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

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

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

    """
    This module contains the main object used to identify the coordination environments in a given structure.
    If you use this module, please cite the following:

    David Waroquiers, Xavier Gonze, Gian-Marco Rignanese, Cathrin Welker-Nieuwoudt, Frank Rosowski,
    Michael Goebel, Stephan Schenk, Peter Degelmann, Rute Andre, Robert Glaum, and Geoffroy Hautier,
    "Statistical analysis of coordination environments in oxides",
    Chem. Mater., 2017, 29 (19), pp 8346–8360,
    DOI: 10.1021/acs.chemmater.7b02766
    """

    __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 itertools
    import logging
    import time
    from collections import OrderedDict
    from random import shuffle

    import numpy as np
    from numpy.linalg import norm
    from numpy.linalg import svd
    from pymatgen.analysis.bond_valence import BVAnalyzer
    from pymatgen.analysis.chemenv.coordination_environments.chemenv_strategies import \
        MultiWeightsChemenvStrategy
    from pymatgen.analysis.chemenv.coordination_environments.coordination_geometries import \
        AllCoordinationGeometries
    from pymatgen.analysis.chemenv.coordination_environments.coordination_geometries import \
        EXPLICIT_PERMUTATIONS
    from pymatgen.analysis.chemenv.coordination_environments.coordination_geometries import \
        SEPARATION_PLANE
    from pymatgen.analysis.chemenv.coordination_environments.structure_environments import \
        ChemicalEnvironments
    from pymatgen.analysis.chemenv.coordination_environments.structure_environments import \
        LightStructureEnvironments
    from pymatgen.analysis.chemenv.coordination_environments.structure_environments import \
        StructureEnvironments
    from pymatgen.analysis.chemenv.coordination_environments.voronoi import \
        DetailedVoronoiContainer
    from pymatgen.analysis.chemenv.utils.coordination_geometry_utils import Plane
    from pymatgen.analysis.chemenv.utils.coordination_geometry_utils import \
        collinear, separation_in_list
    from pymatgen.analysis.chemenv.utils.coordination_geometry_utils import \
        sort_separation, sort_separation_tuple
    from pymatgen.analysis.chemenv.utils.defs_utils import chemenv_citations
    from pymatgen.core.lattice import Lattice
    from pymatgen.core.structure import Structure
    from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
    from pymatgen.core.periodic_table import Specie

    debug = False
    DIST_TOLERANCES = [0.02, 0.05, 0.1, 0.2, 0.3]

    class AbstractGeometry:
        """
        Class used to describe a geometry (perfect or distorted)
        """

        def __init__(self, central_site=None, bare_coords=None,
                     centering_type='standard',
                     include_central_site_in_centroid=False,
                     optimization=None):
            """
            Constructor for the abstract geometry
            :param central_site: Coordinates of the central site
            :param bare_coords: Coordinates of the neighbors of the central site
            :param centering_type: How to center the abstract geometry
            :param include_central_site_in_centroid: When the centering is on the centroid, the central site is included
                if this parameter is set to True.
            :raise: ValueError if the parameters are not consistent
            """
            bcoords = np.array(bare_coords)
            self.bare_centre = np.array(central_site)
            self.bare_points_without_centre = bcoords
            self.bare_points_with_centre = np.array(central_site)
            self.bare_points_with_centre = np.concatenate(([self.bare_points_with_centre], bcoords))
            self.centroid_without_centre = np.mean(self.bare_points_without_centre,
                                                   axis=0)
            self.centroid_with_centre = np.mean(self.bare_points_with_centre,
                                                axis=0)
            self._points_wcs_csc = self.bare_points_with_centre - self.bare_centre
            self._points_wocs_csc = self.bare_points_without_centre - self.bare_centre
            self._points_wcs_ctwcc = self.bare_points_with_centre - self.centroid_with_centre
            self._points_wocs_ctwcc = self.bare_points_without_centre - self.centroid_with_centre
            self._points_wcs_ctwocc = self.bare_points_with_centre - self.centroid_without_centre
            self._points_wocs_ctwocc = self.bare_points_without_centre - self.centroid_without_centre

            self.centering_type = centering_type
            self.include_central_site_in_centroid = include_central_site_in_centroid
            self.bare_central_site = np.array(central_site)
            if centering_type == 'standard':
                if len(bare_coords) < 5:
                    if include_central_site_in_centroid:
                        raise ValueError(
                            "The center is the central site, no calculation of the centroid, "
                            "variable include_central_site_in_centroid should be set to False")
                    if central_site is None:
                        raise ValueError(
                            "Centering_type is central_site, the central site should be given")
                    self.centre = np.array(central_site)
                else:
                    total = np.sum(bcoords, axis=0)
                    if include_central_site_in_centroid:
                        if central_site is None:
                            raise ValueError(
                                "The centroid includes the central site but no central site is given")
                        total += self.bare_centre
                        self.centre = total / (np.float(len(bare_coords)) + 1.0)
                    else:
                        self.centre = total / np.float(len(bare_coords))
            elif centering_type == 'central_site':
                if include_central_site_in_centroid:
                    raise ValueError(
                        "The center is the central site, no calculation of the centroid, "
                        "variable include_central_site_in_centroid should be set to False")
                if central_site is None:
                    raise ValueError(
                        "Centering_type is central_site, the central site should be given")
                self.centre = np.array(central_site)
            elif centering_type == 'centroid':
                total = np.sum(bcoords, axis=0)
                if include_central_site_in_centroid:
                    if central_site is None:
                        raise ValueError(
                            "The centroid includes the central site but no central site is given")
                    total += self.bare_centre
                    self.centre = total / (np.float(len(bare_coords)) + 1.0)
                else:
                    self.centre = total / np.float(len(bare_coords))
            self._bare_coords = self.bare_points_without_centre
            self._coords = self._bare_coords - self.centre
            self.central_site = self.bare_central_site - self.centre
            self.coords = self._coords
            self.bare_coords = self._bare_coords

        def __str__(self):
            """
            String representation of the AbstractGeometry
            :return: String representation of the AbstractGeometry
            """
            outs = [
                '\nAbstract Geometry with {n} points :'.format(n=len(self.coords))]
            for pp in self.coords:
                outs.append('  {pp}'.format(pp=pp))
            if self.centering_type == 'standard':
                if self.include_central_site_in_centroid:
                    outs.append(
                        'Points are referenced to the central site for coordination numbers < 5'
                        ' and to the centroid (calculated with the central site) for coordination'
                        ' numbers >= 5 : {c}\n'.format(c=self.centre))
                else:
                    outs.append(
                        'Points are referenced to the central site for coordination numbers < 5'
                        ' and to the centroid (calculated without the central site) for coordination'
                        ' numbers >= 5 : {c}\n'.format(c=self.centre))
            elif self.centering_type == 'central_site':
                outs.append('Points are referenced to the central site : {c}\n'.format(c=self.centre))
            elif self.centering_type == 'centroid':
                if self.include_central_site_in_centroid:
                    outs.append('Points are referenced to the centroid '
                                '(calculated with the central site) :\n  {c}\n'.format(c=self.centre))
                else:
                    outs.append('Points are referenced to the centroid'
                                ' (calculated without the central site) :\n  {c}\n'.format(c=self.centre))
            return '\n'.join(outs)

        @classmethod
        def from_cg(cls, cg, centering_type='standard',
                    include_central_site_in_centroid=False):
            """
            :param cg:
            :param centering_type:
            :param include_central_site_in_centroid:
            :return:
            """
            central_site = cg.get_central_site()
            bare_coords = [np.array(pt, np.float) for pt in cg.points]
            return cls(central_site=central_site, bare_coords=bare_coords,
                       centering_type=centering_type,
                       include_central_site_in_centroid=include_central_site_in_centroid)

        def points_wcs_csc(self, permutation=None):
            """
            :param permutation:
            :return:
            """
            if permutation is None:
                return self._points_wcs_csc
            return np.concatenate((self._points_wcs_csc[0:1], self._points_wocs_csc.take(permutation, axis=0)))

        def points_wocs_csc(self, permutation=None):
            """
            :param permutation:
            :return:
            """
            if permutation is None:
                return self._points_wocs_csc
            return self._points_wocs_csc.take(permutation, axis=0)

        def points_wcs_ctwcc(self, permutation=None):
            """
            :param permutation:
            :return:
            """
            if permutation is None:
                return self._points_wcs_ctwcc
            return np.concatenate((self._points_wcs_ctwcc[0:1], self._points_wocs_ctwcc.take(permutation, axis=0)))

        def points_wocs_ctwcc(self, permutation=None):
            """
            :param permutation:
            :return:
            """
            if permutation is None:
                return self._points_wocs_ctwcc
            return self._points_wocs_ctwcc.take(permutation, axis=0)

        def points_wcs_ctwocc(self, permutation=None):
            """
            :param permutation:
            :return:
            """
            if permutation is None:
                return self._points_wcs_ctwocc
            return np.concatenate((self._points_wcs_ctwocc[0:1], self._points_wocs_ctwocc.take(permutation, axis=0)))

        def points_wocs_ctwocc(self, permutation=None):
            """
            :param permutation:
            :return:
            """
            if permutation is None:
                return self._points_wocs_ctwocc
            return self._points_wocs_ctwocc.take(permutation, axis=0)

        @property
        def cn(self):
            """
            :return: Coordination number
            """
            return len(self.coords)

        @property
        def coordination_number(self):
            """
            :return: Coordination number
            """
            return len(self.coords)

    def symmetry_measure(points_distorted, points_perfect):
        """
        Computes the continuous symmetry measure of the (distorted) set of points "points_distorted" with respect to the
        (perfect) set of points "points_perfect".
        :param points_distorted: List of points describing a given (distorted) polyhedron for which the symmetry measure
            has to be computed with respect to the model polyhedron described by the list of points
            "points_perfect".
        :param points_perfect: List of "perfect" points describing a given model polyhedron.
        :return: The continuous symmetry measure of the distorted polyhedron with respect to the perfect polyhedron
        """
        # When there is only one point, the symmetry measure is 0.0 by definition
        if len(points_distorted) == 1:
            return {'symmetry_measure': 0.0, 'scaling_factor': None, 'rotation_matrix': None}
        # Find the rotation matrix that aligns the distorted points to the perfect points in a least-square sense.
        rot = find_rotation(points_distorted=points_distorted,
                            points_perfect=points_perfect)
        # Find the scaling factor between the distorted points and the perfect points in a least-square sense.
        scaling_factor, rotated_coords, points_perfect = find_scaling_factor(points_distorted=points_distorted,
                                                                             points_perfect=points_perfect,
                                                                             rot=rot)
        # Compute the continuous symmetry measure [see Eq. 1 in Pinsky et al., Inorganic Chemistry 37, 5575 (1998)]
        rotated_coords = scaling_factor * rotated_coords
        diff = points_perfect - rotated_coords
        num = np.tensordot(diff, diff)
        denom = np.tensordot(points_perfect, points_perfect)
        return {'symmetry_measure': num / denom * 100.0, 'scaling_factor': scaling_factor, 'rotation_matrix': rot}

    def find_rotation(points_distorted, points_perfect):
        """
        This finds the rotation matrix that aligns the (distorted) set of points "points_distorted" with respect to the
        (perfect) set of points "points_perfect" in a least-square sense.
        :param points_distorted: List of points describing a given (distorted) polyhedron for which the rotation that
            aligns these points in a least-square sense to the set of perfect points "points_perfect"
        :param points_perfect: List of "perfect" points describing a given model polyhedron.
        :return: The rotation matrix
        """
        H = np.matmul(points_distorted.T, points_perfect)
        [U, S, Vt] = svd(H)
        rot = np.matmul(Vt.T, U.T)
        return rot

    def find_scaling_factor(points_distorted, points_perfect, rot):
        """
        This finds the scaling factor between the (distorted) set of points "points_distorted" and the
        (perfect) set of points "points_perfect" in a least-square sense.
        :param points_distorted: List of points describing a given (distorted) polyhedron for which the scaling factor has
                                 to be obtained.
        :param points_perfect: List of "perfect" points describing a given model polyhedron.
        :param rot: The rotation matrix
        :return: The scaling factor between the two structures and the rotated set of (distorted) points.
        """
        rotated_coords = np.matmul(rot, points_distorted.T).T
        num = np.tensordot(rotated_coords, points_perfect)
        denom = np.tensordot(rotated_coords, rotated_coords)
        return num / denom, rotated_coords, points_perfect

    class LocalGeometryFinder:
        """
        Main class used to find the local environments in a structure
        """
        DEFAULT_BVA_DISTANCE_SCALE_FACTOR = 1.0
        BVA_DISTANCE_SCALE_FACTORS = {'experimental': 1.0, 'GGA_relaxed': 1.015,
                                      'LDA_relaxed': 0.995}
        DEFAULT_SPG_ANALYZER_OPTIONS = {'symprec': 1e-3, 'angle_tolerance': 5}
        STRUCTURE_REFINEMENT_NONE = 'none'
        STRUCTURE_REFINEMENT_REFINED = 'refined'
        STRUCTURE_REFINEMENT_SYMMETRIZED = 'symmetrized'

        DEFAULT_STRATEGY = MultiWeightsChemenvStrategy.stats_article_weights_parameters()

        PRESETS = {'DEFAULT': {'maximum_distance_factor': 2.0,
                               'minimum_angle_factor': 0.05,
                               'voronoi_normalized_distance_tolerance': 0.05,
                               'voronoi_normalized_angle_tolerance': 0.03,
                               'optimization': 2}}

        def __init__(self, permutations_safe_override=False,
                     plane_ordering_override=True, debug_level=None,
                     plane_safe_permutations=False,
                     only_symbols=None):
            """
            Constructor for the LocalGeometryFinder, initializes the list of coordination geometries
            :param permutations_safe_override: If set to True, all permutations are tested (very time-consuming for large
                coordination numbers!)
            :param plane_ordering_override: If set to False, the ordering of the points in the plane is disabled
            """
            self.allcg = AllCoordinationGeometries(
                permutations_safe_override=permutations_safe_override,
                only_symbols=only_symbols)
            self.permutations_safe_override = permutations_safe_override
            self.plane_ordering_override = plane_ordering_override
            self.plane_safe_permutations = plane_safe_permutations
            self.setup_parameters(centering_type='centroid',
                                  include_central_site_in_centroid=True,
                                  bva_distance_scale_factor=None,
                                  structure_refinement=self.STRUCTURE_REFINEMENT_NONE)
            print(chemenv_citations())

        def setup_parameters(self, centering_type='standard',
                             include_central_site_in_centroid=False,
                             bva_distance_scale_factor=None,
                             structure_refinement=STRUCTURE_REFINEMENT_REFINED,
                             spg_analyzer_options=None):
            """
            Setup of the parameters for the coordination geometry finder. A reference point for the geometries has to be
            chosen. This can be the centroid of the structure (including or excluding the atom for which the coordination
            geometry is looked for) or the atom itself. In the 'standard' centering_type, the reference point is the central
            atom for coordination numbers 1, 2, 3 and 4 and the centroid for coordination numbers > 4.
            :param centering_type: Type of the reference point (centering) 'standard', 'centroid' or 'central_site'
            :param include_central_site_in_centroid: In case centering_type is 'centroid', the central site is included if
                this value is set to True.
            :param bva_distance_scale_factor: Scaling factor for the bond valence analyzer (this might be different whether
                the structure is an experimental one, an LDA or a GGA relaxed one, or any other relaxation scheme (where
                under- or over-estimation of bond lengths is known).
            :param structure_refinement: Refinement of the structure. Can be "none", "refined" or "symmetrized".
            :param spg_analyzer_options: Options for the SpaceGroupAnalyzer (dictionary specifying "symprec"
                and "angle_tolerance". See pymatgen's SpaceGroupAnalyzer for more information.
            """
            self.centering_type = centering_type
            self.include_central_site_in_centroid = include_central_site_in_centroid
            if bva_distance_scale_factor is not None:
                self.bva_distance_scale_factor = bva_distance_scale_factor
            else:
                self.bva_distance_scale_factor = self.DEFAULT_BVA_DISTANCE_SCALE_FACTOR
            self.structure_refinement = structure_refinement
            if spg_analyzer_options is None:
                self.spg_analyzer_options = self.DEFAULT_SPG_ANALYZER_OPTIONS
            else:
                self.spg_analyzer_options = spg_analyzer_options

        def setup_parameter(self, parameter, value):
            """
            Setup of one specific parameter to the given value. The other parameters are unchanged. See setup_parameters
            method for the list of possible parameters
            :param parameter: Parameter to setup/update
            :param value: Value of the parameter
            """
            self.__dict__[parameter] = value

        def setup_structure(self, structure):
            """
            Sets up the structure for which the coordination geometries have to be identified. The structure is analyzed
            with the space group analyzer and a refined structure is used
            :param structure: A pymatgen Structure
            """
            self.initial_structure = structure.copy()
            if self.structure_refinement == self.STRUCTURE_REFINEMENT_NONE:
                self.structure = structure.copy()
                self.spg_analyzer = None
                self.symmetrized_structure = None
            else:
                self.spg_analyzer = SpacegroupAnalyzer(self.initial_structure,
                                                       symprec=self.spg_analyzer_options['symprec'],
                                                       angle_tolerance=self.spg_analyzer_options['angle_tolerance'])
                if self.structure_refinement == self.STRUCTURE_REFINEMENT_REFINED:
                    self.structure = self.spg_analyzer.get_refined_structure()
                    self.symmetrized_structure = None
                elif self.structure_refinement == self.STRUCTURE_REFINEMENT_SYMMETRIZED:
                    self.structure = self.spg_analyzer.get_refined_structure()
                    self.spg_analyzer_refined = SpacegroupAnalyzer(
                        self.structure,
                        symprec=self.spg_analyzer_options['symprec'],
                        angle_tolerance=self.spg_analyzer_options['angle_tolerance'])
                    self.symmetrized_structure = self.spg_analyzer_refined.get_symmetrized_structure()

        def get_structure(self):
            """
            Returns the pymatgen Structure that has been setup for the identification of geometries (the initial one
            might have been refined/symmetrized using the SpaceGroupAnalyzer).
            :return: The pymatgen Structure that has been setup for the identification of geometries (the initial one
            might have been refined/symmetrized using the SpaceGroupAnalyzer).
            """
            return self.structure

        def set_structure(self, lattice, species, coords, coords_are_cartesian):
            """
            Sets up the pymatgen structure for which the coordination geometries have to be identified starting from the
            lattice, the species and the coordinates
            :param lattice: The lattice of the structure
            :param species: The species on the sites
            :param coords: The coordinates of the sites
            :param coords_are_cartesian: If set to True, the coordinates are given in cartesian coordinates
            """
            self.setup_structure(
                Structure(lattice, species, coords, coords_are_cartesian))

        def compute_coordination_environments(
                self, structure, indices=None, only_cations=True, strategy=DEFAULT_STRATEGY,
                valences='bond-valence-analysis', initial_structure_environments=None):
            """
            :param structure:
            :param indices:
            :param only_cations:
            :param strategy:
            :param valences:
            :param initial_structure_environments:
            :return:
            """
            self.setup_structure(structure=structure)
            if valences == 'bond-valence-analysis':
                bva = BVAnalyzer()
                try:
                    vals = bva.get_valences(structure=structure)
                except ValueError:
                    vals = 'undefined'
            else:
                if valences == 'undefined':
                    vals = valences
                else:
                    if len(valences) != len(structure):
                        raise ValueError('Valences do not match the number of sites in the structure')
                    vals = valences
            # TODO: add something to compute only the neighbors sets needed for the strategy.
            se = self.compute_structure_environments(only_cations=only_cations, only_indices=indices, valences=vals,
                                                     initial_structure_environments=initial_structure_environments)
            lse = LightStructureEnvironments.from_structure_environments(strategy=strategy, structure_environments=se)
            return lse.coordination_environments

        def compute_structure_environments(self,
                                           excluded_atoms=None,
                                           only_atoms=None,
                                           only_cations=True,
                                           only_indices=None,
                                           maximum_distance_factor=PRESETS['DEFAULT']['maximum_distance_factor'],
                                           minimum_angle_factor=PRESETS['DEFAULT']['minimum_angle_factor'],
                                           max_cn=None,
                                           min_cn=None,
                                           only_symbols=None,
                                           valences='undefined',
                                           additional_conditions=None,
                                           info=None,
                                           timelimit=None,
                                           initial_structure_environments=None,
                                           get_from_hints=False,
                                           voronoi_normalized_distance_tolerance=PRESETS['DEFAULT']
                                           ['voronoi_normalized_distance_tolerance'],
                                           voronoi_normalized_angle_tolerance=PRESETS['DEFAULT']
                                           ['voronoi_normalized_angle_tolerance'],
                                           recompute=None,
                                           optimization=PRESETS['DEFAULT']['optimization']):
            """
            Computes and returns the StructureEnvironments object containing all the information about the coordination
            environments in the structure
            :param excluded_atoms: Atoms for which the coordination geometries does not have to be identified
            :param only_atoms: If not set to None, atoms for which the coordination geometries have to be identified
            :param only_cations: If set to True, will only compute environments for cations
            :param only_indices: If not set to None, will only compute environments the atoms of the given indices
            :param maximum_distance_factor: If not set to None, neighbors beyond
                maximum_distance_factor*closest_neighbor_distance are not considered
            :param minimum_angle_factor: If not set to None, neighbors for which the angle is lower than
                minimum_angle_factor*largest_angle_neighbor are not considered
            :param max_cn: maximum coordination number to be considered
            :param min_cn: minimum coordination number to be considered
            :param only_symbols: if not set to None, consider only coordination environments with the given symbols
            :param valences: valences of the atoms
            :param additional_conditions: additional conditions to be considered in the bonds (example : only bonds
                between cation and anion
            :param info: additional info about the calculation
            :param timelimit: time limit (in secs) after which the calculation of the StructureEnvironments object stops
            :param initial_structure_environments: initial StructureEnvironments object (most probably incomplete)
            :param get_from_hints: whether to add neighbors sets from "hints" (e.g. capped environment => test the
                neighbors without the cap)
            :param voronoi_normalized_distance_tolerance: tolerance for the normalized distance used to distinguish
                neighbors sets
            :param voronoi_normalized_angle_tolerance: tolerance for the normalized angle used to distinguish
                neighbors sets
            :param recompute: whether to recompute the sites already computed (when initial_structure_environments
                is not None)
            :param optimization: optimization algorithm
            :return: The StructureEnvironments object containing all the information about the coordination
                environments in the structure
            """
            time_init = time.process_time()
            if info is None:
                info = {}
            info.update({
                'local_geometry_finder': {
                    'parameters': {
                        'centering_type': self.centering_type,
                        'include_central_site_in_centroid': self.include_central_site_in_centroid,
                        'structure_refinement': self.structure_refinement,
                        'spg_analyzer_options': self.spg_analyzer_options
                    }
                }
            })
            if only_symbols is not None:
                self.allcg = AllCoordinationGeometries(
                    permutations_safe_override=self.permutations_safe_override,
                    only_symbols=only_symbols)

            if valences == 'undefined':
                firstsite = self.structure[0]
                try:
                    sp = firstsite.specie
                    if isinstance(sp, Specie):
                        self.valences = [int(site.specie.oxi_state) for site in self.structure]
                    else:
                        self.valences = valences
                except AttributeError:
                    self.valences = valences
            else:
                self.valences = valences

            # Get a list of indices of unequivalent sites from the initial structure
            self.equivalent_sites = [[site] for site in self.structure]
            self.struct_sites_to_irreducible_site_list_map = list(
                range(len(self.structure)))
            self.sites_map = list(range(len(self.structure)))
            indices = list(range(len(self.structure)))

            # Get list of unequivalent sites with valence >= 0
            if only_cations and self.valences != 'undefined':
                sites_indices = [isite for isite in indices if
                                 self.valences[isite] >= 0]
            else:
                sites_indices = [isite for isite in indices]

            # Include atoms that are in the list of "only_atoms" if it is provided
            if only_atoms is not None:
                sites_indices = [isite for isite in sites_indices
                                 if any([at in [sp.symbol for sp in self.structure[isite].species]
                                         for at in only_atoms])]

            # Exclude atoms that are in the list of excluded atoms
            if excluded_atoms:
                sites_indices = [isite for isite in sites_indices
                                 if not any([at in [sp.symbol for sp in
                                                    self.structure[
                                                        isite].species]
                                             for at in excluded_atoms])]

            if only_indices is not None:
                sites_indices = [isite for isite in indices if
                                 isite in only_indices]

            # Get the VoronoiContainer for the sites defined by their indices (sites_indices)
            logging.debug('Getting DetailedVoronoiContainer')
            if voronoi_normalized_distance_tolerance is None:
                normalized_distance_tolerance = DetailedVoronoiContainer.default_normalized_distance_tolerance
            else:
                normalized_distance_tolerance = voronoi_normalized_distance_tolerance
            if voronoi_normalized_angle_tolerance is None:
                normalized_angle_tolerance = DetailedVoronoiContainer.default_normalized_angle_tolerance
            else:
                normalized_angle_tolerance = voronoi_normalized_angle_tolerance
            self.detailed_voronoi = DetailedVoronoiContainer(self.structure,
                                                             isites=sites_indices,
                                                             valences=self.valences,
                                                             maximum_distance_factor=maximum_distance_factor,
                                                             minimum_angle_factor=minimum_angle_factor,
                                                             additional_conditions=additional_conditions,
                                                             normalized_distance_tolerance=normalized_distance_tolerance,
                                                             normalized_angle_tolerance=normalized_angle_tolerance)
            logging.debug('DetailedVoronoiContainer has been set up')

            # Initialize the StructureEnvironments object (either from initial_structure_environments or from scratch)
            if initial_structure_environments is not None:
                se = initial_structure_environments
                if se.structure != self.structure:
                    raise ValueError('Structure is not the same in initial_structure_environments')
                if se.voronoi != self.detailed_voronoi:
                    if self.detailed_voronoi.is_close_to(se.voronoi):
                        self.detailed_voronoi = se.voronoi
                    else:
                        raise ValueError('Detailed Voronoi is not the same in initial_structure_environments')
                se.info = info
            else:
                se = StructureEnvironments(voronoi=self.detailed_voronoi, valences=self.valences,
                                           sites_map=self.sites_map, equivalent_sites=self.equivalent_sites,
                                           ce_list=[None] * len(self.structure), structure=self.structure,
                                           info=info)

            # Set up the coordination numbers that have to be computed based on min_cn, max_cn and possibly the settings
            # for an update (argument "recompute") of an existing StructureEnvironments
            if min_cn is None:
                min_cn = 1
            if max_cn is None:
                max_cn = 20
            all_cns = range(min_cn, max_cn + 1)
            do_recompute = False
            if recompute is not None:
                if 'cns' in recompute:
                    cns_to_recompute = recompute['cns']
                    all_cns = list(set(all_cns).intersection(cns_to_recompute))
                do_recompute = True

            # Variables used for checking timelimit
            max_time_one_site = 0.0
            breakit = False

            if optimization > 0:
                self.detailed_voronoi.local_planes = [None] * len(self.structure)
                self.detailed_voronoi.separations = [None] * len(self.structure)

            # Loop on all the sites
            for isite in range(len(self.structure)):
                if isite not in sites_indices:
                    logging.debug(' ... in site #{:d}/{:d} ({}) : '
                                  'skipped'.format(isite, len(self.structure),
                                                   self.structure[isite].species_string))
                    continue
                if breakit:
                    logging.debug(' ... in site #{:d}/{:d} ({}) : '
                                  'skipped (timelimit)'.format(isite, len(self.structure),
                                                               self.structure[isite].species_string))
                    continue
                logging.debug(' ... in site #{:d}/{:d} ({})'.format(isite, len(self.structure),
                                                                    self.structure[isite].species_string))
                t1 = time.process_time()
                if optimization > 0:
                    self.detailed_voronoi.local_planes[isite] = OrderedDict()
                    self.detailed_voronoi.separations[isite] = {}
                se.init_neighbors_sets(isite=isite, additional_conditions=additional_conditions, valences=valences)

                to_add_from_hints = []
                nb_sets_info = {}

                for cn, nb_sets in se.neighbors_sets[isite].items():
                    if cn not in all_cns:
                        continue
                    for inb_set, nb_set in enumerate(nb_sets):
                        logging.debug('    ... getting environments for nb_set ({:d}, {:d})'.format(cn, inb_set))
                        tnbset1 = time.process_time()
                        ce = self.update_nb_set_environments(se=se, isite=isite, cn=cn, inb_set=inb_set, nb_set=nb_set,
                                                             recompute=do_recompute, optimization=optimization)
                        tnbset2 = time.process_time()
                        if cn not in nb_sets_info:
                            nb_sets_info[cn] = {}
                        nb_sets_info[cn][inb_set] = {'time': tnbset2 - tnbset1}
                        if get_from_hints:
                            for cg_symbol, cg_dict in ce:
                                cg = self.allcg[cg_symbol]
                                # Get possibly missing neighbors sets
                                if cg.neighbors_sets_hints is None:
                                    continue
                                logging.debug('       ... getting hints from cg with mp_symbol "{}" ...'.format(cg_symbol))
                                hints_info = {'csm': cg_dict['symmetry_measure'],
                                              'nb_set': nb_set,
                                              'permutation': cg_dict['permutation']}
                                for nb_sets_hints in cg.neighbors_sets_hints:
                                    suggested_nb_set_voronoi_indices = nb_sets_hints.hints(hints_info)
                                    for inew, new_nb_set_voronoi_indices in enumerate(suggested_nb_set_voronoi_indices):
                                        logging.debug('           hint # {:d}'.format(inew))
                                        new_nb_set = se.NeighborsSet(structure=se.structure, isite=isite,
                                                                     detailed_voronoi=se.voronoi,
                                                                     site_voronoi_indices=new_nb_set_voronoi_indices,
                                                                     sources={'origin': 'nb_set_hints',
                                                                              'hints_type': nb_sets_hints.hints_type,
                                                                              'suggestion_index': inew,
                                                                              'cn_map_source': [cn, inb_set],
                                                                              'cg_source_symbol': cg_symbol})
                                        cn_new_nb_set = len(new_nb_set)
                                        if max_cn is not None and cn_new_nb_set > max_cn:
                                            continue
                                        if min_cn is not None and cn_new_nb_set < min_cn:
                                            continue
                                        if new_nb_set in [ta['new_nb_set'] for ta in to_add_from_hints]:
                                            has_nb_set = True
                                        elif cn_new_nb_set not in se.neighbors_sets[isite]:
                                            has_nb_set = False
                                        else:
                                            has_nb_set = new_nb_set in se.neighbors_sets[isite][cn_new_nb_set]
                                        if not has_nb_set:
                                            to_add_from_hints.append({'isite': isite,
                                                                      'new_nb_set': new_nb_set,
                                                                      'cn_new_nb_set': cn_new_nb_set})
                                            logging.debug('              => to be computed')
                                        else:
                                            logging.debug('              => already present')
                logging.debug('    ... getting environments for nb_sets added from hints')
                for missing_nb_set_to_add in to_add_from_hints:
                    se.add_neighbors_set(isite=isite, nb_set=missing_nb_set_to_add['new_nb_set'])
                for missing_nb_set_to_add in to_add_from_hints:
                    isite_new_nb_set = missing_nb_set_to_add['isite']
                    cn_new_nb_set = missing_nb_set_to_add['cn_new_nb_set']
                    new_nb_set = missing_nb_set_to_add['new_nb_set']
                    inew_nb_set = se.neighbors_sets[isite_new_nb_set][cn_new_nb_set].index(new_nb_set)
                    logging.debug('    ... getting environments for nb_set ({:d}, {:d}) - '
                                  'from hints'.format(cn_new_nb_set, inew_nb_set))
                    tnbset1 = time.process_time()
                    self.update_nb_set_environments(se=se,
                                                    isite=isite_new_nb_set,
                                                    cn=cn_new_nb_set,
                                                    inb_set=inew_nb_set,
                                                    nb_set=new_nb_set,
                                                    optimization=optimization)
                    tnbset2 = time.process_time()
                    if cn not in nb_sets_info:
                        nb_sets_info[cn] = {}
                    nb_sets_info[cn][inew_nb_set] = {'time': tnbset2 - tnbset1}
                t2 = time.process_time()
                se.update_site_info(isite=isite, info_dict={'time': t2 - t1, 'nb_sets_info': nb_sets_info})
                if timelimit is not None:
                    time_elapsed = t2 - time_init
                    time_left = timelimit - time_elapsed
                    if time_left < 2.0 * max_time_one_site:
                        breakit = True
                max_time_one_site = max(max_time_one_site, t2 - t1)
                logging.debug('    ... computed in {:.2f} seconds'.format(t2 - t1))
            time_end = time.process_time()
            logging.debug('    ... compute_structure_environments ended in {:.2f} seconds'.format(time_end - time_init))
            return se

        def update_nb_set_environments(self, se, isite, cn, inb_set, nb_set, recompute=False, optimization=None):
            """
            :param se:
            :param isite:
            :param cn:
            :param inb_set:
            :param nb_set:
            :param recompute:
            :param optimization:
            :return:
            """
            ce = se.get_coordination_environments(isite=isite, cn=cn, nb_set=nb_set)
            if ce is not None and not recompute:
                return ce
            ce = ChemicalEnvironments()
            if optimization == 2:
                neighb_coords = nb_set.neighb_coordsOpt
            else:
                neighb_coords = nb_set.neighb_coords
            self.setup_local_geometry(isite, coords=neighb_coords, optimization=optimization)
            if optimization > 0:
                logging.debug('Getting StructureEnvironments with optimized algorithm')
                nb_set.local_planes = OrderedDict()
                nb_set.separations = {}
                cncgsm = self.get_coordination_symmetry_measures_optim(nb_set=nb_set, optimization=optimization)
            else:
                logging.debug('Getting StructureEnvironments with standard algorithm')
                cncgsm = self.get_coordination_symmetry_measures()
            for cg in cncgsm:
                other_csms = {
                    'csm_wocs_ctwocc': cncgsm[cg]['csm_wocs_ctwocc'],
                    'csm_wocs_ctwcc': cncgsm[cg]['csm_wocs_ctwcc'],
                    'csm_wocs_csc': cncgsm[cg]['csm_wocs_csc'],
                    'csm_wcs_ctwocc': cncgsm[cg]['csm_wcs_ctwocc'],
                    'csm_wcs_ctwcc': cncgsm[cg]['csm_wcs_ctwcc'],
                    'csm_wcs_csc': cncgsm[cg]['csm_wcs_csc'],
                    'rotation_matrix_wocs_ctwocc': cncgsm[cg]['rotation_matrix_wocs_ctwocc'],
                    'rotation_matrix_wocs_ctwcc': cncgsm[cg]['rotation_matrix_wocs_ctwcc'],
                    'rotation_matrix_wocs_csc': cncgsm[cg]['rotation_matrix_wocs_csc'],
                    'rotation_matrix_wcs_ctwocc': cncgsm[cg]['rotation_matrix_wcs_ctwocc'],
                    'rotation_matrix_wcs_ctwcc': cncgsm[cg]['rotation_matrix_wcs_ctwcc'],
                    'rotation_matrix_wcs_csc': cncgsm[cg]['rotation_matrix_wcs_csc'],
                    'scaling_factor_wocs_ctwocc': cncgsm[cg]['scaling_factor_wocs_ctwocc'],
                    'scaling_factor_wocs_ctwcc': cncgsm[cg]['scaling_factor_wocs_ctwcc'],
                    'scaling_factor_wocs_csc': cncgsm[cg]['scaling_factor_wocs_csc'],
                    'scaling_factor_wcs_ctwocc': cncgsm[cg]['scaling_factor_wcs_ctwocc'],
                    'scaling_factor_wcs_ctwcc': cncgsm[cg]['scaling_factor_wcs_ctwcc'],
                    'scaling_factor_wcs_csc': cncgsm[cg]['scaling_factor_wcs_csc'],
                    'translation_vector_wocs_ctwocc': cncgsm[cg]['translation_vector_wocs_ctwocc'],
                    'translation_vector_wocs_ctwcc': cncgsm[cg]['translation_vector_wocs_ctwcc'],
                    'translation_vector_wocs_csc': cncgsm[cg]['translation_vector_wocs_csc'],
                    'translation_vector_wcs_ctwocc': cncgsm[cg]['translation_vector_wcs_ctwocc'],
                    'translation_vector_wcs_ctwcc': cncgsm[cg]['translation_vector_wcs_ctwcc'],
                    'translation_vector_wcs_csc': cncgsm[cg]['translation_vector_wcs_csc']
                }
                ce.add_coord_geom(cg, cncgsm[cg]['csm'],
                                  algo=cncgsm[cg]['algo'],
                                  permutation=cncgsm[cg]['indices'],
                                  local2perfect_map=cncgsm[cg][
                                      'local2perfect_map'],
                                  perfect2local_map=cncgsm[cg][
                                      'perfect2local_map'],
                                  detailed_voronoi_index={'cn': cn,
                                                          'index': inb_set},
                                  other_symmetry_measures=other_csms,
                                  rotation_matrix=cncgsm[cg]['rotation_matrix'],
                                  scaling_factor=cncgsm[cg]['scaling_factor']
                                  )
            se.update_coordination_environments(isite=isite, cn=cn, nb_set=nb_set, ce=ce)
            return ce

        def setup_local_geometry(self, isite, coords, optimization=None):
            """
            Sets up the AbstractGeometry for the local geometry of site with index isite.
            :param isite: Index of the site for which the local geometry has to be set up
            :param coords: The coordinates of the (local) neighbors
            """
            self.local_geometry = AbstractGeometry(
                central_site=self.structure.cart_coords[isite],
                bare_coords=coords,
                centering_type=self.centering_type,
                include_central_site_in_centroid=self.include_central_site_in_centroid,
                optimization=optimization)

        def setup_test_perfect_environment(self, symbol, randomness=False,
                                           max_random_dist=0.1,
                                           symbol_type='mp_symbol',
                                           indices='RANDOM',
                                           random_translation='NONE',
                                           random_rotation='NONE',
                                           random_scale='NONE',
                                           points=None):
            """
            :param symbol:
            :param randomness:
            :param max_random_dist:
            :param symbol_type:
            :param indices:
            :param random_translation:
            :param random_rotation:
            :param random_scale:
            :param points:
            :return:
            """
            if symbol_type == 'IUPAC':
                cg = self.allcg.get_geometry_from_IUPAC_symbol(symbol)
            elif symbol_type == 'MP' or symbol_type == 'mp_symbol':
                cg = self.allcg.get_geometry_from_mp_symbol(symbol)
            elif symbol_type == 'CoordinationGeometry':
                cg = symbol
            else:
                raise ValueError('Wrong mp_symbol to setup coordination geometry')
            neighb_coords = []
            if points is not None:
                mypoints = points
            else:
                mypoints = cg.points
            if randomness:
                rv = np.random.random_sample(3)
                while norm(rv) > 1.0:
                    rv = np.random.random_sample(3)
                coords = [np.zeros(3, np.float) + max_random_dist * rv]
                for pp in mypoints:
                    rv = np.random.random_sample(3)
                    while norm(rv) > 1.0:
                        rv = np.random.random_sample(3)
                    neighb_coords.append(np.array(pp) + max_random_dist * rv)
            else:
                coords = [np.zeros(3, np.float)]
                for pp in mypoints:
                    neighb_coords.append(np.array(pp))
            if indices == 'RANDOM':
                shuffle(neighb_coords)
            elif indices == 'ORDERED':
                pass
            else:
                neighb_coords = [neighb_coords[ii] for ii in indices]

            # Scaling the test environment
            if random_scale == 'RANDOM':
                scale = 0.1 * np.random.random_sample() + 0.95
            elif random_scale == 'NONE':
                scale = 1.0
            else:
                scale = random_scale
            coords = [scale * cc for cc in coords]
            neighb_coords = [scale * cc for cc in neighb_coords]

            # Rotating the test environment
            if random_rotation == 'RANDOM':
                uu = np.random.random_sample(3) + 0.1
                uu = uu / norm(uu)
                theta = np.pi * np.random.random_sample()
                cc = np.cos(theta)
                ss = np.sin(theta)
                ux = uu[0]
                uy = uu[1]
                uz = uu[2]
                RR = [[ux * ux + (1.0 - ux * ux) * cc, ux * uy * (1.0 - cc) - uz * ss, ux * uz * (1.0 - cc) + uy * ss],
                      [ux * uy * (1.0 - cc) + uz * ss, uy * uy + (1.0 - uy * uy) * cc, uy * uz * (1.0 - cc) - ux * ss],
                      [ux * uz * (1.0 - cc) - uy * ss, uy * uz * (1.0 - cc) + ux * ss, uz * uz + (1.0 - uz * uz) * cc]]
            elif random_rotation == 'NONE':
                RR = [[1.0, 0.0, 0.0],
                      [0.0, 1.0, 0.0],
                      [0.0, 0.0, 1.0]]
            else:
                RR = random_rotation
            newcoords = []
            for cc in coords:
                newcc = np.dot(RR, cc).T
                newcoords.append(newcc.ravel())
            coords = newcoords
            newcoords = []
            for cc in neighb_coords:
                newcc = np.dot(RR, cc.T)
                newcoords.append(newcc.ravel())
            neighb_coords = newcoords

            # Translating the test environment
            if random_translation == 'RANDOM':
                translation = 10.0 * (2.0 * np.random.random_sample(3) - 1.0)
            elif random_translation == 'NONE':
                translation = np.zeros(3, np.float)
            else:
                translation = random_translation
            coords = [cc + translation for cc in coords]
            neighb_coords = [cc + translation for cc in neighb_coords]

            coords.extend(neighb_coords)
            myspecies = ["O"] * (len(coords))
            myspecies[0] = "Cu"

            amin = np.min([cc[0] for cc in coords])
            amax = np.max([cc[0] for cc in coords])
            bmin = np.min([cc[1] for cc in coords])
            bmax = np.max([cc[1] for cc in coords])
            cmin = np.min([cc[2] for cc in coords])
            cmax = np.max([cc[2] for cc in coords])

            factor = 5.0
            aa = factor * max([amax - amin, bmax - bmin, cmax - cmin])

            lattice = Lattice.cubic(a=aa)
            structure = Structure(lattice=lattice, species=myspecies, coords=coords,
                                  to_unit_cell=False, coords_are_cartesian=True)

            self.setup_structure(structure=structure)
            self.setup_local_geometry(isite=0, coords=neighb_coords)
            self.perfect_geometry = AbstractGeometry.from_cg(cg=cg)

        def setup_random_structure(self, coordination):
            """
            Sets up a purely random structure with a given coordination.
            :param coordination: coordination number for the random structure
            """
            aa = 0.4
            bb = -0.2
            coords = list()
            for ii in range(coordination + 1):
                coords.append(aa * np.random.random_sample(3, ) + bb)
            self.set_structure(
                lattice=np.array([[10, 0, 0], [0, 10, 0], [0, 0, 10]], np.float),
                species=["Si"] * (coordination + 1),
                coords=coords,
                coords_are_cartesian=False)
            self.setup_random_indices_local_geometry(coordination)

        def setup_random_indices_local_geometry(self, coordination):
            """
            Sets up random indices for the local geometry, for testing purposes
            :param coordination: coordination of the local geometry
            """
            self.icentral_site = 0
            self.indices = list(range(1, coordination + 1))
            np.random.shuffle(self.indices)

        def setup_ordered_indices_local_geometry(self, coordination):
            """
            Sets up ordered indices for the local geometry, for testing purposes
            :param coordination: coordination of the local geometry
            """
            self.icentral_site = 0
            self.indices = list(range(1, coordination + 1))

        def setup_explicit_indices_local_geometry(self, explicit_indices):
            """
            Sets up explicit indices for the local geometry, for testing purposes
            :param explicit_indices: explicit indices for the neighbors (set of numbers
            from 0 to CN-1 in a given order)
            """
            self.icentral_site = 0
            self.indices = [ii + 1 for ii in explicit_indices]

        def get_coordination_symmetry_measures(self, only_minimum=True,
                                               all_csms=True, optimization=None):
            """
            Returns the continuous symmetry measures of the current local geometry in a dictionary.
            :return: the continuous symmetry measures of the current local geometry in a dictionary.
            """
            test_geometries = self.allcg.get_implemented_geometries(
                len(self.local_geometry.coords))
            if len(self.local_geometry.coords) == 1:
                if len(test_geometries) == 0:
                    return {}
                result_dict = {'S:1': {'csm': 0.0, 'indices': [0], 'algo': 'EXPLICIT',
                                       'local2perfect_map': {0: 0}, 'perfect2local_map': {0: 0},
                                       'scaling_factor': None, 'rotation_matrix': None, 'translation_vector': None}}
                if all_csms:
                    for csmtype in ['wocs_ctwocc', 'wocs_ctwcc', 'wocs_csc', 'wcs_ctwocc', 'wcs_ctwcc', 'wcs_csc']:
                        result_dict['S:1']['csm_{}'.format(csmtype)] = 0.0
                        result_dict['S:1']['scaling_factor_{}'.format(csmtype)] = None
                        result_dict['S:1']['rotation_matrix_{}'.format(csmtype)] = None
                        result_dict['S:1']['translation_vector_{}'.format(csmtype)] = None
                return result_dict
            result_dict = {}
            for geometry in test_geometries:
                self.perfect_geometry = AbstractGeometry.from_cg(
                    cg=geometry,
                    centering_type=self.centering_type,
                    include_central_site_in_centroid=self.include_central_site_in_centroid)
                points_perfect = self.perfect_geometry.points_wcs_ctwcc()
                cgsm = self.coordination_geometry_symmetry_measures(geometry,
                                                                    points_perfect=points_perfect,
                                                                    optimization=optimization)
                result, permutations, algos, local2perfect_maps, perfect2local_maps = cgsm
                if only_minimum:
                    if len(result) > 0:
                        imin = np.argmin([rr['symmetry_measure'] for rr in result])
                        if geometry.algorithms is not None:
                            algo = algos[imin]
                        else:
                            algo = algos
                        result_dict[geometry.mp_symbol] = {'csm': result[imin]['symmetry_measure'],
                                                           'indices': permutations[
                                                               imin],
                                                           'algo': algo,
                                                           'local2perfect_map':
                                                               local2perfect_maps[
                                                                   imin],
                                                           'perfect2local_map':
                                                               perfect2local_maps[
                                                                   imin],
                                                           'scaling_factor': 1.0 / result[imin]['scaling_factor'],
                                                           'rotation_matrix':
                                                               np.linalg.inv(result[imin]['rotation_matrix']),
                                                           'translation_vector': result[imin]['translation_vector']}
                        if all_csms:
                            self._update_results_all_csms(result_dict, permutations, imin, geometry)
                else:
                    result_dict[geometry.mp_symbol] = {'csm': result,
                                                       'indices': permutations,
                                                       'algo': algos,
                                                       'local2perfect_map': local2perfect_maps,
                                                       'perfect2local_map': perfect2local_maps}
            return result_dict

        def _update_results_all_csms(self, result_dict, permutations, imin, geometry):
            permutation = permutations[imin]
            # Without central site, centered on the centroid (centroid does not include the central site)
            # result_dict[geometry.mp_symbol]['csm_wocs_ctwocc'] = \
            # result[imin]
            pdist = self.local_geometry.points_wocs_ctwocc(
                permutation=permutation)
            pperf = self.perfect_geometry.points_wocs_ctwocc()
            sm_info = symmetry_measure(points_distorted=pdist,
                                       points_perfect=pperf)
            result_dict[geometry.mp_symbol]['csm_wocs_ctwocc'] = sm_info['symmetry_measure']
            result_dict[geometry.mp_symbol]['rotation_matrix_wocs_ctwocc'] = \
                np.linalg.inv(sm_info['rotation_matrix'])
            result_dict[geometry.mp_symbol]['scaling_factor_wocs_ctwocc'] = 1.0 / sm_info['scaling_factor']
            result_dict[geometry.mp_symbol]['translation_vector_wocs_ctwocc'] = \
                self.local_geometry.centroid_without_centre
            # Without central site, centered on the centroid (centroid includes the central site)
            pdist = self.local_geometry.points_wocs_ctwcc(
                permutation=permutation)
            pperf = self.perfect_geometry.points_wocs_ctwcc()
            sm_info = symmetry_measure(points_distorted=pdist,
                                       points_perfect=pperf)
            result_dict[geometry.mp_symbol]['csm_wocs_ctwcc'] = sm_info['symmetry_measure']
            result_dict[geometry.mp_symbol]['rotation_matrix_wocs_ctwcc'] = \
                np.linalg.inv(sm_info['rotation_matrix'])
            result_dict[geometry.mp_symbol]['scaling_factor_wocs_ctwcc'] = 1.0 / sm_info['scaling_factor']
            result_dict[geometry.mp_symbol]['translation_vector_wocs_ctwcc'] = \
                self.local_geometry.centroid_with_centre
            # Without central site, centered on the central site
            pdist = self.local_geometry.points_wocs_csc(
                permutation=permutation)
            pperf = self.perfect_geometry.points_wocs_csc()
            sm_info = symmetry_measure(points_distorted=pdist,
                                       points_perfect=pperf)
            result_dict[geometry.mp_symbol]['csm_wocs_csc'] = sm_info['symmetry_measure']
            result_dict[geometry.mp_symbol]['rotation_matrix_wocs_csc'] = \
                np.linalg.inv(sm_info['rotation_matrix'])
            result_dict[geometry.mp_symbol]['scaling_factor_wocs_csc'] = 1.0 / sm_info['scaling_factor']
            result_dict[geometry.mp_symbol]['translation_vector_wocs_csc'] = \
                self.local_geometry.bare_centre
            # With central site, centered on the centroid (centroid does not include the central site)
            pdist = self.local_geometry.points_wcs_ctwocc(
                permutation=permutation)
            pperf = self.perfect_geometry.points_wcs_ctwocc()
            sm_info = symmetry_measure(points_distorted=pdist,
                                       points_perfect=pperf)
            result_dict[geometry.mp_symbol]['csm_wcs_ctwocc'] = sm_info['symmetry_measure']
            result_dict[geometry.mp_symbol]['rotation_matrix_wcs_ctwocc'] = \
                np.linalg.inv(sm_info['rotation_matrix'])
            result_dict[geometry.mp_symbol]['scaling_factor_wcs_ctwocc'] = 1.0 / sm_info['scaling_factor']
            result_dict[geometry.mp_symbol]['translation_vector_wcs_ctwocc'] = \
                self.local_geometry.centroid_without_centre
            # With central site, centered on the centroid (centroid includes the central site)
            pdist = self.local_geometry.points_wcs_ctwcc(
                permutation=permutation)
            pperf = self.perfect_geometry.points_wcs_ctwcc()
            sm_info = symmetry_measure(points_distorted=pdist,
                                       points_perfect=pperf)
            result_dict[geometry.mp_symbol]['csm_wcs_ctwcc'] = sm_info['symmetry_measure']
            result_dict[geometry.mp_symbol]['rotation_matrix_wcs_ctwcc'] = \
                np.linalg.inv(sm_info['rotation_matrix'])
            result_dict[geometry.mp_symbol]['scaling_factor_wcs_ctwcc'] = 1.0 / sm_info['scaling_factor']
            result_dict[geometry.mp_symbol]['translation_vector_wcs_ctwcc'] = \
                self.local_geometry.centroid_with_centre
            # With central site, centered on the central site
            pdist = self.local_geometry.points_wcs_csc(
                permutation=permutation)
            pperf = self.perfect_geometry.points_wcs_csc()
            sm_info = symmetry_measure(points_distorted=pdist,
                                       points_perfect=pperf)
            result_dict[geometry.mp_symbol]['csm_wcs_csc'] = sm_info['symmetry_measure']
            result_dict[geometry.mp_symbol]['rotation_matrix_wcs_csc'] = \
                np.linalg.inv(sm_info['rotation_matrix'])
            result_dict[geometry.mp_symbol]['scaling_factor_wcs_csc'] = 1.0 / sm_info['scaling_factor']
            result_dict[geometry.mp_symbol]['translation_vector_wcs_csc'] = \
                self.local_geometry.bare_centre

        def get_coordination_symmetry_measures_optim(self, only_minimum=True,
                                                     all_csms=True, nb_set=None, optimization=None):
            """
            Returns the continuous symmetry measures of the current local geometry in a dictionary.
            :return: the continuous symmetry measures of the current local geometry in a dictionary.
            """
            cn = len(self.local_geometry.coords)
            test_geometries = self.allcg.get_implemented_geometries(cn)
            if all([cg.algorithms[0].algorithm_type == EXPLICIT_PERMUTATIONS for cg in test_geometries]):
                return self.get_coordination_symmetry_measures(only_minimum=only_minimum, all_csms=all_csms,
                                                               optimization=optimization)
            if not all([all([algo.algorithm_type == SEPARATION_PLANE
                             for algo in cg.algorithms]) for cg in test_geometries]):
                raise ValueError('All algorithms should be EXPLICIT_PERMUTATIONS or SEPARATION_PLANE')

            result_dict = {}
            for geometry in test_geometries:
                logging.log(level=5, msg='Getting Continuous Symmetry Measure with Separation Plane '
                                         'algorithm for geometry "{}"'.format(geometry.ce_symbol))
                self.perfect_geometry = AbstractGeometry.from_cg(
                    cg=geometry,
                    centering_type=self.centering_type,
                    include_central_site_in_centroid=self.include_central_site_in_centroid)
                points_perfect = self.perfect_geometry.points_wcs_ctwcc()
                cgsm = self.coordination_geometry_symmetry_measures_sepplane_optim(geometry,
                                                                                   points_perfect=points_perfect,
                                                                                   nb_set=nb_set,
                                                                                   optimization=optimization)
                result, permutations, algos, local2perfect_maps, perfect2local_maps = cgsm
                if only_minimum:
                    if len(result) > 0:
                        imin = np.argmin([rr['symmetry_measure'] for rr in result])
                        if geometry.algorithms is not None:
                            algo = algos[imin]
                        else:
                            algo = algos
                        result_dict[geometry.mp_symbol] = {'csm': result[imin]['symmetry_measure'],
                                                           'indices': permutations[
                                                               imin],
                                                           'algo': algo,
                                                           'local2perfect_map':
                                                               local2perfect_maps[
                                                                   imin],
                                                           'perfect2local_map':
                                                               perfect2local_maps[
                                                                   imin],
                                                           'scaling_factor': 1.0 / result[imin]['scaling_factor'],
                                                           'rotation_matrix':
                                                               np.linalg.inv(result[imin]['rotation_matrix']),
                                                           'translation_vector': result[imin]['translation_vector']}
                        if all_csms:
                            self._update_results_all_csms(result_dict, permutations, imin, geometry)
            return result_dict

        def coordination_geometry_symmetry_measures(self, coordination_geometry,
                                                    tested_permutations=False,
                                                    points_perfect=None,
                                                    optimization=None):
            """
            Returns the symmetry measures of a given coordination_geometry for a set of permutations depending on
            the permutation setup. Depending on the parameters of the LocalGeometryFinder and on the coordination
             geometry, different methods are called.
            :param coordination_geometry: Coordination geometry for which the symmetry measures are looked for
            :return: the symmetry measures of a given coordination_geometry for a set of permutations
            :raise: NotImplementedError if the permutation_setup does not exists
            """
            if tested_permutations:
                tested_permutations = set()
            if self.permutations_safe_override:
                raise ValueError('No permutations safe override anymore')
            csms = []
            permutations = []
            algos = []
            local2perfect_maps = []
            perfect2local_maps = []
            for algo in coordination_geometry.algorithms:
                if algo.algorithm_type == EXPLICIT_PERMUTATIONS:
                    return self.coordination_geometry_symmetry_measures_standard(
                        coordination_geometry, algo,
                        points_perfect=points_perfect,
                        optimization=optimization)
                if algo.algorithm_type == SEPARATION_PLANE:
                    cgsm = self.coordination_geometry_symmetry_measures_separation_plane(
                        coordination_geometry,
                        algo,
                        tested_permutations=tested_permutations,
                        points_perfect=points_perfect)
                    csm, perm, algo, local2perfect_map, perfect2local_map = cgsm

                    csms.extend(csm)
                    permutations.extend(perm)
                    algos.extend(algo)
                    local2perfect_maps.extend(local2perfect_map)
                    perfect2local_maps.extend(perfect2local_map)
            return csms, permutations, algos, local2perfect_maps, perfect2local_maps

        def coordination_geometry_symmetry_measures_sepplane_optim(self, coordination_geometry,
                                                                   points_perfect=None,
                                                                   nb_set=None, optimization=None):
            """
            Returns the symmetry measures of a given coordination_geometry for a set of permutations depending on
            the permutation setup. Depending on the parameters of the LocalGeometryFinder and on the coordination
             geometry, different methods are called.
            :param coordination_geometry: Coordination geometry for which the symmetry measures are looked for
            :return: the symmetry measures of a given coordination_geometry for a set of permutations
            :raise: NotImplementedError if the permutation_setup does not exists
            """
            csms = []
            permutations = []
            algos = []
            local2perfect_maps = []
            perfect2local_maps = []
            for algo in coordination_geometry.algorithms:
                if algo.algorithm_type == SEPARATION_PLANE:
                    cgsm = self.coordination_geometry_symmetry_measures_separation_plane_optim(
                        coordination_geometry,
                        algo,
                        points_perfect=points_perfect,
                        nb_set=nb_set,
                        optimization=optimization)
                    csm, perm, algo, local2perfect_map, perfect2local_map = cgsm

                    csms.extend(csm)
                    permutations.extend(perm)
                    algos.extend(algo)
                    local2perfect_maps.extend(local2perfect_map)
                    perfect2local_maps.extend(perfect2local_map)
            return csms, permutations, algos, local2perfect_maps, perfect2local_maps

        def coordination_geometry_symmetry_measures_standard(self,
                                                             coordination_geometry,
                                                             algo,
                                                             points_perfect=None,
                                                             optimization=None):
            """
            Returns the symmetry measures for a set of permutations (whose setup depends on the coordination geometry)
            for the coordination geometry "coordination_geometry". Standard implementation looking for the symmetry
            measures of each permutation

            :param coordination_geometry: The coordination geometry to be investigated
            :return: The symmetry measures for the given coordination geometry for each permutation investigated
            """
            # permutations_symmetry_measures = np.zeros(len(algo.permutations),
            #                                           np.float)
            if optimization == 2:
                permutations_symmetry_measures = [None] * len(algo.permutations)
                permutations = list()
                algos = list()
                local2perfect_maps = list()
                perfect2local_maps = list()
                for iperm, perm in enumerate(algo.permutations):

                    local2perfect_map = {}
                    perfect2local_map = {}
                    permutations.append(perm)
                    for iperfect, ii in enumerate(perm):
                        perfect2local_map[iperfect] = ii
                        local2perfect_map[ii] = iperfect
                    local2perfect_maps.append(local2perfect_map)
                    perfect2local_maps.append(perfect2local_map)

                    points_distorted = self.local_geometry.points_wcs_ctwcc(
                        permutation=perm)

                    sm_info = symmetry_measure(points_distorted=points_distorted,
                                               points_perfect=points_perfect)
                    sm_info['translation_vector'] = self.local_geometry.centroid_with_centre

                    permutations_symmetry_measures[iperm] = sm_info
                    algos.append(str(algo))
                return permutations_symmetry_measures, permutations, algos, local2perfect_maps, perfect2local_maps
            else:
                permutations_symmetry_measures = [None] * len(algo.permutations)
                permutations = list()
                algos = list()
                local2perfect_maps = list()
                perfect2local_maps = list()
                for iperm, perm in enumerate(algo.permutations):

                    local2perfect_map = {}
                    perfect2local_map = {}
                    permutations.append(perm)
                    for iperfect, ii in enumerate(perm):
                        perfect2local_map[iperfect] = ii
                        local2perfect_map[ii] = iperfect
                    local2perfect_maps.append(local2perfect_map)
                    perfect2local_maps.append(perfect2local_map)

                    points_distorted = self.local_geometry.points_wcs_ctwcc(
                        permutation=perm)

                    sm_info = symmetry_measure(points_distorted=points_distorted,
                                               points_perfect=points_perfect)
                    sm_info['translation_vector'] = self.local_geometry.centroid_with_centre

                    permutations_symmetry_measures[iperm] = sm_info
                    algos.append(str(algo))
                return permutations_symmetry_measures, permutations, algos, local2perfect_maps, perfect2local_maps

        def coordination_geometry_symmetry_measures_separation_plane(self,
                                                                     coordination_geometry,
                                                                     separation_plane_algo,
                                                                     testing=False,
                                                                     tested_permutations=False,
                                                                     points_perfect=None):

            """
            Returns the symmetry measures of the given coordination geometry "coordination_geometry" using separation
            facets to reduce the complexity of the system. Caller to the refined 2POINTS, 3POINTS and other ...
            :param coordination_geometry: The coordination geometry to be investigated
            :return: The symmetry measures for the given coordination geometry for each plane and permutation investigated
            """
            permutations = list()
            permutations_symmetry_measures = list()
            plane_separations = list()
            algos = list()
            perfect2local_maps = list()
            local2perfect_maps = list()
            if testing:
                separation_permutations = list()
            nplanes = 0
            for npoints in range(separation_plane_algo.minimum_number_of_points,
                                 min(separation_plane_algo.maximum_number_of_points,
                                     4) + 1):
                for points_combination in itertools.combinations(
                        self.local_geometry.coords, npoints):
                    if npoints == 2:
                        if collinear(points_combination[0], points_combination[1],
                                     self.local_geometry.central_site,
                                     tolerance=0.25):
                            continue
                        plane = Plane.from_3points(points_combination[0],
                                                   points_combination[1],
                                                   self.local_geometry.central_site)
                    elif npoints == 3:
                        if collinear(points_combination[0], points_combination[1],
                                     points_combination[2], tolerance=0.25):
                            continue
                        plane = Plane.from_3points(points_combination[0],
                                                   points_combination[1],
                                                   points_combination[2])
                    elif npoints > 3:
                        plane = Plane.from_npoints(points_combination,
                                                   best_fit='least_square_distance')
                    else:
                        raise ValueError(
                            'Wrong number of points to initialize separation plane')
                    cgsm = self._cg_csm_separation_plane(
                        coordination_geometry=coordination_geometry,
                        sepplane=separation_plane_algo,
                        local_plane=plane,
                        plane_separations=plane_separations,
                        dist_tolerances=DIST_TOLERANCES,
                        testing=testing,
                        tested_permutations=tested_permutations,
                        points_perfect=points_perfect)
                    csm, perm, algo = cgsm[0], cgsm[1], cgsm[2]

                    if csm is not None:
                        permutations_symmetry_measures.extend(csm)
                        permutations.extend(perm)
                        for thisperm in perm:
                            p2l = {}
                            l2p = {}
                            for i_p, pp in enumerate(thisperm):
                                p2l[i_p] = pp
                                l2p[pp] = i_p
                            perfect2local_maps.append(p2l)
                            local2perfect_maps.append(l2p)
                        algos.extend(algo)
                        if testing:
                            separation_permutations.extend(cgsm[3])
                        nplanes += 1
                if nplanes > 0:
                    break
            if nplanes == 0:
                return self.coordination_geometry_symmetry_measures_fallback_random(
                    coordination_geometry,
                    points_perfect=points_perfect)
            if testing:
                return permutations_symmetry_measures, permutations, separation_permutations
            return permutations_symmetry_measures, permutations, algos, local2perfect_maps, perfect2local_maps

        def coordination_geometry_symmetry_measures_separation_plane_optim(self,
                                                                           coordination_geometry,
                                                                           separation_plane_algo,
                                                                           points_perfect=None,
                                                                           nb_set=None,
                                                                           optimization=None):
            """
            Returns the symmetry measures of the given coordination geometry "coordination_geometry" using separation
            facets to reduce the complexity of the system. Caller to the refined 2POINTS, 3POINTS and other ...
            Args:
                coordination_geometry: The coordination geometry to be investigated.
                separation_plane_algo: Separation Plane algorithm used.
                points_perfect: Points corresponding to the perfect geometry.
                nb_set: Neighbor set for this set of points. (used to store already computed separation planes)
                optimization: Optimization level (1 or 2).

            Returns:
                tuple: Continuous symmetry measures for the given coordination geometry for each plane and permutation
                       investigated, corresponding permutations, corresponding algorithms,
                       corresponding mappings from local to perfect environment and corresponding mappings
                       from perfect to local environment.
            """
            if optimization == 2:
                logging.log(level=5, msg='... using optimization = 2')
                cgcsmoptim = self._cg_csm_separation_plane_optim2
            elif optimization == 1:
                logging.log(level=5, msg='... using optimization = 2')
                cgcsmoptim = self._cg_csm_separation_plane_optim1
            else:
                raise ValueError('Optimization should be 1 or 2')
            cn = len(self.local_geometry.coords)

            permutations = list()
            permutations_symmetry_measures = list()
            algos = list()
            perfect2local_maps = list()
            local2perfect_maps = list()

            if separation_plane_algo.separation in nb_set.separations:
                for sep_indices, (local_plane, npsep) in nb_set.separations[separation_plane_algo.separation].items():
                    cgsm = cgcsmoptim(coordination_geometry=coordination_geometry,
                                      sepplane=separation_plane_algo,
                                      local_plane=local_plane,
                                      points_perfect=points_perfect,
                                      separation_indices=npsep)
                    csm, perm, algo, _ = cgsm[0], cgsm[1], cgsm[2], cgsm[3]
                    permutations_symmetry_measures.extend(csm)
                    permutations.extend(perm)
                    for thisperm in perm:
                        p2l = {}
                        l2p = {}
                        for i_p, pp in enumerate(thisperm):
                            p2l[i_p] = pp
                            l2p[pp] = i_p
                        perfect2local_maps.append(p2l)
                        local2perfect_maps.append(l2p)
                    algos.extend(algo)

            # Get the local planes and separations up to 3 points
            for npoints in range(self.allcg.minpoints[cn], min(self.allcg.maxpoints[cn], 3) + 1):
                for ipoints_combination in itertools.combinations(
                        range(self.local_geometry.cn), npoints):
                    if ipoints_combination in nb_set.local_planes:
                        continue
                    # Set up new plane
                    nb_set.local_planes[ipoints_combination] = None
                    points_combination = [self.local_geometry.coords[ip] for ip in ipoints_combination]
                    if npoints == 2:
                        if collinear(points_combination[0], points_combination[1],
                                     self.local_geometry.central_site,
                                     tolerance=0.25):
                            continue
                        plane = Plane.from_3points(points_combination[0],
                                                   points_combination[1],
                                                   self.local_geometry.central_site)
                    elif npoints == 3:
                        if collinear(points_combination[0], points_combination[1],
                                     points_combination[2], tolerance=0.25):
                            continue
                        plane = Plane.from_3points(points_combination[0],
                                                   points_combination[1],
                                                   points_combination[2])
                    elif npoints > 3:
                        plane = Plane.from_npoints(points_combination,
                                                   best_fit='least_square_distance')
                    else:
                        raise ValueError(
                            'Wrong number of points to initialize separation plane')
                    # Takes a lot of time and happens rarely ...
                    # if any([plane.is_same_plane_as(plane2) for comb2, plane2 in nb_set.local_planes.items()
                    #         if plane2 is not None]):
                    #     continue
                    nb_set.local_planes[ipoints_combination] = plane
                    # Get the separations for this plane
                    # TODO: check sensitivity to delta/delta_factor parameter
                    dig = plane.distances_indices_groups(points=self.local_geometry._coords, delta_factor=0.1,
                                                         sign=True)
                    grouped_indices = dig[2]
                    new_seps = []
                    for ng in range(1, len(grouped_indices) + 1):
                        inplane = list(itertools.chain(*grouped_indices[:ng]))
                        if len(inplane) > self.allcg.maxpoints_inplane[cn]:
                            break
                        inplane = [ii[0] for ii in inplane]
                        outplane = list(itertools.chain(*grouped_indices[ng:]))
                        s1 = [ii_sign[0] for ii_sign in outplane if ii_sign[1] < 0]
                        s2 = [ii_sign[0] for ii_sign in outplane if ii_sign[1] > 0]
                        separation = sort_separation_tuple([s1, inplane, s2])
                        sep = tuple([len(gg) for gg in separation])
                        if sep not in self.allcg.separations_cg[cn]:
                            continue
                        if sep not in nb_set.separations:
                            nb_set.separations[sep] = {}
                        mysep = [np.array(ss, dtype=np.int8) for ss in separation]
                        nb_set.separations[sep][separation] = (plane, mysep)
                        if sep == separation_plane_algo.separation:
                            new_seps.append(mysep)

                    for separation_indices in new_seps:
                        cgsm = cgcsmoptim(coordination_geometry=coordination_geometry,
                                          sepplane=separation_plane_algo,
                                          local_plane=plane,
                                          points_perfect=points_perfect,
                                          separation_indices=separation_indices)
                        csm, perm, algo, _ = cgsm[0], cgsm[1], cgsm[2], cgsm[3]
                        permutations_symmetry_measures.extend(csm)
                        permutations.extend(perm)
                        for thisperm in perm:
                            p2l = {}
                            l2p = {}
                            for i_p, pp in enumerate(thisperm):
                                p2l[i_p] = pp
                                l2p[pp] = i_p
                            perfect2local_maps.append(p2l)
                            local2perfect_maps.append(l2p)
                        algos.extend(algo)

            if len(permutations_symmetry_measures) == 0:
                return self.coordination_geometry_symmetry_measures_fallback_random(
                    coordination_geometry,
                    points_perfect=points_perfect)
            return permutations_symmetry_measures, permutations, algos, local2perfect_maps, perfect2local_maps

        def _cg_csm_separation_plane(self, coordination_geometry, sepplane,
                                     local_plane,
                                     plane_separations,
                                     dist_tolerances=DIST_TOLERANCES,
                                     testing=False, tested_permutations=False,
                                     points_perfect=None):
            argref_separation = sepplane.argsorted_ref_separation_perm
            plane_found = False
            for dist_tolerance in dist_tolerances:
                permutations = []
                permutations_symmetry_measures = []
                if testing:
                    separation_permutations = []
                algo = 'NOT_FOUND'
                separation = local_plane.indices_separate(
                    self.local_geometry._coords, dist_tolerance)
                # Do not consider facets leading to the same separation indices
                separation = sort_separation(separation)

                if separation_in_list(separation, plane_separations):
                    continue
                # Do not consider a separation which does not follow the reference separation of the perfect
                # coordination geometry
                if len(separation[1]) != len(sepplane.plane_points):
                    continue
                if len(separation[0]) == len(sepplane.point_groups[0]):
                    this_separation = separation
                    plane_separations.append(this_separation)
                elif len(separation[0]) == len(sepplane.point_groups[1]):
                    this_separation = [list(separation[2]), list(separation[1]),
                                       list(separation[0])]
                    plane_separations.append(this_separation)
                else:
                    continue

                if sepplane.ordered_plane:
                    inp = [pp for ip, pp in enumerate(self.local_geometry._coords)
                           if ip in this_separation[1]]

                    if sepplane.ordered_point_groups[0]:
                        pp_s0 = [pp for ip, pp in
                                 enumerate(self.local_geometry._coords) if
                                 ip in this_separation[0]]
                        ordind_s0 = local_plane.project_and_to2dim_ordered_indices(
                            pp_s0)
                        sep0 = [this_separation[0][ii] for ii in ordind_s0]
                    else:
                        sep0 = list(this_separation[0])
                    if sepplane.ordered_point_groups[1]:
                        pp_s2 = [pp for ip, pp in
                                 enumerate(self.local_geometry._coords) if
                                 ip in this_separation[2]]
                        ordind_s2 = local_plane.project_and_to2dim_ordered_indices(
                            pp_s2)
                        sep2 = [this_separation[2][ii] for ii in ordind_s2]
                    else:
                        sep2 = list(this_separation[2])
                    separation_perm = list(sep0)
                    ordind = local_plane.project_and_to2dim_ordered_indices(inp)
                    separation_perm.extend(
                        [this_separation[1][ii] for ii in ordind])
                    algo = 'SEPARATION_PLANE_2POINTS_ORDERED'
                    separation_perm.extend(sep2)
                else:
                    separation_perm = list(this_separation[0])
                    separation_perm.extend(this_separation[1])
                    algo = 'SEPARATION_PLANE_2POINTS'
                    separation_perm.extend(this_separation[2])
                if self.plane_safe_permutations:
                    sep_perms = sepplane.safe_separation_permutations(
                        ordered_plane=sepplane.ordered_plane,
                        ordered_point_groups=sepplane.ordered_point_groups)
                else:
                    sep_perms = sepplane.permutations

                # plane_found = True

                for i_sep_perm, sep_perm in enumerate(sep_perms):
                    perm1 = [separation_perm[ii] for ii in sep_perm]
                    pp = [perm1[ii] for ii in argref_separation]
                    # Skip permutations that have already been performed
                    if isinstance(tested_permutations, set) and coordination_geometry.equivalent_indices is not None:
                        tuple_ref_perm = coordination_geometry.ref_permutation(pp)
                        if tuple_ref_perm in tested_permutations:
                            continue
                        tested_permutations.add(tuple_ref_perm)

                    permutations.append(pp)
                    if testing:
                        separation_permutations.append(sep_perm)

                    points_distorted = self.local_geometry.points_wcs_ctwcc(
                        permutation=pp)

                    sm_info = symmetry_measure(points_distorted=points_distorted,
                                               points_perfect=points_perfect)
                    sm_info['translation_vector'] = self.local_geometry.centroid_with_centre

                    permutations_symmetry_measures.append(sm_info)
                if plane_found:
                    break
            if len(permutations_symmetry_measures) > 0:
                if testing:
                    return permutations_symmetry_measures, permutations, algo, separation_permutations
                else:
                    return permutations_symmetry_measures, permutations, [
                        sepplane.algorithm_type] * len(permutations)
            else:
                if plane_found:
                    if testing:
                        return permutations_symmetry_measures, permutations, [], []
                    else:
                        return permutations_symmetry_measures, permutations, []
                else:
                    if testing:
                        return None, None, None, None
                    else:
                        return None, None, None

        def _cg_csm_separation_plane_optim1(self, coordination_geometry,
                                            sepplane,
                                            local_plane,
                                            points_perfect=None,
                                            separation_indices=None):
            argref_separation = sepplane.argsorted_ref_separation_perm
            permutations = []
            permutations_symmetry_measures = []
            stop_search = False
            # TODO: do not do that several times ... also keep in memory
            if sepplane.ordered_plane:
                inp = [pp for ip, pp in enumerate(self.local_geometry._coords)
                       if ip in separation_indices[1]]
                if sepplane.ordered_point_groups[0]:
                    pp_s0 = [pp for ip, pp in
                             enumerate(self.local_geometry._coords) if
                             ip in separation_indices[0]]
                    ordind_s0 = local_plane.project_and_to2dim_ordered_indices(
                        pp_s0)
                    sep0 = [separation_indices[0][ii] for ii in ordind_s0]
                else:
                    sep0 = list(separation_indices[0])
                if sepplane.ordered_point_groups[1]:
                    pp_s2 = [pp for ip, pp in
                             enumerate(self.local_geometry._coords) if
                             ip in separation_indices[2]]
                    ordind_s2 = local_plane.project_and_to2dim_ordered_indices(
                        pp_s2)
                    sep2 = [separation_indices[2][ii] for ii in ordind_s2]
                else:
                    sep2 = list(separation_indices[2])
                separation_perm = list(sep0)
                ordind = local_plane.project_and_to2dim_ordered_indices(inp)
                separation_perm.extend(
                    [separation_indices[1][ii] for ii in ordind])
                separation_perm.extend(sep2)
            else:
                separation_perm = list(separation_indices[0])
                separation_perm.extend(separation_indices[1])
                separation_perm.extend(separation_indices[2])

            if self.plane_safe_permutations:
                sep_perms = sepplane.safe_separation_permutations(
                    ordered_plane=sepplane.ordered_plane,
                    ordered_point_groups=sepplane.ordered_point_groups)
            else:
                sep_perms = sepplane.permutations

            for i_sep_perm, sep_perm in enumerate(sep_perms):
                perm1 = [separation_perm[ii] for ii in sep_perm]
                pp = [perm1[ii] for ii in argref_separation]

                permutations.append(pp)

                points_distorted = self.local_geometry.points_wcs_ctwcc(
                    permutation=pp)

                sm_info = symmetry_measure(points_distorted=points_distorted,
                                           points_perfect=points_perfect)

                sm_info['translation_vector'] = self.local_geometry.centroid_with_centre

                permutations_symmetry_measures.append(sm_info)

            if len(permutations_symmetry_measures) > 0:
                return permutations_symmetry_measures, permutations, [sepplane.algorithm_type] * len(
                    permutations), stop_search
            else:
                return [], [], [], stop_search

        def _cg_csm_separation_plane_optim2(self, coordination_geometry,
                                            sepplane,
                                            local_plane,
                                            points_perfect=None,
                                            separation_indices=None):
            argref_separation = sepplane.argsorted_ref_separation_perm
            permutations = []
            permutations_symmetry_measures = []
            stop_search = False
            # TODO: do not do that several times ... also keep in memory
            if sepplane.ordered_plane:
                inp = self.local_geometry.coords.take(separation_indices[1], axis=0)
                if sepplane.ordered_point_groups[0]:
                    pp_s0 = self.local_geometry.coords.take(separation_indices[0], axis=0)
                    ordind_s0 = local_plane.project_and_to2dim_ordered_indices(
                        pp_s0)
                    # sep0 = [separation_indices[0][ii] for ii in ordind_s0]
                    sep0 = separation_indices[0].take(ordind_s0)
                else:
                    # sep0 = list(separation_indices[0])
                    sep0 = separation_indices[0]
                if sepplane.ordered_point_groups[1]:
                    pp_s2 = self.local_geometry.coords.take(separation_indices[2], axis=0)
                    ordind_s2 = local_plane.project_and_to2dim_ordered_indices(
                        pp_s2)
                    # sep2 = [separation_indices[2][ii] for ii in ordind_s2]
                    sep2 = separation_indices[2].take(ordind_s2)
                else:
                    # sep2 = list(separation_indices[2])
                    sep2 = separation_indices[2]
                # separation_perm = list(sep0)
                ordind = local_plane.project_and_to2dim_ordered_indices(inp)
                # separation_perm.extend(
                #     [separation_indices[1][ii] for ii in ordind])
                inp1 = separation_indices[1].take(ordind)
                # separation_perm.extend(sep2)
                separation_perm = np.concatenate((sep0, inp1, sep2))
            else:
                # separation_perm = list(separation_indices[0])
                # separation_perm.extend(separation_indices[1])
                # separation_perm.extend(separation_indices[2])
                separation_perm = np.concatenate(separation_indices)

            if self.plane_safe_permutations:
                sep_perms = sepplane.safe_separation_permutations(
                    ordered_plane=sepplane.ordered_plane,
                    ordered_point_groups=sepplane.ordered_point_groups)
            else:
                sep_perms = sepplane.permutations

            for i_sep_perm, sep_perm in enumerate(sep_perms):
                perm1 = separation_perm.take(sep_perm)
                pp = perm1.take(argref_separation)

                permutations.append(pp)

                points_distorted = self.local_geometry.points_wcs_ctwcc(
                    permutation=pp)

                sm_info = symmetry_measure(points_distorted=points_distorted,
                                           points_perfect=points_perfect)

                sm_info['translation_vector'] = self.local_geometry.centroid_with_centre

                permutations_symmetry_measures.append(sm_info)

            if len(permutations_symmetry_measures) > 0:
                return permutations_symmetry_measures, permutations, [sepplane.algorithm_type] * len(
                    permutations), stop_search
            else:
                return [], [], [], stop_search

        def coordination_geometry_symmetry_measures_fallback_random(self,
                                                                    coordination_geometry,
                                                                    NRANDOM=10,
                                                                    points_perfect=None):
            """
            Returns the symmetry measures for a random set of permutations for the coordination geometry
            "coordination_geometry". Fallback implementation for the plane separation algorithms measures
            of each permutation

            :param coordination_geometry: The coordination geometry to be investigated
            :param NRANDOM: Number of random permutations to be tested
            :return: The symmetry measures for the given coordination geometry for each permutation investigated
            """
            permutations_symmetry_measures = [None] * NRANDOM
            permutations = list()
            algos = list()
            perfect2local_maps = list()
            local2perfect_maps = list()
            for iperm in range(NRANDOM):
                perm = np.random.permutation(
                    coordination_geometry.coordination_number)
                permutations.append(perm)
                p2l = {}
                l2p = {}
                for i_p, pp in enumerate(perm):
                    p2l[i_p] = pp
                    l2p[pp] = i_p
                perfect2local_maps.append(p2l)
                local2perfect_maps.append(l2p)

                points_distorted = self.local_geometry.points_wcs_ctwcc(
                    permutation=perm)
                sm_info = symmetry_measure(points_distorted=points_distorted,
                                           points_perfect=points_perfect)
                sm_info['translation_vector'] = self.local_geometry.centroid_with_centre

                permutations_symmetry_measures[iperm] = sm_info
                algos.append('APPROXIMATE_FALLBACK')
            return permutations_symmetry_measures, permutations, algos, local2perfect_maps, perfect2local_maps