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/pymatgen/analysis/chemenv/coordination_environments/coordination_geometry_finder.py

# 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
D. Waroquiers, J. George, M. Horton, S. Schenk, K. A. Persson, G.-M. Rignanese, X. Gonze, G. Hautier
"ChemEnv: a fast and robust coordination environment identification tool",
Acta Cryst. B 2020, 76, pp 683-695,
DOI: 10.1107/S2052520620007994
"""

from __future__ import annotations

import itertools
import logging
import time
from random import shuffle

import numpy as np
from numpy.linalg import norm, 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 (
    EXPLICIT_PERMUTATIONS,
    SEPARATION_PLANE,
    AllCoordinationGeometries,
)
from pymatgen.analysis.chemenv.coordination_environments.structure_environments import (
    ChemicalEnvironments,
    LightStructureEnvironments,
    StructureEnvironments,
)
from pymatgen.analysis.chemenv.coordination_environments.voronoi import (
    DetailedVoronoiContainer,
)
from pymatgen.analysis.chemenv.utils.coordination_geometry_utils import (
    Plane,
    collinear,
    separation_in_list,
    sort_separation,
    sort_separation_tuple,
)
from pymatgen.analysis.chemenv.utils.defs_utils import chemenv_citations
from pymatgen.core.lattice import Lattice
from pymatgen.core.periodic_table import Species
from pymatgen.core.structure import Structure
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer

__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"

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 = [f"\nAbstract Geometry with {len(self.coords)} points :"]
        for pp in self.coords:
            outs.append(f"  {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"
                    f" numbers >= 5 : {self.centre}\n"
                )
            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"
                    f" numbers >= 5 : {self.centre}\n"
                )
        elif self.centering_type == "central_site":
            outs.append(f"Points are referenced to the central site : {self.centre}\n")
        elif self.centering_type == "centroid":
            if self.include_central_site_in_centroid:
                outs.append(
                    f"Points are referenced to the centroid (calculated with the central site) :\n  {self.centre}\n"
                )
            else:
                outs.append(
                    "Points are referenced to the centroid (calculated without the central site)"
                    f" :\n  {self.centre}\n"
                )
        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: bool = False,
        plane_ordering_override: bool = True,
        plane_safe_permutations: bool = False,
        only_symbols=None,
        print_citation: bool = False,
    ):
        """
        Args:
            permutations_safe_override: If set to True, all permutations are tested (very time-consuming for large
            coordination numbers!)
            plane_ordering_override: If set to False, the ordering of the points in the plane is disabled
            plane_safe_permutations: Whether to use safe permutations.
            only_symbols: Whether to restrict the list of environments to be identified.
            print_citation: If True, the ChemEnv citation will be printed
        """
        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,
        )
        if print_citation:
            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: 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:
                len_vals, len_sites = len(valences), len(structure)
                if len_vals != len_sites:
                    raise ValueError(
                        f"Valences ({len_vals}) do not match the number of sites in the structure ({len_sites})"
                    )
                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"],
        voronoi_distance_cutoff=None,
        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 voronoi_distance_cutoff: determines distance of considered neighbors. Especially important to increase it
            for molecules in a box.
        :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, Species):
                    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 = list(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
        if voronoi_distance_cutoff is None:
            voronoi_distance_cutoff = DetailedVoronoiContainer.default_voronoi_cutoff
        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,
            voronoi_cutoff=voronoi_distance_cutoff,
        )
        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, site in enumerate(self.structure):
            if isite not in sites_indices:
                logging.debug(f" ... in site #{isite:d}/{len(self.structure):d} ({site.species_string}) : skipped")
                continue
            if breakit:
                logging.debug(
                    f" ... in site #{isite}/{len(self.structure)} ({site.species_string}) : skipped (timelimit)"
                )
                continue
            logging.debug(f" ... in site #{isite:d}/{len(self.structure):d} ({site.species_string})")
            t1 = time.process_time()
            if optimization > 0:
                self.detailed_voronoi.local_planes[isite] = {}
                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(f"    ... getting environments for nb_set ({cn:d}, {inb_set:d})")
                    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(f"       ... getting hints from cg with mp_symbol {cg_symbol!r} ...")
                            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(f"           hint # {inew:d}")
                                    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(f"    ... getting environments for nb_set ({cn_new_nb_set}, {inew_nb_set}) - from hints")
                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(f"    ... computed in {t2 - t1:.2f} seconds")
        time_end = time.process_time()
        logging.debug(f"    ... compute_structure_environments ended in {time_end - time_init:.2f} seconds")
        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 = {}
            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, d in cncgsm.items():
            other_csms = {
                "csm_wocs_ctwocc": d["csm_wocs_ctwocc"],
                "csm_wocs_ctwcc": d["csm_wocs_ctwcc"],
                "csm_wocs_csc": d["csm_wocs_csc"],
                "csm_wcs_ctwocc": d["csm_wcs_ctwocc"],
                "csm_wcs_ctwcc": d["csm_wcs_ctwcc"],
                "csm_wcs_csc": d["csm_wcs_csc"],
                "rotation_matrix_wocs_ctwocc": d["rotation_matrix_wocs_ctwocc"],
                "rotation_matrix_wocs_ctwcc": d["rotation_matrix_wocs_ctwcc"],
                "rotation_matrix_wocs_csc": d["rotation_matrix_wocs_csc"],
                "rotation_matrix_wcs_ctwocc": d["rotation_matrix_wcs_ctwocc"],
                "rotation_matrix_wcs_ctwcc": d["rotation_matrix_wcs_ctwcc"],
                "rotation_matrix_wcs_csc": d["rotation_matrix_wcs_csc"],
                "scaling_factor_wocs_ctwocc": d["scaling_factor_wocs_ctwocc"],
                "scaling_factor_wocs_ctwcc": d["scaling_factor_wocs_ctwcc"],
                "scaling_factor_wocs_csc": d["scaling_factor_wocs_csc"],
                "scaling_factor_wcs_ctwocc": d["scaling_factor_wcs_ctwocc"],
                "scaling_factor_wcs_ctwcc": d["scaling_factor_wcs_ctwcc"],
                "scaling_factor_wcs_csc": d["scaling_factor_wcs_csc"],
                "translation_vector_wocs_ctwocc": d["translation_vector_wocs_ctwocc"],
                "translation_vector_wocs_ctwcc": d["translation_vector_wocs_ctwcc"],
                "translation_vector_wocs_csc": d["translation_vector_wocs_csc"],
                "translation_vector_wcs_ctwocc": d["translation_vector_wcs_ctwocc"],
                "translation_vector_wcs_ctwcc": d["translation_vector_wcs_ctwcc"],
                "translation_vector_wcs_csc": d["translation_vector_wcs_csc"],
            }
            ce.add_coord_geom(
                cg,
                d["csm"],
                algo=d["algo"],
                permutation=d["indices"],
                local2perfect_map=d["local2perfect_map"],
                perfect2local_map=d["perfect2local_map"],
                detailed_voronoi_index={"cn": cn, "index": inb_set},
                other_symmetry_measures=other_csms,
                rotation_matrix=d["rotation_matrix"],
                scaling_factor=d["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 in ("MP", "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 = []
        for _ 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"][f"csm_{csmtype}"] = 0.0
                    result_dict["S:1"][f"scaling_factor_{csmtype}"] = None
                    result_dict["S:1"][f"rotation_matrix_{csmtype}"] = None
                    result_dict["S:1"][f"translation_vector_{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 "
                f'algorithm for geometry "{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 = []
            algos = []
            local2perfect_maps = []
            perfect2local_maps = []
            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,
            )

        permutations_symmetry_measures = [None] * len(algo.permutations)
        permutations = []
        algos = []
        local2perfect_maps = []
        perfect2local_maps = []
        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 = []
        permutations_symmetry_measures = []
        plane_separations = []
        algos = []
        perfect2local_maps = []
        local2perfect_maps = []
        if testing:
            separation_permutations = []
        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 = []
        permutations_symmetry_measures = []
        algos = []
        perfect2local_maps = []
        local2perfect_maps = []

        if separation_plane_algo.separation in nb_set.separations:
            for local_plane, npsep in nb_set.separations[separation_plane_algo.separation].values():
                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=int) 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=None,
        testing=False,
        tested_permutations=False,
        points_perfect=None,
    ):
        argref_separation = sepplane.argsorted_ref_separation_perm
        plane_found = False
        permutations = []
        permutations_symmetry_measures = []
        if testing:
            separation_permutations = []
        dist_tolerances = dist_tolerances or DIST_TOLERANCES
        for dist_tolerance in dist_tolerances:
            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 sep_perm in 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,
                )
            return (
                permutations_symmetry_measures,
                permutations,
                [sepplane.algorithm_type] * len(permutations),
            )
        if plane_found:
            if testing:
                return permutations_symmetry_measures, permutations, [], []
            return permutations_symmetry_measures, permutations, []
        if testing:
            return None, None, None, None
        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 sep_perm in 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,
            )
        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 sep_perm in 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,
            )
        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 = []
        algos = []
        perfect2local_maps = []
        local2perfect_maps = []
        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,
        )

materialsproject / pymatgen / 4075885785

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