pymatgen.analysis.chemenv.coordination_environments.voronoi — pymatgen 2020.7.3 documentation

# Source code for pymatgen.analysis.chemenv.coordination_environments.voronoi

    # coding: utf-8
    # Copyright (c) Pymatgen Development Team.
    # Distributed under the terms of the MIT License.

    """
    This module contains the object used to describe the possible bonded atoms based on a Voronoi analysis.
    """

    __author__ = "David Waroquiers"
    __copyright__ = "Copyright 2012, The Materials Project"
    __credits__ = "Geoffroy Hautier"
    __version__ = "2.0"
    __maintainer__ = "David Waroquiers"
    __email__ = "david.waroquiers@gmail.com"
    __date__ = "Feb 20, 2016"

    import logging
    import numpy as np
    import time
    from pymatgen.core.structure import Structure
    from pymatgen.core.sites import PeriodicSite
    from monty.json import MSONable
    from scipy.spatial import Voronoi

    from pymatgen.analysis.chemenv.utils.coordination_geometry_utils import my_solid_angle
    from pymatgen.analysis.chemenv.utils.coordination_geometry_utils import get_lower_and_upper_f
    from pymatgen.analysis.chemenv.utils.coordination_geometry_utils import rectangle_surface_intersection
    from pymatgen.analysis.chemenv.utils.defs_utils import AdditionalConditions
    from pymatgen.analysis.chemenv.utils.math_utils import normal_cdf_step

    def from_bson_voronoi_list2(bson_nb_voro_list2, structure):
        """
        Returns the voronoi_list needed for the VoronoiContainer object from a bson-encoded voronoi_list.

        Args:
            bson_nb_voro_list2: List of periodic sites involved in the Voronoi.
            structure: Structure object.

        Returns:
            The voronoi_list needed for the VoronoiContainer (with PeriodicSites as keys of the dictionary - not
            allowed in the BSON format).
        """
        voronoi_list = [None] * len(bson_nb_voro_list2)
        for isite, voro in enumerate(bson_nb_voro_list2):
            if voro is None or voro == 'None':
                continue
            voronoi_list[isite] = []
            for psd, dd in voro:
                struct_site = structure[dd['index']]
                periodic_site = PeriodicSite(struct_site._species, struct_site.frac_coords + psd[1],
                                             struct_site._lattice, properties=struct_site.properties)
                dd['site'] = periodic_site
                voronoi_list[isite].append(dd)
        return voronoi_list

    class DetailedVoronoiContainer(MSONable):
        """
        Class used to store the full Voronoi of a given structure.
        """
        AC = AdditionalConditions()
        default_voronoi_cutoff = 10.0
        default_normalized_distance_tolerance = 1e-5
        default_normalized_angle_tolerance = 1e-3

        def __init__(self, structure=None, voronoi_list2=None,
                     voronoi_cutoff=default_voronoi_cutoff, isites=None,
                     normalized_distance_tolerance=default_normalized_distance_tolerance,
                     normalized_angle_tolerance=default_normalized_angle_tolerance,
                     additional_conditions=None, valences=None,
                     maximum_distance_factor=None, minimum_angle_factor=None):
            """
            Constructor for the VoronoiContainer object. Either a structure is given, in which case the Voronoi is
            computed, or the different components of the VoronoiContainer are given (used in the from_dict method).

            Args:
                structure: Structure for which the Voronoi is computed.
                voronoi_list2: List of voronoi polyhedrons for each site.
                voronoi_cutoff: cutoff used for the voronoi.
                isites: indices of sites for which the Voronoi has to be computed.
                normalized_distance_tolerance: Tolerance for two normalized distances to be considered equal.
                normalized_angle_tolerance:Tolerance for two normalized angles to be considered equal.
                additional_conditions: Additional conditions to be used.
                valences: Valences of all the sites in the structure (used when additional conditions require it).
                maximum_distance_factor: The maximum distance factor to be considered.
                minimum_angle_factor: The minimum angle factor to be considered.

            Raises:
                RuntimeError if the Voronoi cannot be constructed.
            """
            self.normalized_distance_tolerance = normalized_distance_tolerance
            self.normalized_angle_tolerance = normalized_angle_tolerance
            if additional_conditions is None:
                self.additional_conditions = [self.AC.NONE, self.AC.ONLY_ACB]
            else:
                self.additional_conditions = additional_conditions
            self.valences = valences
            self.maximum_distance_factor = maximum_distance_factor
            self.minimum_angle_factor = minimum_angle_factor
            if isites is None:
                indices = list(range(len(structure)))
            else:
                indices = isites
            self.structure = structure
            logging.debug('Setting Voronoi list')
            if voronoi_list2 is not None:
                self.voronoi_list2 = voronoi_list2
            else:
                self.setup_voronoi_list(indices=indices, voronoi_cutoff=voronoi_cutoff)
            logging.debug('Setting neighbors distances and angles')
            t1 = time.process_time()
            self.setup_neighbors_distances_and_angles(indices=indices)
            t2 = time.process_time()
            logging.debug('Neighbors distances and angles set up in {:.2f} seconds'.format(t2 - t1))

        def setup_voronoi_list(self, indices, voronoi_cutoff):
            """
            Set up of the voronoi list of neighbours by calling qhull.

            Args:
                indices: indices of the sites for which the Voronoi is needed.
                voronoi_cutoff: Voronoi cutoff for the search of neighbours.

            Raises:
                RuntimeError: If an infinite vertex is found in the voronoi construction.
            """
            self.voronoi_list2 = [None] * len(self.structure)
            self.voronoi_list_coords = [None] * len(self.structure)
            logging.debug('Getting all neighbors in structure')
            struct_neighbors = self.structure.get_all_neighbors(voronoi_cutoff, include_index=True)
            t1 = time.process_time()
            logging.debug('Setting up Voronoi list :')

            for jj, isite in enumerate(indices):
                logging.debug('  - Voronoi analysis for site #{:d} ({:d}/{:d})'.format(isite, jj + 1, len(indices)))
                site = self.structure[isite]
                neighbors1 = [(site, 0.0, isite)]
                neighbors1.extend(struct_neighbors[isite])
                distances = [i[1] for i in sorted(neighbors1, key=lambda s: s[1])]
                neighbors = [i[0] for i in sorted(neighbors1, key=lambda s: s[1])]
                qvoronoi_input = [s.coords for s in neighbors]
                voro = Voronoi(points=qvoronoi_input, qhull_options="o Fv")
                all_vertices = voro.vertices

                results2 = []
                maxangle = 0.0
                mindist = 10000.0
                for iridge, ridge_points in enumerate(voro.ridge_points):
                    if 0 in ridge_points:
                        ridge_vertices_indices = voro.ridge_vertices[iridge]
                        if -1 in ridge_vertices_indices:
                            raise RuntimeError("This structure is pathological,"
                                               " infinite vertex in the voronoi "
                                               "construction")

                        ridge_point2 = max(ridge_points)
                        facets = [all_vertices[i] for i in ridge_vertices_indices]
                        sa = my_solid_angle(site.coords, facets)
                        maxangle = max([sa, maxangle])

                        mindist = min([mindist, distances[ridge_point2]])
                        for iii, sss in enumerate(self.structure):
                            if neighbors[ridge_point2].is_periodic_image(sss, tolerance=1.0e-6):
                                myindex = iii
                                break
                        results2.append({'site': neighbors[ridge_point2],
                                         'angle': sa,
                                         'distance': distances[ridge_point2],
                                         'index': myindex})
                for dd in results2:
                    dd['normalized_angle'] = dd['angle'] / maxangle
                    dd['normalized_distance'] = dd['distance'] / mindist
                self.voronoi_list2[isite] = results2
                self.voronoi_list_coords[isite] = np.array([dd['site'].coords for dd in results2])
            t2 = time.process_time()
            logging.debug('Voronoi list set up in {:.2f} seconds'.format(t2 - t1))

        def setup_neighbors_distances_and_angles(self, indices):
            """
            Initializes the angle and distance separations.

            Args:
                indices: Indices of the sites for which the Voronoi is needed.
            """
            self.neighbors_distances = [None] * len(self.structure)
            self.neighbors_normalized_distances = [None] * len(self.structure)
            self.neighbors_angles = [None] * len(self.structure)
            self.neighbors_normalized_angles = [None] * len(self.structure)
            for isite in indices:
                results = self.voronoi_list2[isite]
                if results is None:
                    continue
                # Initializes neighbors distances and normalized distances groups
                self.neighbors_distances[isite] = []
                self.neighbors_normalized_distances[isite] = []
                normalized_distances = [nb_dict['normalized_distance'] for nb_dict in results]
                isorted_distances = np.argsort(normalized_distances)
                self.neighbors_normalized_distances[isite].append({'min': normalized_distances[isorted_distances[0]],
                                                                   'max': normalized_distances[isorted_distances[0]]})
                self.neighbors_distances[isite].append({'min': results[isorted_distances[0]]['distance'],
                                                        'max': results[isorted_distances[0]]['distance']})
                icurrent = 0
                nb_indices = {int(isorted_distances[0])}
                dnb_indices = {int(isorted_distances[0])}
                for idist in iter(isorted_distances):
                    wd = normalized_distances[idist]
                    if self.maximum_distance_factor is not None:
                        if wd > self.maximum_distance_factor:
                            self.neighbors_normalized_distances[isite][icurrent]['nb_indices'] = list(nb_indices)
                            self.neighbors_distances[isite][icurrent]['nb_indices'] = list(nb_indices)
                            self.neighbors_normalized_distances[isite][icurrent]['dnb_indices'] = list(dnb_indices)
                            self.neighbors_distances[isite][icurrent]['dnb_indices'] = list(dnb_indices)
                            break
                    if np.isclose(wd, self.neighbors_normalized_distances[isite][icurrent]['max'],
                                  rtol=0.0, atol=self.normalized_distance_tolerance):
                        self.neighbors_normalized_distances[isite][icurrent]['max'] = wd
                        self.neighbors_distances[isite][icurrent]['max'] = results[idist]['distance']
                        dnb_indices.add(int(idist))
                    else:
                        self.neighbors_normalized_distances[isite][icurrent]['nb_indices'] = list(nb_indices)
                        self.neighbors_distances[isite][icurrent]['nb_indices'] = list(nb_indices)
                        self.neighbors_normalized_distances[isite][icurrent]['dnb_indices'] = list(dnb_indices)
                        self.neighbors_distances[isite][icurrent]['dnb_indices'] = list(dnb_indices)
                        dnb_indices = {int(idist)}
                        self.neighbors_normalized_distances[isite].append({'min': wd,
                                                                           'max': wd})
                        self.neighbors_distances[isite].append({'min': results[idist]['distance'],
                                                                'max': results[idist]['distance']})
                        icurrent += 1
                    nb_indices.add(int(idist))
                else:
                    self.neighbors_normalized_distances[isite][icurrent]['nb_indices'] = list(nb_indices)
                    self.neighbors_distances[isite][icurrent]['nb_indices'] = list(nb_indices)
                    self.neighbors_normalized_distances[isite][icurrent]['dnb_indices'] = list(dnb_indices)
                    self.neighbors_distances[isite][icurrent]['dnb_indices'] = list(dnb_indices)
                for idist in range(len(self.neighbors_distances[isite]) - 1):
                    dist_dict = self.neighbors_distances[isite][idist]
                    dist_dict_next = self.neighbors_distances[isite][idist + 1]
                    dist_dict['next'] = dist_dict_next['min']
                    ndist_dict = self.neighbors_normalized_distances[isite][idist]
                    ndist_dict_next = self.neighbors_normalized_distances[isite][idist + 1]
                    ndist_dict['next'] = ndist_dict_next['min']
                if self.maximum_distance_factor is not None:
                    dfact = self.maximum_distance_factor
                else:
                    dfact = self.default_voronoi_cutoff / self.neighbors_distances[isite][0]['min']
                self.neighbors_normalized_distances[isite][-1]['next'] = dfact
                self.neighbors_distances[isite][-1]['next'] = dfact * self.neighbors_distances[isite][0]['min']
                # Initializes neighbors angles and normalized angles groups
                self.neighbors_angles[isite] = []
                self.neighbors_normalized_angles[isite] = []
                normalized_angles = [nb_dict['normalized_angle'] for nb_dict in results]
                isorted_angles = np.argsort(normalized_angles)[::-1]
                self.neighbors_normalized_angles[isite].append({'max': normalized_angles[isorted_angles[0]],
                                                                'min': normalized_angles[isorted_angles[0]]})
                self.neighbors_angles[isite].append({'max': results[isorted_angles[0]]['angle'],
                                                     'min': results[isorted_angles[0]]['angle']})
                icurrent = 0
                nb_indices = {int(isorted_angles[0])}
                dnb_indices = {int(isorted_angles[0])}
                for iang in iter(isorted_angles):
                    wa = normalized_angles[iang]
                    if self.minimum_angle_factor is not None:
                        if wa < self.minimum_angle_factor:
                            self.neighbors_normalized_angles[isite][icurrent]['nb_indices'] = list(nb_indices)
                            self.neighbors_angles[isite][icurrent]['nb_indices'] = list(nb_indices)
                            self.neighbors_normalized_angles[isite][icurrent]['dnb_indices'] = list(dnb_indices)
                            self.neighbors_angles[isite][icurrent]['dnb_indices'] = list(dnb_indices)
                            break
                    if np.isclose(wa, self.neighbors_normalized_angles[isite][icurrent]['min'],
                                  rtol=0.0, atol=self.normalized_angle_tolerance):
                        self.neighbors_normalized_angles[isite][icurrent]['min'] = wa
                        self.neighbors_angles[isite][icurrent]['min'] = results[iang]['angle']
                        dnb_indices.add(int(iang))
                    else:
                        self.neighbors_normalized_angles[isite][icurrent]['nb_indices'] = list(nb_indices)
                        self.neighbors_angles[isite][icurrent]['nb_indices'] = list(nb_indices)
                        self.neighbors_normalized_angles[isite][icurrent]['dnb_indices'] = list(dnb_indices)
                        self.neighbors_angles[isite][icurrent]['dnb_indices'] = list(dnb_indices)
                        dnb_indices = {int(iang)}
                        self.neighbors_normalized_angles[isite].append({'max': wa,
                                                                        'min': wa})
                        self.neighbors_angles[isite].append({'max': results[iang]['angle'],
                                                             'min': results[iang]['angle']})
                        icurrent += 1
                    nb_indices.add(int(iang))
                else:
                    self.neighbors_normalized_angles[isite][icurrent]['nb_indices'] = list(nb_indices)
                    self.neighbors_angles[isite][icurrent]['nb_indices'] = list(nb_indices)
                    self.neighbors_normalized_angles[isite][icurrent]['dnb_indices'] = list(dnb_indices)
                    self.neighbors_angles[isite][icurrent]['dnb_indices'] = list(dnb_indices)
                for iang in range(len(self.neighbors_angles[isite]) - 1):
                    ang_dict = self.neighbors_angles[isite][iang]
                    ang_dict_next = self.neighbors_angles[isite][iang + 1]
                    ang_dict['next'] = ang_dict_next['max']
                    nang_dict = self.neighbors_normalized_angles[isite][iang]
                    nang_dict_next = self.neighbors_normalized_angles[isite][iang + 1]
                    nang_dict['next'] = nang_dict_next['max']
                if self.minimum_angle_factor is not None:
                    afact = self.minimum_angle_factor
                else:
                    afact = 0.0
                self.neighbors_normalized_angles[isite][-1]['next'] = afact
                self.neighbors_angles[isite][-1]['next'] = afact * self.neighbors_angles[isite][0]['max']

        def _precompute_additional_conditions(self, ivoronoi, voronoi, valences):
            additional_conditions = {ac: [] for ac in self.additional_conditions}
            for ips, (ps, vals) in enumerate(voronoi):
                for ac in self.additional_conditions:
                    additional_conditions[ac].append(self.AC.check_condition(condition=ac, structure=self.structure,
                                                                             parameters={'valences': valences,
                                                                                         'neighbor_index': vals['index'],
                                                                                         'site_index': ivoronoi}))
            return additional_conditions

        def _precompute_distance_conditions(self, ivoronoi, voronoi):
            distance_conditions = []
            for idp, dp_dict in enumerate(self.neighbors_normalized_distances[ivoronoi]):
                distance_conditions.append([])
                dp = dp_dict['max']
                for ips, (ps, vals) in enumerate(voronoi):
                    distance_conditions[idp].append(vals['normalized_distance'] <= dp or
                                                    np.isclose(vals['normalized_distance'], dp,
                                                               rtol=0.0, atol=self.normalized_distance_tolerance / 2.0))
            return distance_conditions

        def _precompute_angle_conditions(self, ivoronoi, voronoi):
            angle_conditions = []
            for iap, ap_dict in enumerate(self.neighbors_normalized_angles[ivoronoi]):
                angle_conditions.append([])
                ap = ap_dict['max']
                for ips, (ps, vals) in enumerate(voronoi):
                    angle_conditions[iap].append(vals['normalized_angle'] >= ap or
                                                 np.isclose(vals['normalized_angle'], ap,
                                                            rtol=0.0, atol=self.normalized_angle_tolerance / 2.0))
            return angle_conditions

        # def neighbors_map(self, isite, distfactor, angfactor, additional_condition):
        #     if self.neighbors_normalized_distances[isite] is None:
        #         return None
        #     dist_where = np.argwhere(
        #         np.array([wd['min'] for wd in self.neighbors_normalized_distances[isite]]) <= distfactor)
        #     if len(dist_where) == 0:
        #         return None
        #     idist = dist_where[-1][0]
        #     ang_where = np.argwhere(np.array([wa['max'] for wa in self.neighbors_normalized_angles[isite]]) >= angfactor)
        #     if len(ang_where) == 0:
        #         return None
        #     iang = ang_where[0][0]
        #     if self.additional_conditions.count(additional_condition) != 1:
        #         return None
        #     i_additional_condition = self.additional_conditions.index(additional_condition)
        #     return {'i_distfactor': idist, 'i_angfactor': iang, 'i_additional_condition': i_additional_condition}

        def neighbors_surfaces(self, isite, surface_calculation_type=None, max_dist=2.0):
            """
            Get the different surfaces corresponding to the different distance-angle cutoffs for a given site.

            Args:
                isite: Index of the site
                surface_calculation_type: How to compute the surface.
                max_dist: The maximum distance factor to be considered.

            Returns:
                Surfaces for each distance-angle cutoff.
            """
            if self.voronoi_list2[isite] is None:
                return None
            bounds_and_limits = self.voronoi_parameters_bounds_and_limits(isite, surface_calculation_type, max_dist)
            distance_bounds = bounds_and_limits['distance_bounds']
            angle_bounds = bounds_and_limits['angle_bounds']
            surfaces = np.zeros((len(distance_bounds), len(angle_bounds)), np.float)
            for idp in range(len(distance_bounds) - 1):
                this_dist_plateau = distance_bounds[idp + 1] - distance_bounds[idp]
                for iap in range(len(angle_bounds) - 1):
                    this_ang_plateau = angle_bounds[iap + 1] - angle_bounds[iap]
                    surfaces[idp][iap] = np.absolute(this_dist_plateau * this_ang_plateau)
            return surfaces

        def neighbors_surfaces_bounded(self, isite, surface_calculation_options=None):
            """
            Get the different surfaces (using boundaries) corresponding to the different distance-angle cutoffs
            for a given site.

            Args:
                isite: Index of the site.
                surface_calculation_options: Options for the boundaries.

            Returns:
                Surfaces for each distance-angle cutoff.
            """
            if self.voronoi_list2[isite] is None:
                return None
            if surface_calculation_options is None:
                surface_calculation_options = {'type': 'standard_elliptic',
                                               'distance_bounds': {'lower': 1.2, 'upper': 1.8},
                                               'angle_bounds': {'lower': 0.1, 'upper': 0.8}}
            if surface_calculation_options['type'] in ['standard_elliptic', 'standard_diamond', 'standard_spline']:
                plot_type = {'distance_parameter': ('initial_normalized', None),
                             'angle_parameter': ('initial_normalized', None)}
            else:
                raise ValueError('Type "{}" for the surface calculation in DetailedVoronoiContainer '
                                 'is invalid'.format(surface_calculation_options['type']))
            max_dist = surface_calculation_options['distance_bounds']['upper'] + 0.1
            bounds_and_limits = self.voronoi_parameters_bounds_and_limits(isite=isite,
                                                                          plot_type=plot_type,
                                                                          max_dist=max_dist)

            distance_bounds = bounds_and_limits['distance_bounds']
            angle_bounds = bounds_and_limits['angle_bounds']
            lower_and_upper_functions = get_lower_and_upper_f(surface_calculation_options=surface_calculation_options)
            mindist = surface_calculation_options['distance_bounds']['lower']
            maxdist = surface_calculation_options['distance_bounds']['upper']
            minang = surface_calculation_options['angle_bounds']['lower']
            maxang = surface_calculation_options['angle_bounds']['upper']

            f_lower = lower_and_upper_functions['lower']
            f_upper = lower_and_upper_functions['upper']
            surfaces = np.zeros((len(distance_bounds), len(angle_bounds)), np.float)
            for idp in range(len(distance_bounds) - 1):
                dp1 = distance_bounds[idp]
                dp2 = distance_bounds[idp + 1]
                if dp2 < mindist or dp1 > maxdist:
                    continue
                if dp1 < mindist:
                    d1 = mindist
                else:
                    d1 = dp1
                if dp2 > maxdist:
                    d2 = maxdist
                else:
                    d2 = dp2
                for iap in range(len(angle_bounds) - 1):
                    ap1 = angle_bounds[iap]
                    ap2 = angle_bounds[iap + 1]
                    if ap1 > ap2:
                        ap1 = angle_bounds[iap + 1]
                        ap2 = angle_bounds[iap]
                    if ap2 < minang or ap1 > maxang:
                        continue
                    intersection, interror = rectangle_surface_intersection(rectangle=((d1, d2),
                                                                                       (ap1, ap2)),
                                                                            f_lower=f_lower,
                                                                            f_upper=f_upper,
                                                                            bounds_lower=[mindist, maxdist],
                                                                            bounds_upper=[mindist, maxdist],
                                                                            check=False)
                    surfaces[idp][iap] = intersection
            return surfaces

        @staticmethod
        def _get_vertices_dist_ang_indices(parameter_indices_list):
            pp0 = [pp[0] for pp in parameter_indices_list]
            pp1 = [pp[1] for pp in parameter_indices_list]
            min_idist = min(pp0)
            min_iang = min(pp1)
            max_idist = max(pp0)
            max_iang = max(pp1)
            i_min_angs = np.argwhere(np.array(pp1) == min_iang)
            i_max_dists = np.argwhere(np.array(pp0) == max_idist)
            pp0_at_min_iang = [pp0[ii[0]] for ii in i_min_angs]
            pp1_at_max_idist = [pp1[ii[0]] for ii in i_max_dists]
            max_idist_at_min_iang = max(pp0_at_min_iang)
            min_iang_at_max_idist = min(pp1_at_max_idist)

            p1 = (min_idist, min_iang)
            p2 = (max_idist_at_min_iang, min_iang)
            p3 = (max_idist_at_min_iang, min_iang_at_max_idist)
            p4 = (max_idist, min_iang_at_max_idist)
            p5 = (max_idist, max_iang)
            p6 = (min_idist, max_iang)

            return [p1, p2, p3, p4, p5, p6]

        def maps_and_surfaces(self, isite, surface_calculation_type=None, max_dist=2.0, additional_conditions=None):
            """
            Get the different surfaces and their cn_map corresponding to the different distance-angle cutoffs
            for a given site.

            Args:
                isite: Index of the site
                surface_calculation_type: How to compute the surface.
                max_dist: The maximum distance factor to be considered.
                additional_conditions: If additional conditions have to be considered.

            Returns:
                Surfaces and cn_map's for each distance-angle cutoff.
            """
            if self.voronoi_list2[isite] is None:
                return None
            if additional_conditions is None:
                additional_conditions = [self.AC.ONLY_ACB]
            surfaces = self.neighbors_surfaces(isite=isite, surface_calculation_type=surface_calculation_type,
                                               max_dist=max_dist)
            maps_and_surfaces = []
            for cn, value in self._unique_coordinated_neighbors_parameters_indices[isite].items():
                for imap, list_parameters_indices in enumerate(value):
                    thissurf = 0.0
                    for (idp, iap, iacb) in list_parameters_indices:
                        if iacb in additional_conditions:
                            thissurf += surfaces[idp, iap]
                    maps_and_surfaces.append({'map': (cn, imap), 'surface': thissurf,
                                              'parameters_indices': list_parameters_indices})
            return maps_and_surfaces

        def maps_and_surfaces_bounded(self, isite, surface_calculation_options=None, additional_conditions=None):
            """
            Get the different surfaces (using boundaries) and their cn_map corresponding to the different
            distance-angle cutoffs for a given site.

            Args:
                isite: Index of the site
                surface_calculation_options: Options for the boundaries.
                additional_conditions: If additional conditions have to be considered.

            Returns:
                Surfaces and cn_map's for each distance-angle cutoff.
            """
            if self.voronoi_list2[isite] is None:
                return None
            if additional_conditions is None:
                additional_conditions = [self.AC.ONLY_ACB]
            surfaces = self.neighbors_surfaces_bounded(isite=isite, surface_calculation_options=surface_calculation_options)
            maps_and_surfaces = []
            for cn, value in self._unique_coordinated_neighbors_parameters_indices[isite].items():
                for imap, list_parameters_indices in enumerate(value):
                    thissurf = 0.0
                    for (idp, iap, iacb) in list_parameters_indices:
                        if iacb in additional_conditions:
                            thissurf += surfaces[idp, iap]
                    maps_and_surfaces.append({'map': (cn, imap), 'surface': thissurf,
                                              'parameters_indices': list_parameters_indices})
            return maps_and_surfaces

        def neighbors(self, isite, distfactor, angfactor, additional_condition=None):
            """
            Get the neighbors of a given site corresponding to a given distance and angle factor.

            Args:
                isite: Index of the site.
                distfactor: Distance factor.
                angfactor: Angle factor.
                additional_condition: Additional condition to be used (currently not implemented).

            Returns:
                List of neighbors of the given site for the given distance and angle factors.
            """
            idist = None
            dfact = None
            for iwd, wd in enumerate(self.neighbors_normalized_distances[isite]):
                if distfactor >= wd['min']:
                    idist = iwd
                    dfact = wd['max']
                else:
                    break
            iang = None
            afact = None
            for iwa, wa in enumerate(self.neighbors_normalized_angles[isite]):
                if angfactor <= wa['max']:
                    iang = iwa
                    afact = wa['min']
                else:
                    break
            if idist is None or iang is None:
                raise ValueError('Distance or angle parameter not found ...')

            return [nb for nb in self.voronoi_list2[isite] if
                    nb['normalized_distance'] <= dfact and nb['normalized_angle'] >= afact]

        def voronoi_parameters_bounds_and_limits(self, isite, plot_type, max_dist):
            """
            Get the different boundaries and limits of the distance and angle factors for the given site.

            Args:
                isite: Index of the site.
                plot_type: Types of distance/angle parameters to get.
                max_dist: Maximum distance factor.

            Returns:
                Distance and angle bounds and limits.
            """
            # Initializes the distance and angle parameters
            if self.voronoi_list2[isite] is None:
                return None
            if plot_type is None:
                plot_type = {'distance_parameter': ('initial_inverse_opposite', None),
                             'angle_parameter': ('initial_opposite', None)}
            dd = [dist['min'] for dist in self.neighbors_normalized_distances[isite]]
            dd[0] = 1.0
            if plot_type['distance_parameter'][0] == 'initial_normalized':
                dd.append(max_dist)
                distance_bounds = np.array(dd)
                dist_limits = [1.0, max_dist]
            elif plot_type['distance_parameter'][0] == 'initial_inverse_opposite':
                ddinv = [1.0 / dist for dist in dd]
                ddinv.append(0.0)
                distance_bounds = np.array([1.0 - invdist for invdist in ddinv])
                dist_limits = [0.0, 1.0]
            elif plot_type['distance_parameter'][0] == 'initial_inverse3_opposite':
                ddinv = [1.0 / dist ** 3.0 for dist in dd]
                ddinv.append(0.0)
                distance_bounds = np.array([1.0 - invdist for invdist in ddinv])
                dist_limits = [0.0, 1.0]
            else:
                raise NotImplementedError('Plotting type "{}" '
                                          'for the distance is not implemented'.format(plot_type['distance_parameter']))
            if plot_type['angle_parameter'][0] == 'initial_normalized':
                aa = [0.0]
                aa.extend([ang['max'] for ang in self.neighbors_normalized_angles[isite]])
                angle_bounds = np.array(aa)
            elif plot_type['angle_parameter'][0] == 'initial_opposite':
                aa = [0.0]
                aa.extend([ang['max'] for ang in self.neighbors_normalized_angles[isite]])
                aa = [1.0 - ang for ang in aa]
                angle_bounds = np.array(aa)
            else:
                raise NotImplementedError('Plotting type "{}" '
                                          'for the angle is not implemented'.format(plot_type['angle_parameter']))
            ang_limits = [0.0, 1.0]
            return {'distance_bounds': distance_bounds, 'distance_limits': dist_limits,
                    'angle_bounds': angle_bounds, 'angle_limits': ang_limits}

        def is_close_to(self, other, rtol=0.0, atol=1e-8):
            """
            Whether two DetailedVoronoiContainer objects are close to each other.

            Args:
                other: Another DetailedVoronoiContainer to be compared with.
                rtol: Relative tolerance to compare values.
                atol: Absolute tolerance to compare values.

            Returns:
                True if the two DetailedVoronoiContainer are close to each other.
            """
            isclose = (np.isclose(self.normalized_angle_tolerance, other.normalized_angle_tolerance,
                                  rtol=rtol, atol=atol) and
                       np.isclose(self.normalized_distance_tolerance, other.normalized_distance_tolerance,
                                  rtol=rtol, atol=atol) and
                       self.additional_conditions == other.additional_conditions and
                       self.valences == other.valences)
            if not isclose:
                return isclose
            for isite, site_voronoi in enumerate(self.voronoi_list2):
                self_to_other_nbs = {}
                for inb, nb in enumerate(site_voronoi):
                    if nb is None:
                        if other.voronoi_list2[isite] is None:
                            continue
                        else:
                            return False
                    else:
                        if other.voronoi_list2[isite] is None:
                            return False
                    nb_other = None
                    for inb2, nb2 in enumerate(other.voronoi_list2[isite]):
                        if nb['site'] == nb2['site']:
                            self_to_other_nbs[inb] = inb2
                            nb_other = nb2
                            break
                    if nb_other is None:
                        return False
                    if not np.isclose(nb['distance'], nb_other['distance'],
                                      rtol=rtol, atol=atol):
                        return False
                    if not np.isclose(nb['angle'], nb_other['angle'],
                                      rtol=rtol, atol=atol):
                        return False
                    if not np.isclose(nb['normalized_distance'], nb_other['normalized_distance'],
                                      rtol=rtol, atol=atol):
                        return False
                    if not np.isclose(nb['normalized_angle'], nb_other['normalized_angle'],
                                      rtol=rtol, atol=atol):
                        return False
                    if nb['index'] != nb_other['index']:
                        return False
                    if nb['site'] != nb_other['site']:
                        return False
            return True

        def get_rdf_figure(self, isite, normalized=True, figsize=None,
                           step_function=None):
            """
            Get the Radial Distribution Figure for a given site.

            Args:
                isite: Index of the site.
                normalized: Whether to normalize distances.
                figsize: Size of the figure.
                step_function: Type of step function to be used for the RDF.

            Returns:
                Matplotlib figure.
            """
            def dp_func(dp):
                return 1.0 - 1.0 / np.power(dp, 3.0)

            import matplotlib.pyplot as plt

            if step_function is None:
                step_function = {'type': 'normal_cdf', 'scale': 0.0001}

            # Initializes the figure
            if figsize is None:
                fig = plt.figure()
            else:
                fig = plt.figure(figsize=figsize)
            subplot = fig.add_subplot(111)
            if normalized:
                dists = self.neighbors_normalized_distances[isite]
            else:
                dists = self.neighbors_distances[isite]

            if step_function['type'] == 'step_function':
                isorted = np.argsort([dd['min'] for dd in dists])
                sorted_dists = [dists[ii]['min'] for ii in isorted]
                dnb_dists = [len(dists[ii]['dnb_indices']) for ii in isorted]
                xx = [0.0]
                yy = [0.0]
                for idist, dist in enumerate(sorted_dists):
                    xx.append(dist)
                    xx.append(dist)
                    yy.append(yy[-1])
                    yy.append(yy[-1] + dnb_dists[idist])
                xx.append(1.1 * xx[-1])
                yy.append(yy[-1])
            elif step_function['type'] == 'normal_cdf':
                scale = step_function['scale']
                mydists = [dp_func(dd['min']) for dd in dists]
                mydcns = [len(dd['dnb_indices']) for dd in dists]
                xx = np.linspace(0.0, 1.1 * max(mydists), num=500)
                yy = np.zeros_like(xx)
                for idist, dist in enumerate(mydists):
                    yy += mydcns[idist] * normal_cdf_step(xx, mean=dist, scale=scale)
            else:
                raise ValueError('Step function of type "{}" is not allowed'.format(step_function['type']))
            subplot.plot(xx, yy)

            return fig

        def get_sadf_figure(self, isite, normalized=True, figsize=None,
                            step_function=None):
            """
            Get the Solid Angle Distribution Figure for a given site.
            Args:
                isite: Index of the site.
                normalized: Whether to normalize angles.
                figsize: Size of the figure.
                step_function: Type of step function to be used for the SADF.

            Returns:
                Matplotlib figure.
            """
            def ap_func(ap):
                return np.power(ap, -0.1)

            import matplotlib.pyplot as plt

            if step_function is None:
                step_function = {'type': 'step_function', 'scale': 0.0001}

            # Initializes the figure
            if figsize is None:
                fig = plt.figure()
            else:
                fig = plt.figure(figsize=figsize)
            subplot = fig.add_subplot(111)
            if normalized:
                angs = self.neighbors_normalized_angles[isite]
            else:
                angs = self.neighbors_angles[isite]

            if step_function['type'] == 'step_function':
                isorted = np.argsort([ap_func(aa['min']) for aa in angs])
                sorted_angs = [ap_func(angs[ii]['min']) for ii in isorted]
                dnb_angs = [len(angs[ii]['dnb_indices']) for ii in isorted]
                xx = [0.0]
                yy = [0.0]
                for iang, ang in enumerate(sorted_angs):
                    xx.append(ang)
                    xx.append(ang)
                    yy.append(yy[-1])
                    yy.append(yy[-1] + dnb_angs[iang])
                xx.append(1.1 * xx[-1])
                yy.append(yy[-1])
            elif step_function['type'] == 'normal_cdf':
                scale = step_function['scale']
                myangs = [ap_func(aa['min']) for aa in angs]
                mydcns = [len(dd['dnb_indices']) for dd in angs]
                xx = np.linspace(0.0, 1.1 * max(myangs), num=500)
                yy = np.zeros_like(xx)
                for iang, ang in enumerate(myangs):
                    yy += mydcns[iang] * normal_cdf_step(xx, mean=ang, scale=scale)
            else:
                raise ValueError('Step function of type "{}" is not allowed'.format(step_function['type']))
            subplot.plot(xx, yy)

            return fig

        def __eq__(self, other):
            return (self.normalized_angle_tolerance == other.normalized_angle_tolerance and
                    self.normalized_distance_tolerance == other.normalized_distance_tolerance and
                    self.additional_conditions == other.additional_conditions and
                    self.valences == other.valences and
                    self.voronoi_list2 == other.voronoi_list2 and
                    self.structure == other.structure)

        def __ne__(self, other):
            return not self == other

        def to_bson_voronoi_list2(self):
            """
            Transforms the voronoi_list into a vlist + bson_nb_voro_list, that are BSON-encodable.

            Returns:
                [vlist, bson_nb_voro_list], to be used in the as_dict method.
            """
            bson_nb_voro_list2 = [None] * len(self.voronoi_list2)
            for ivoro, voro in enumerate(self.voronoi_list2):
                if voro is None or voro == 'None':
                    continue
                site_voro = []
                # {'site': neighbors[nn[1]],
                #  'angle': sa,
                #  'distance': distances[nn[1]],
                #  'index': myindex}
                for nb_dict in voro:
                    site = nb_dict['site']
                    site_dict = {key: val for key, val in nb_dict.items() if key not in ['site']}
                    # site_voro.append([ps.as_dict(), dd]) [float(c) for c in self.frac_coords]
                    diff = site.frac_coords - self.structure[nb_dict['index']].frac_coords
                    site_voro.append([[nb_dict['index'], [float(c) for c in diff]],
                                      site_dict])
                bson_nb_voro_list2[ivoro] = site_voro
            return bson_nb_voro_list2

        def as_dict(self):
            """
            Bson-serializable dict representation of the VoronoiContainer.

            Returns:
                dictionary that is BSON-encodable.
            """
            bson_nb_voro_list2 = self.to_bson_voronoi_list2()
            return {"@module": self.__class__.__module__,
                    "@class": self.__class__.__name__,
                    "bson_nb_voro_list2": bson_nb_voro_list2,
                    # "neighbors_lists": self.neighbors_lists,
                    "structure": self.structure.as_dict(),
                    "normalized_angle_tolerance": self.normalized_angle_tolerance,
                    "normalized_distance_tolerance": self.normalized_distance_tolerance,
                    "additional_conditions": self.additional_conditions,
                    "valences": self.valences,
                    "maximum_distance_factor": self.maximum_distance_factor,
                    "minimum_angle_factor": self.minimum_angle_factor}

        @classmethod
        def from_dict(cls, d):
            """
            Reconstructs the VoronoiContainer object from a dict representation of the VoronoiContainer created using
            the as_dict method.

            Args:
                d: dict representation of the VoronoiContainer object.

            Returns:
                VoronoiContainer object.
            """
            structure = Structure.from_dict(d['structure'])
            voronoi_list2 = from_bson_voronoi_list2(d['bson_nb_voro_list2'], structure)
            maximum_distance_factor = d['maximum_distance_factor'] if 'maximum_distance_factor' in d else None
            minimum_angle_factor = d['minimum_angle_factor'] if 'minimum_angle_factor' in d else None
            return cls(structure=structure, voronoi_list2=voronoi_list2,
                       # neighbors_lists=neighbors_lists,
                       normalized_angle_tolerance=d['normalized_angle_tolerance'],
                       normalized_distance_tolerance=d['normalized_distance_tolerance'],
                       additional_conditions=d['additional_conditions'],
                       valences=d['valences'],
                       maximum_distance_factor=maximum_distance_factor,
                       minimum_angle_factor=minimum_angle_factor)