project_partition(l + 1, l)
            clabel.fa += (clabel.fa.max() + 1) * b.fa
        return clabel

    def _consistency_check(self):
        for l in range(1, len(self.levels)):
            b = self.levels[l].b.fa.copy()
            state = self.levels[l-1]
            args = self.hstate_args
            if l == len(self.levels) - 1:
                args = dict(args, clabel=None, pclabel=None)
            bstate = state.get_block_state(b=b, **args)
            b2 = bstate.b.fa.copy()
            continuous_map(b)
            continuous_map(b2)
            assert ((b == b2).all() and
                    math.isclose(bstate.entropy(dl=False),
                                 self.levels[l].entropy(dl=False),
                                 abs_tol=1e-8)), \
                "inconsistent level %d (%s %g,  %s %g): %s" % \
                (l, str(bstate), bstate.entropy(), str(self.levels[l]),
                 self.levels[l].entropy(), str(self))
            assert (bstate.get_N() >= bstate.get_nonempty_B()), \
                (l, bstate.get_N(), bstate.get_nonempty_B(), str(self))

    def replace_level(self, l, b):
        """Replace level ``l`` given the new partition ``b``"""

        if l < len(self.levels) - 1:
            clabel = self.project_partition(l + 1, l)
        self.levels[l] = self.levels[l].copy(b=b)
        if l < len(self.levels) - 1:
            bclabel = self.levels[l].bg.new_vertex_property("int")
            reverse_map(self.levels[l].b, bclabel)
            pmap(bclabel, clabel)
            bstate = self.levels[l].get_block_state(b=bclabel,
                                                    **self.hstate_args)
            self.levels[l + 1] = bstate

        self._regen_Lrecdx()

        if _bm_test():
            self._consistency_check()

    def delete_level(self, l):
        """Delete level ``l``."""
        if l == 0:
            raise ValueError("cannot delete level l=0")
        b = self.project_partition(l, l - 1)
        self.replace_level(l - 1, b.fa)
        del self.levels[l]

        self._regen_Lrecdx()

        if _bm_test():
            self._consistency_check()

    def duplicate_level(self, l):
        """Duplicate level ``l``."""
        bstate = self.levels[l].copy(b=self.levels[l].g.vertex_index.copy("int").fa)
        self.levels.insert(l, bstate)
        self._regen_Lrecdx()
        if _bm_test():
            self._consistency_check()

    def level_entropy(self, l, bstate=None, **kwargs):
        """Compute the entropy of level ``l``."""

        if bstate is None:
            bstate = self.levels[l]

        kwargs = kwargs.copy()
        hentropy_args = dict(self.hentropy_args,
                             **kwargs.pop("hentropy_args", {}))
        hentropy_args_top = dict(dict(hentropy_args, edges_dl=True,
                                      recs_dl=True),
                                 **kwargs.pop("hentropy_args_top", {}))

        if l > 0:
            if l == (len(self.levels) - 1):
                eargs = hentropy_args_top
            else:
                eargs = hentropy_args
        else:
            eargs = dict(kwargs, edges_dl=False)

        S = bstate.entropy(**eargs)

        if l > 0:
            S *= kwargs.get("beta_dl", 1.)

        return S

    def _Lrecdx_entropy(self, Lrecdx=None):
        if self.base_type is not LayeredBlockState:
            S_D = 0

            if Lrecdx is None:
                Lrecdx = self.Lrecdx
                for s in self.levels:
                    B_E_D = s._state.get_B_E_D()
                    if B_E_D > 0:
                        S_D -= log(B_E_D)

            S = 0
            for i in range(len(self.levels[0].rec)):
                if self.levels[0].rec_types[i] != libinference.rec_type.real_normal:
                    continue
                assert not _bm_test() or Lrecdx[i+1] >= 0, (i, Lrecdx[i+1])
                S += -libinference.positive_w_log_P(Lrecdx[0], Lrecdx[i+1],
                                                    numpy.nan, numpy.nan,
                                                    self.levels[0].epsilon[i])
                S += S_D
            return S
        else:
            S_D = [0 for j in range(self.levels[0].C)]
            if Lrecdx is None:
                Lrecdx = self.Lrecdx
                for s in self.levels:
                    for j in range(self.levels[0].C):
                        B_E_D = s._state.get_layer(j).get_B_E_D()
                        if B_E_D > 0:
                            S_D[j] -= log(B_E_D)

            S = 0
            for i in range(len(self.levels[0].rec)):
                if self.levels[0].rec_types[i] != libinference.rec_type.real_normal:
                    continue
                for j in range(self.levels[0].C):
                    assert not _bm_test() or Lrecdx[j+1][i+1] >= 0, (i, j, Lrecdx[j+1][i+1])
                    S += -libinference.positive_w_log_P(Lrecdx[j+1][0],
                                                        Lrecdx[j+1][i+1],
                                                        numpy.nan, numpy.nan,
                                                        self.levels[0].epsilon[i])
                    S += S_D[j]
            return S


    def entropy(self, **kwargs):
        """Compute the entropy of whole hierarchy.

        The keyword arguments are passed to the ``entropy()`` method of the
        underlying state objects
        (e.g. :class:`graph_tool.inference.blockmodel.BlockState.entropy`,
        :class:`graph_tool.inference.overlap_blockmodel.OverlapBlockState.entropy`, or
        :class:`graph_tool.inference.layered_blockmodel.LayeredBlockState.entropy`).  """
        S = 0
        for l in range(len(self.levels)):
            S += self.level_entropy(l, **dict(kwargs, test=False))

        S += kwargs.get("beta_dl", 1.) * self._Lrecdx_entropy()

        if _bm_test() and kwargs.pop("test", True):
            state = self.copy()
            Salt = state.entropy(test=False, **kwargs)
            assert math.isclose(S, Salt, abs_tol=1e-8), \
                "inconsistent entropy after copying (%g, %g, %g): %s" % \
                (S, Salt, S-Salt, str(kwargs))

        return S

    def move_vertex(self, v, s):
        r"""Move vertex ``v`` to block ``s``."""
        self.levels[0].move_vertex(v, s)
        self._regen_levels()

    def remove_vertex(self, v):
        r"""Remove vertex ``v`` from its current group.

        This optionally accepts a list of vertices to remove.

        .. warning::

           This will leave the state in an inconsistent state before the vertex
           is returned to some other group, or if the same vertex is removed
           twice.
        """
        self.levels[0].remove_vertex(v)
        self._regen_levels()

    def add_vertex(self, v, r):
        r"""Add vertex ``v`` to block ``r``.

        This optionally accepts a list of vertices and blocks to add.

        .. warning::

           This can leave the state in an inconsistent state if a vertex is
           added twice to the same group.
        """
        self.levels[0].add_vertex(v, r)
        self._regen_levels()

    def get_edges_prob(self, missing, spurious=[], entropy_args={}):
        r"""Compute the joint log-probability of the missing and spurious edges given by
        ``missing`` and ``spurious`` (a list of ``(source, target)``
        tuples, or :meth:`~graph_tool.Edge` instances), together with the
        observed edges.

        More precisely, the log-likelihood returned is

        .. math::

            \ln \frac{P(\boldsymbol G + \delta \boldsymbol G | \boldsymbol b)}{P(\boldsymbol G| \boldsymbol b)}

        where :math:`\boldsymbol G + \delta \boldsymbol G` is the modified graph
        (with missing edges added and spurious edges deleted).

        The values in ``entropy_args`` are passed to
        :meth:`graph_tool.inference.blockmodel.BlockState.entropy()` to calculate the
        log-probability.
        """

        entropy_args = entropy_args.copy()
        hentropy_args = dict(self.hentropy_args,
                             **entropy_args.pop("hentropy_args", {}))
        hentropy_args_top = dict(dict(hentropy_args, edges_dl=True,
                                      recs_dl=True),
                                 **entropy_args.pop("hentropy_args_top", {}))

        L = 0
        for l, lstate in enumerate(self.levels):
            if l > 0:
                if l == (len(self.levels) - 1):
                    eargs = hentropy_args_top
                else:
                    eargs = hentropy_args
            else:
                eargs = entropy_args

            if self.sampling:
                lstate._couple_state(None, None)
                if l > 0:
                    lstate._state.sync_emat()
                    lstate._state.clear_egroups()

            L += lstate.get_edges_prob(missing, spurious, entropy_args=eargs)
            if isinstance(self.levels[0], LayeredBlockState):
                missing = [(lstate.b[u], lstate.b[v], l_) for u, v, l_ in missing]
                spurious = [(lstate.b[u], lstate.b[v], l_) for u, v, l_ in spurious]
            else:
                missing = [(lstate.b[u], lstate.b[v]) for u, v in missing]
                spurious = [(lstate.b[u], lstate.b[v]) for u, v in spurious]

        return L

    def get_bstack(self):
        """Return the nested levels as individual graphs.

        This returns a list of :class:`~graph_tool.Graph` instances
        representing the inferred hierarchy at each level. Each graph has two
        internal vertex and edge property maps named "count" which correspond to
        the vertex and edge counts at the lower level, respectively. Additionally,
        an internal vertex property map named "b" specifies the block partition.
        """

        bstack = []
        for l, bstate in enumerate(self.levels):
            cg = bstate.g
            if l == 0:
                cg = GraphView(cg, skip_properties=True)
            cg.vp["b"] = bstate.b.copy()
            if bstate.is_weighted:
                cg.ep["count"] = cg.own_property(bstate.eweight.copy())
                cg.vp["count"] = cg.own_property(bstate.vweight.copy())
            else:
                cg.ep["count"] = cg.new_ep("int", 1)

            bstack.append(cg)
            if bstate.get_N() == 1:
                break
        return bstack

    def project_level(self, l):
        """Project the partition at level ``l`` onto the lowest level, and return the
        corresponding state."""
        b = self.project_partition(l, 0)
        return self.levels[0].copy(b=b)

    def print_summary(self):
        """Print a hierarchy summary."""
        for l, state in enumerate(self.levels):
            print("l: %d, N: %d, B: %d" % (l, state.get_N(),
                                           state.get_nonempty_B()))

    def find_new_level(self, l, bisection_args={}, B_min=None, B_max=None,
                       b_min=None, b_max=None):
        """Attempt to find a better network partition at level ``l``, using
        :func:`~graph_tool.inference.bisection.bisection_minimize` with arguments given by
        ``bisection_args``.
        """

        # assemble minimization arguments
        mcmc_multilevel_args = bisection_args.get("mcmc_multilevel_args", {})
        mcmc_equilibrate_args = mcmc_multilevel_args.get("mcmc_equilibrate_args", {})
        mcmc_args = mcmc_equilibrate_args.get("mcmc_args", {})
        entropy_args = mcmc_args.get("entropy_args", {})
        if l > 0:
            entropy_args = dict(entropy_args, **self.hentropy_args)
        top = (l == (len(self.levels) - 1))
        entropy_args = dict(entropy_args, edges_dl=top, recs_dl=top)

        def callback(s):
            S = 0
            bstate = None
            if l < len(self.levels) - 1:
                if s._coupled_state is None:
                    bclabel = s.get_bclabel()
                    bstate = s.get_block_state(b=bclabel,
                                               **dict(self.hstate_args,
                                                      Lrecdx=s.Lrecdx))
                    S += bstate.entropy(**dict(self.hentropy_args,
                                               edges_dl=(l + 1 == len(self.levels) - 1),
                                               recs_dl=(l + 1 == len(self.levels) - 1)))
                else:
                    bstate = s._coupled_state[0]
                    S += bstate.entropy(**dict(s._coupled_state[1], recs=True))

            if self.base_type is not LayeredBlockState:
                if s.Lrecdx[0] >= 0:
                    S += self._Lrecdx_entropy(s.Lrecdx)
                    ss = s
                    while ss is not None:
                        B_E_D = ss._state.get_B_E_D()
                        if B_E_D > 0:
                            for i in range(len(s.rec)):
                                if s.rec_types[i] != libinference.rec_type.real_normal:
                                    continue
                                S -= log(B_E_D)
                        if l < len(self.levels) - 1 and ss is not bstate:
                            ss = bstate
                        else:
                            ss = None
            else:
                if s.Lrecdx[0][0] >= 0:
                    S += self._Lrecdx_entropy(s.Lrecdx)
                    ss = s
                    while ss is not None:
                        for j in range(len(ss.layer_states)):
                            B_E_D = ss._state.get_layer(j).get_B_E_D()
                            if B_E_D > 0:
                                for i in range(len(s.rec)):
                                    if s.rec_types[i] != libinference.rec_type.real_normal:
                                        continue
                                    S -= log(B_E_D)
                        if l < len(self.levels) - 1 and ss is not bstate:
                            ss = bstate
                        else:
                            ss = None

            assert (not _bm_test() or bstate is None or
                    s.get_nonempty_B() == bstate.get_N()), (s.get_nonempty_B(),
                                                            bstate.get_N())
            return S

        entropy_args = dict(entropy_args, callback=callback)
        mcmc_args = dict(mcmc_args, entropy_args=entropy_args)
        if l > 0:
            mcmc_args = dmask(mcmc_args, ["bundled"])
        mcmc_equilibrate_args = dict(mcmc_equilibrate_args,
                                     mcmc_args=mcmc_args)
        shrink_args = mcmc_multilevel_args.get("shrink_args", {})
        shrink_args = dict(shrink_args,
                           entropy_args=dict(shrink_args.get("entropy_args", {}),
                                             **entropy_args))
        if l > 0:
            shrink_args["entropy_args"].update(dict(multigraph=True, dense=True))
        elif not shrink_args["entropy_args"].get("dense", False):
            shrink_args["entropy_args"]["multigraph"] = False

        mcmc_multilevel_args = dict(mcmc_multilevel_args,
                                    shrink_args=shrink_args,
                                    mcmc_equilibrate_args=mcmc_equilibrate_args)
        bisection_args = dict(bisection_args,
                              mcmc_multilevel_args=mcmc_multilevel_args)

        # construct boundary states and constraints
        clabel = self.get_clabel(l)
        state = self.levels[l]
        if b_max is None:
            b_max = state.g.vertex_index.copy("int").fa
        else:
            b_max = state.g.new_vp("int", b_max)
            b_max = group_vector_property([b_max, clabel])
            b_max = perfect_prop_hash([b_max])[0].fa
        continuous_map(b_max)
        max_state = state.copy(b=b_max, clabel=clabel,
                               recs=[r.copy() for r in state.rec],
                               drec=[r.copy() for r in state.drec])
        max_Lrecdx = self._regen_Lrecdx(lstate=(l, max_state))
        max_state = max_state.copy(Lrecdx=max_Lrecdx)
        if B_max is not None and max_state.B > B_max:
            max_state = mcmc_multilevel(max_state, B_max,
                                        **mcmc_multilevel_args)

        if l < len(self.levels) - 1:
            if B_min is None:
                min_state = state.copy(b=clabel.fa, clabel=clabel.fa,
                                       recs=[r.copy() for r in state.rec],
                                       drec=[r.copy() for r in state.drec])
                B_min = min_state.B
            else:
                B_min = max(B_min, clabel.fa.max() + 1)
                min_state = mcmc_multilevel(max_state, B_min,
                                            **mcmc_multilevel_args)
            if _bm_test():
                assert (min_state.B == self.levels[l+1].B or
                        min_state.B == B_min), (B_min, min_state.B,
                                                self.levels[l+1].B)
        else:
            min_state = state.copy(b=clabel.fa, clabel=clabel.fa)
        min_Lrecdx = self._regen_Lrecdx(lstate=(l, min_state))
        min_state = min_state.copy(Lrecdx=min_Lrecdx)
        if B_min is not None and  min_state.B > B_min:
            min_state = mcmc_multilevel(min_state, B_min,
                                        **mcmc_multilevel_args)

        if l < len(self.levels) - 1:
            eargs = dict(self.hentropy_args,
                         edges_dl=(l + 1 == len(self.levels) - 1))
            min_state._couple_state(min_state.get_block_state(**dict(self.hstate_args,
                                                                     b=min_state.get_bclabel(),
                                                                     copy_bg=False,
                                                                     Lrecdx=min_state.Lrecdx)),
                                    eargs)
            max_state._couple_state(max_state.get_block_state(**dict(self.hstate_args,
                                                                     b=max_state.get_bclabel(),
                                                                     copy_bg=False,
                                                                     Lrecdx=max_state.Lrecdx)),
                                    eargs)

        if _bm_test():
            assert min_state._check_clabel(), "invalid clabel %s" % str((l, self))
            assert max_state._check_clabel(), "invalid clabel %s" % str((l, self))

        # find new state
        state = bisection_minimize([min_state, max_state], **bisection_args)

        if _bm_test():
            assert state.B >= min_state.B, (l, state.B, min_state.B, str(self))
            assert state._check_clabel(), "invalid clabel %s" % str((l, self))

        state._couple_state(None, None)
        return state

    def _couple_levels(self, hentropy_args, hentropy_args_top):
        if hentropy_args_top is None:
            hentropy_args_top = dict(hentropy_args, edges_dl=True, recs_dl=True)
        for l in range(len(self.levels) - 1):
            if l + 1 == len(self.levels) - 1:
                eargs = hentropy_args_top
            else:
                eargs = hentropy_args
            self.levels[l]._couple_state(self.levels[l + 1], eargs)

    def _clear_egroups(self):
        for lstate in self.levels:
            lstate._clear_egroups()

    def _h_sweep_gen(self, **kwargs):

        if not self.sampling:
            raise ValueError("NestedBlockState must be constructed with 'sampling=True'")

        verbose = kwargs.get("verbose", False)
        entropy_args = dict(kwargs.get("entropy_args", {}), edges_dl=False)
        hentropy_args = dict(self.hentropy_args,
                             **entropy_args.pop("hentropy_args", {}))
        hentropy_args_top = dict(dict(hentropy_args, edges_dl=True,
                                      recs_dl=True),
                                 **entropy_args.pop("hentropy_args_top", {}))

        self._couple_levels(hentropy_args, hentropy_args_top)

        c = kwargs.get("c", None)

        lrange = list(kwargs.pop("ls", range(len(self.levels))))
        if kwargs.pop("ls_shuffle", True):
            numpy.random.shuffle(lrange)
        for l in lrange:
            if check_verbose(verbose):
                print(verbose_pad(verbose) + "level:", l)
            if l > 0:
                if l == len(self.levels) - 1:
                    eargs = hentropy_args_top
                else:
                    eargs = hentropy_args
            else:
                eargs = entropy_args

            if c is None:
                args = dict(kwargs, entropy_args=eargs)
            else:
                args = dict(kwargs, entropy_args=eargs, c=c[l])

            if l > 0 and "beta_dl" in entropy_args:
                args = dict(args, beta=args.get("beta", 1.) * entropy_args["beta_dl"])

            yield l, self.levels[l], args

    def _h_sweep(self, algo, **kwargs):
        entropy_args = kwargs.get("entropy_args", {})

        dS = 0
        nattempts = 0
        nmoves = 0

        try:
            for l, lstate, args in self._h_sweep_gen(**kwargs):

                ret = algo(self.levels[l], **args)

                if l > 0 and "beta_dl" in entropy_args:
                    dS += ret[0] * entropy_args["beta_dl"]
                else:
                    dS += ret[0]
                nattempts += ret[1]
                nmoves += ret[2]
        finally:
            for state in self.levels:
                state.B = state.bg.num_vertices()

        return dS, nattempts, nmoves

    def _h_sweep_states(self, algo, **kwargs):
        entropy_args = kwargs.get("entropy_args", {})
        for l, lstate, args in self._h_sweep_gen(**kwargs):
            beta_dl = entropy_args.get("beta_dl", 1) if l > 0 else 1
            yield l, lstate, algo(self.levels[l], dispatch=False, **args), beta_dl

    def _h_sweep_parallel_dispatch(states, sweeps, algo):
        ret = None
        for lsweep in zip(*sweeps):
            ls = [x[0] for x in lsweep]
            lstates = [x[1] for x in lsweep]
            lsweep_states = [x[2] for x in lsweep]
            beta_dl = [x[3] for x in lsweep]
            lret = algo(type(lstates[0]), lstates, lsweep_states)
            if ret is None:
                ret = lret
            else:
                ret = [(ret[i][0] + lret[i][0] * beta_dl[i],
                        ret[i][1] + lret[i][1],
                        ret[i][2] + lret[i][2]) for i in range(len(lret))]
        return ret

    def mcmc_sweep(self, **kwargs):
        r"""Perform ``niter`` sweeps of a Metropolis-Hastings acceptance-rejection
        MCMC to sample hierarchical network partitions.

        The arguments accepted are the same as in
        :meth:`graph_tool.inference.blockmodel.BlockState.mcmc_sweep`.

        If the parameter ``c`` is a scalar, the values used at each level are
        ``c * 2 ** l`` for ``l`` in the range ``[0, L-1]``. Optionally, a list
        of values may be passed instead, which specifies the value of ``c[l]``
        to be used at each level.
        """

        c = kwargs.pop("c", 1)
        if not isinstance(c, collections.Iterable):
            c = [c * 2 ** l for l in range(0, len(self.levels))]

        if kwargs.pop("dispatch", True):
            if _bm_test():
                kwargs = dict(kwargs, test=False)
                entropy_args = kwargs.get("entropy_args", {})
                Si = self.entropy(**entropy_args)

            dS, nattempts, nmoves = self._h_sweep(lambda s, **a: s.mcmc_sweep(**a),
                                                  c=c, **kwargs)

            if _bm_test():
                Sf = self.entropy(**entropy_args)
                assert math.isclose(dS, (Sf - Si), abs_tol=1e-8), \
                    "inconsistent entropy delta %g (%g): %s" % (dS, Sf - Si,
                                                                str(entropy_args))
            return dS, nattempts, nmoves
        else:
            return self._h_sweep_states(lambda s, **a: s.mcmc_sweep(**a),
                                        c=c, **kwargs)

    def _mcmc_sweep_parallel_dispatch(states, sweeps):
        algo = lambda s, lstates, lsweep_states: s._mcmc_sweep_parallel_dispatch(lstates, lsweep_states)
        return NestedBlockState._h_sweep_parallel_dispatch(states, sweeps, algo)

    def multiflip_mcmc_sweep(self, **kwargs):
        r"""Perform ``niter`` sweeps of a Metropolis-Hastings acceptance-rejection MCMC
        with multiple moves to sample hierarchical network partitions.

        The arguments accepted are the same as in
        :meth:`graph_tool.inference.blockmodel.BlockState.multiflip_mcmc_sweep`.

        If the parameter ``c`` is a scalar, the values used at each level are
        ``c * 2 ** l`` for ``l`` in the range ``[0, L-1]``. Optionally, a list
        of values may be passed instead, which specifies the value of ``c[l]``
        to be used at each level.

        """

        psingle = kwargs.get("psingle", self.g.num_vertices())
        kwargs["psingle"] = psingle

        c = kwargs.pop("c", 1)
        if not isinstance(c, collections.Iterable):
            c = [c * 2 ** l for l in range(0, len(self.levels))]

        if kwargs.pop("dispatch", True):
            if _bm_test():
                kwargs = dict(kwargs, test=False)
                entropy_args = kwargs.get("entropy_args", {})
                Si = self.entropy(**entropy_args)

            dS, nattempts, nmoves = self._h_sweep(lambda s, **a: s.multiflip_mcmc_sweep(**a),
                                                  c=c, **kwargs)
            if _bm_test():
                Sf = self.entropy(**entropy_args)
                assert math.isclose(dS, (Sf - Si), abs_tol=1e-8), \
                    r"inconsistent entropy delta %g (%g): %s" % (dS, Sf - Si,
                                                                 str(entropy_args))
            return dS, nattempts, nmoves
        else:
            return self._h_sweep_states(lambda s, **a: s.multiflip_mcmc_sweep(**a),
                                        c=c, **kwargs)

    def _multiflip_mcmc_sweep_parallel_dispatch(states, sweeps):
        algo = lambda s, lstates, lsweep_states: s._multiflip_mcmc_sweep_parallel_dispatch(lstates, lsweep_states)
        return NestedBlockState._h_sweep_parallel_dispatch(states, sweeps, algo)

    def gibbs_sweep(self, **kwargs):
        r"""Perform ``niter`` sweeps of a rejection-free Gibbs sampling MCMC
        to sample network partitions.

        The arguments accepted are the same as in
        :meth:`graph_tool.inference.blockmodel.BlockState.gibbs_sweep`.
        """
        if _bm_test():
            kwargs = dict(kwargs, test=False)
            entropy_args = kwargs.get("entropy_args", {})
            Si = self.entropy(**entropy_args)

        dS, nattempts, nmoves = self._h_sweep(lambda s, **a: s.gibbs_sweep(**a),
                                              **kwargs)

        if _bm_test():
            Sf = self.entropy(**entropy_args)
            assert math.isclose(dS, (Sf - Si), abs_tol=1e-8), \
                "inconsistent entropy delta %g (%g): %s" % (dS, Sf - Si,
                                                            str(entropy_args))
        return dS, nattempts, nmoves

    def _gibbs_sweep_parallel_dispatch(states, sweeps):
        algo = lambda s, lstates, lsweep_states: s._gibbs_sweep_parallel_dispatch(lstates, lsweep_states)
        return NestedBlockState._h_sweep_parallel_dispatch(states, sweeps, algo)

    def multicanonical_sweep(self, **kwargs):
        r"""Perform ``niter`` sweeps of a non-Markovian multicanonical sampling using the
        Wang-Landau algorithm.

        The arguments accepted are the same as in
        :meth:`graph_tool.inference.blockmodel.BlockState.multicanonical_sweep`.
        """
        if _bm_test():
            kwargs = dict(kwargs, test=False)
            entropy_args = kwargs.get("entropy_args", {})
            Si = self.entropy(**entropy_args)

        dS, nattempts, nmoves = self._h_sweep(lambda s, **a: s.multicanonical_sweep(**a))

        if _bm_test():
            Sf = self.entropy(**entropy_args)
            assert math.isclose(dS, (Sf - Si), abs_tol=1e-8), \
                "inconsistent entropy delta %g (%g): %s" % (dS, Sf - Si,
                                                            str(entropy_args))
        return dS, nattempts, nmoves

    def collect_partition_histogram(self, h=None, update=1):
        r"""Collect a histogram of partitions.

        This should be called multiple times, e.g. after repeated runs of the
        :meth:`graph_tool.inference.nested_blockmodel.NestedBlockState.mcmc_sweep` function.

        Parameters
        ----------
        h : :class:`~graph_tool.inference.blockmodel.PartitionHist` (optional, default: ``None``)
            Partition histogram. If not provided, an empty histogram will be created.
        update : float (optional, default: ``1``)
            Each call increases the current count by the amount given by this
            parameter.

        Returns
        -------
        h : :class:`~graph_tool.inference.blockmodel.PartitionHist` (optional, default: ``None``)
            Updated Partition histogram.

        """

        if h is None:
            h = PartitionHist()
        bs = [_prop("v", state.g, state.b) for state in self.levels]
        libinference.collect_hierarchical_partitions(bs, h, update)
        return h

    def draw(self, **kwargs):
        r"""Convenience wrapper to :func:`~graph_tool.draw.draw_hierarchy` that
        draws the hierarchical state."""
        import graph_tool.draw
        return graph_tool.draw.draw_hierarchy(self, **kwargs)



def hierarchy_minimize(state, B_min=None, B_max=None, b_min=None, b_max=None,
                       frozen_levels=None, bisection_args={},
                       epsilon=1e-8, verbose=False):
    """Attempt to find a fit of the nested stochastic block model that minimizes the
    description length.

    Parameters
    ----------
    state : :class:`~graph_tool.inference.nested_blockmodel.NestedBlockState`
        The nested block state.
    B_min : ``int`` (optional, default: ``None``)
        The minimum number of blocks.
    B_max : ``int`` (optional, default: ``None``)
        The maximum number of blocks.
    b_min : :class:`~graph_tool.VertexPropertyMap` (optional, default: ``None``)
        The partition to be used with the minimum number of blocks.
    b_max : :class:`~graph_tool.VertexPropertyMap` (optional, default: ``None``)
        The partition to be used with the maximum number of blocks.
    frozen_levels : sequence of ``int`` values (optional, default: ``None``)
        List of hierarchy levels that are kept constant during the minimization.
    bisection_args : ``dict`` (optional, default: ``{}``)
        Arguments to be passed to :func:`~graph_tool.inference.bisection.bisection_minimize`.
    epsilon: ``float`` (optional, default: ``1e-8``)
        Only replace levels if the description length difference is above this
        threshold.
    verbose : ``bool`` or ``tuple`` (optional, default: ``False``)
        If ``True``, progress information will be shown. Optionally, this
        accepts arguments of the type ``tuple`` of the form ``(level, prefix)``
        where ``level`` is a positive integer that specifies the level of
        detail, and ``prefix`` is a string that is prepended to the all output
        messages.

    Returns
    -------
    min_state : :class:`~graph_tool.inference.nested_blockmodel.NestedBlockState`