text: # coding: utf-8
  # Copyright (c) Pymatgen Development Team.
  # Distributed under the terms of the MIT License.
  
  from __future__ import division, unicode_literals
  
  """
  This module provides classes to perform topological analyses of structures.
  """
  
  __author__ = "Shyue Ping Ong, Geoffroy Hautier, Sai Jayaraman"
  __copyright__ = "Copyright 2011, The Materials Project"
  __version__ = "1.0"
  __maintainer__ = "Shyue Ping Ong"
  __email__ = "shyuep@gmail.com"
  __status__ = "Production"
  __date__ = "Sep 23, 2011"
  
  import math
  from math import pi
  import numpy as np
  import itertools
  import collections
  
  from warnings import warn
  from scipy.spatial import Voronoi
  from pymatgen import PeriodicSite
  from pymatgen import Element, Specie, Composition
  from pymatgen.util.num_utils import abs_cap
  from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
  
  
  class VoronoiCoordFinder(object):
      """
      Uses a Voronoi algorithm to determine the coordination for each site in a
      structure.
  
      Args:
          structure (Structure): Input structure
          target ([Element/Specie]): A list of target species to determine
              coordination for.
          cutoff (float): Radius in Angstrom cutoff to look for coordinating
              atoms. Defaults to 10.0.
      """
  
      def __init__(self, structure, target=None, cutoff=10.0):
          self._structure = structure
          self.cutoff = cutoff
          if target is None:
              self._target = structure.composition.elements
          else:
              self._target = target
  
      def get_voronoi_polyhedra(self, n):
          """
          Gives a weighted polyhedra around a site. This uses the voronoi
          construction with solid angle weights.
          See ref: A Proposed Rigorous Definition of Coordination Number,
          M. O'Keeffe, Acta Cryst. (1979). A35, 772-775
  
          Args:
              n (int): Site index
  
          Returns:
              A dict of sites sharing a common Voronoi facet with the site
              n and their solid angle weights
          """
          localtarget = self._target
          center = self._structure[n]
          neighbors = self._structure.get_sites_in_sphere(
              center.coords, self.cutoff)
          neighbors = [i[0] for i in sorted(neighbors, key=lambda s: s[1])]
          qvoronoi_input = [s.coords for s in neighbors]
          voro = Voronoi(qvoronoi_input)
          all_vertices = voro.vertices
  
          results = {}
          for nn, vind in voro.ridge_dict.items():
              if 0 in nn:
                  if -1 in vind:
                      raise RuntimeError("This structure is pathological,"
                                         " infinite vertex in the voronoi "
                                         "construction")
  
                  facets = [all_vertices[i] for i in vind]
                  results[neighbors[sorted(nn)[1]]] = solid_angle(
                      center.coords, facets)
  
          maxangle = max(results.values())
  
          resultweighted = {}
          for nn, angle in results.items():
              # is nn site is ordered use "nn.specie" to get species, else use "nn.species_and_occu" to get species
              if nn.is_ordered:
                  if nn.specie in localtarget:
                      resultweighted[nn] = angle / maxangle
              else:  # is nn site is disordered
                  for disordered_sp in nn.species_and_occu.keys():
                      if disordered_sp in localtarget:
                          resultweighted[nn] = angle / maxangle
  
          return resultweighted
  
      def get_coordination_number(self, n):
          """
          Returns the coordination number of site with index n.
  
          Args:
              n (int): Site index
          """
          return sum(self.get_voronoi_polyhedra(n).values())
  
      def get_coordinated_sites(self, n, tol=0, target=None):
          """
          Returns the sites that are in the coordination radius of site with
          index n.
  
          Args:
              n (int): Site index.
              tol (float): Weight tolerance to determine if a particular pair is
                  considered a neighbor.
              target (Element): Target element
  
          Returns:
              Sites coordinating input site.
          """
          coordinated_sites = []
          for site, weight in self.get_voronoi_polyhedra(n).items():
              if weight > tol and (target is None or site.specie == target):
                  coordinated_sites.append(site)
          return coordinated_sites
  
  
  def average_coordination_number(structures, freq=10):
      """
      Calculates the ensemble averaged Voronoi coordination numbers
      of a list of Structures using VoronoiCoordFinder.
      Typically used for analyzing the output of a Molecular Dynamics run.
      Args:
          structures (list): list of Structures.
          freq (int): sampling frequency of coordination number [every freq steps].
      Returns:
          Dictionary of elements as keys and average coordination numbers as values.
      """
      coordination_numbers = {}
      for el in structures[0].composition.elements:
          coordination_numbers[el.name] = 0.0
      count = 0
      for t in range(len(structures)):
          if t % freq != 0:
              continue
          count += 1
          vor = VoronoiCoordFinder(structures[t])
          for atom in range(len(structures[0])):
              cn = vor.get_coordination_number(atom)
              coordination_numbers[structures[t][atom].species_string] += cn
      elements = structures[0].composition.as_dict()
      for el in coordination_numbers:
          coordination_numbers[el] = coordination_numbers[el] / elements[
              el] / count
      return coordination_numbers
  
  
  class VoronoiAnalyzer(object):
      """
      Performs a statistical analysis of Voronoi polyhedra around each site.
      Each Voronoi polyhedron is described using Schaefli notation.
      That is a set of indices {c_i} where c_i is the number of faces with i
      number of vertices.  E.g. for a bcc crystal, there is only one polyhedron
      notation of which is [0,6,0,8,0,0,...].
      In perfect crystals, these also corresponds to the Wigner-Seitz cells.
      For distorted-crystals, liquids or amorphous structures, rather than one-type,
      there is a statistical distribution of polyhedra.
      See ref: Microstructure and its relaxation in Fe-B amorphous system
      simulated by molecular dynamics,
          Stepanyuk et al., J. Non-cryst. Solids (1993), 159, 80-87.
  
      Args:
          cutoff (float): cutoff distance to search for neighbors of a given atom
              (default = 5.0)
          qhull_options (str): options to pass to qhull (optional)
      """
  
      def __init__(self, cutoff=5.0, qhull_options="Qbb Qc Qz"):
          self.cutoff = cutoff
          self.qhull_options = qhull_options
  
      def analyze(self, structure, n=0):
          """
          Performs Voronoi analysis and returns the polyhedra around atom n
          in Schlaefli notation.
  
          Args:
              structure (Structure): structure to analyze
              n (int): index of the center atom in structure
  
          Returns:
              voronoi index of n: <c3,c4,c6,c6,c7,c8,c9,c10>
                  where c_i denotes number of facets with i vertices.
          """
          center = structure[n]
          neighbors = structure.get_sites_in_sphere(center.coords, self.cutoff)
          neighbors = [i[0] for i in sorted(neighbors, key=lambda s: s[1])]
          qvoronoi_input = np.array([s.coords for s in neighbors])
          voro = Voronoi(qvoronoi_input, qhull_options=self.qhull_options)
          vor_index = np.array([0, 0, 0, 0, 0, 0, 0, 0])
  
          for key in voro.ridge_dict:
              if 0 in key:  # This means if the center atom is in key
                  if -1 in key:  # This means if an infinity point is in key
                      raise ValueError("Cutoff too short.")
                  else:
                      try:
                          vor_index[len(voro.ridge_dict[key]) - 3] += 1
                      except IndexError:
                          # If a facet has more than 10 edges, it's skipped here.
                          pass
          return vor_index
  
      def analyze_structures(self, structures, step_freq=10,
                             most_frequent_polyhedra=15):
          """
          Perform Voronoi analysis on a list of Structures.
          Note that this might take a significant amount of time depending on the
          size and number of structures.
  
          Args:
              structures (list): list of Structures
              cutoff (float: cutoff distance around an atom to search for
                  neighbors
              step_freq (int): perform analysis every step_freq steps
              qhull_options (str): options to pass to qhull
              most_frequent_polyhedra (int): this many unique polyhedra with
                  highest frequences is stored.
  
          Returns:
              A list of tuples in the form (voronoi_index,frequency)
          """
          voro_dict = {}
          step = 0
          for structure in structures:
              step += 1
              if step % step_freq != 0:
                  continue
  
              v = []
              for n in range(len(structure)):
                  v.append(str(self.analyze(structure, n=n).view()))
              for voro in v:
                  if voro in voro_dict:
                      voro_dict[voro] += 1
                  else:
                      voro_dict[voro] = 1
          return sorted(voro_dict.items(),
                        key=lambda x: (x[1], x[0]),
                        reverse=True)[:most_frequent_polyhedra]
  
      @staticmethod
      def plot_vor_analysis(voronoi_ensemble):
          t = zip(*voronoi_ensemble)
          labels = t[0]
          val = list(t[1])
          tot = np.sum(val)
          val = [float(j) / tot for j in val]
          pos = np.arange(len(val)) + .5  # the bar centers on the y axis
          import matplotlib.pyplot as plt
          plt.figure()
          plt.barh(pos, val, align='center', alpha=0.5)
          plt.yticks(pos, labels)
          plt.xlabel('Count')
          plt.title('Voronoi Spectra')
          plt.grid(True)
          return plt
  
  
  class RelaxationAnalyzer(object):
      """
      This class analyzes the relaxation in a calculation.
      """
  
      def __init__(self, initial_structure, final_structure):
          """
          Please note that the input and final structures should have the same
          ordering of sites. This is typically the case for most computational
          codes.
  
          Args:
              initial_structure (Structure): Initial input structure to
                  calculation.
              final_structure (Structure): Final output structure from
                  calculation.
          """
          if final_structure.formula != initial_structure.formula:
              raise ValueError("Initial and final structures have different " +
                               "formulas!")
          self.initial = initial_structure
          self.final = final_structure
  
      def get_percentage_volume_change(self):
          """
          Returns the percentage volume change.
  
          Returns:
              Volume change in percentage, e.g., 0.055 implies a 5.5% increase.
          """
          initial_vol = self.initial.lattice.volume
          final_vol = self.final.lattice.volume
          return final_vol / initial_vol - 1
  
      def get_percentage_lattice_parameter_changes(self):
          """
          Returns the percentage lattice parameter changes.
  
          Returns:
              A dict of the percentage change in lattice parameter, e.g.,
              {'a': 0.012, 'b': 0.021, 'c': -0.031} implies a change of 1.2%,
              2.1% and -3.1% in the a, b and c lattice parameters respectively.
          """
          initial_latt = self.initial.lattice
          final_latt = self.final.lattice
          d = {l: getattr(final_latt, l) / getattr(initial_latt, l) - 1
               for l in ["a", "b", "c"]}
          return d
  
      def get_percentage_bond_dist_changes(self, max_radius=3.0):
          """
          Returns the percentage bond distance changes for each site up to a
          maximum radius for nearest neighbors.
  
          Args:
              max_radius (float): Maximum radius to search for nearest
                 neighbors. This radius is applied to the initial structure,
                 not the final structure.
  
          Returns:
              Bond distance changes as a dict of dicts. E.g.,
              {index1: {index2: 0.011, ...}}. For economy of representation, the
              index1 is always less than index2, i.e., since bonding between
              site1 and siten is the same as bonding between siten and site1,
              there is no reason to duplicate the information or computation.
          """
          data = collections.defaultdict(dict)
          for inds in itertools.combinations(list(range(len(self.initial))), 2):
              (i, j) = sorted(inds)
              initial_dist = self.initial[i].distance(self.initial[j])
              if initial_dist < max_radius:
                  final_dist = self.final[i].distance(self.final[j])
                  data[i][j] = final_dist / initial_dist - 1
          return data
  
  
  class VoronoiConnectivity(object):
      """
      Computes the solid angles swept out by the shared face of the voronoi
      polyhedron between two sites.
  
      Args:
          structure (Structure): Input structure
          cutoff (float) Cutoff distance.
      """
  
      # Radius in Angstrom cutoff to look for coordinating atoms
  
      def __init__(self, structure, cutoff=10):
          self.cutoff = cutoff
          self.s = structure
          recp_len = np.array(self.s.lattice.reciprocal_lattice.abc)
          i = np.ceil(cutoff * recp_len / (2 * math.pi))
          offsets = np.mgrid[-i[0]:i[0] + 1, -i[1]:i[1] + 1, -i[2]:i[2] + 1].T
          self.offsets = np.reshape(offsets, (-1, 3))
          # shape = [image, axis]
          self.cart_offsets = self.s.lattice.get_cartesian_coords(self.offsets)
  
      @property
      def connectivity_array(self):
          """
          Provides connectivity array.
  
          Returns:
              connectivity: An array of shape [atomi, atomj, imagej]. atomi is
              the index of the atom in the input structure. Since the second
              atom can be outside of the unit cell, it must be described
              by both an atom index and an image index. Array data is the
              solid angle of polygon between atomi and imagej of atomj
          """
          # shape = [site, axis]
          cart_coords = np.array(self.s.cart_coords)
          # shape = [site, image, axis]
          all_sites = cart_coords[:, None, :] + self.cart_offsets[None, :, :]
          vt = Voronoi(all_sites.reshape((-1, 3)))
          n_images = all_sites.shape[1]
          cs = (len(self.s), len(self.s), len(self.cart_offsets))
          connectivity = np.zeros(cs)
          vts = np.array(vt.vertices)
          for (ki, kj), v in vt.ridge_dict.items():
              atomi = ki // n_images
              atomj = kj // n_images
  
              imagei = ki % n_images
              imagej = kj % n_images
  
              if imagei != n_images // 2 and imagej != n_images // 2:
                  continue
  
              if imagei == n_images // 2:
                  # atomi is in original cell
                  val = solid_angle(vt.points[ki], vts[v])
                  connectivity[atomi, atomj, imagej] = val
  
              if imagej == n_images // 2:
                  # atomj is in original cell
                  val = solid_angle(vt.points[kj], vts[v])
                  connectivity[atomj, atomi, imagei] = val
  
              if -10.101 in vts[v]:
                  warn('Found connectivity with infinite vertex. '
                       'Cutoff is too low, and results may be '
                       'incorrect')
          return connectivity
  
      @property
      def max_connectivity(self):
          """
          returns the 2d array [sitei, sitej] that represents
          the maximum connectivity of site i to any periodic
          image of site j
          """
          return np.max(self.connectivity_array, axis=2)
  
      def get_connections(self):
          """
          Returns a list of site pairs that are Voronoi Neighbors, along
          with their real-space distances.
          """
          con = []
          maxconn = self.max_connectivity
          for ii in range(0, maxconn.shape[0]):
              for jj in range(0, maxconn.shape[1]):
                  if maxconn[ii][jj] != 0:
                      dist = self.s.get_distance(ii, jj)
                      con.append([ii, jj, dist])
          return con
  
      def get_sitej(self, site_index, image_index):
          """
          Assuming there is some value in the connectivity array at indices
          (1, 3, 12). sitei can be obtained directly from the input structure
          (structure[1]). sitej can be obtained by passing 3, 12 to this function
  
          Args:
              site_index (int): index of the site (3 in the example)
              image_index (int): index of the image (12 in the example)
          """
          atoms_n_occu = self.s[site_index].species_and_occu
          lattice = self.s.lattice
          coords = self.s[site_index].frac_coords + self.offsets[image_index]
          return PeriodicSite(atoms_n_occu, coords, lattice)
  
  
  def solid_angle(center, coords):
      """
      Helper method to calculate the solid angle of a set of coords from the
      center.
  
      Args:
          center (3x1 array): Center to measure solid angle from.
          coords (Nx3 array): List of coords to determine solid angle.
  
      Returns:
          The solid angle.
      """
      o = np.array(center)
      r = [np.array(c) - o for c in coords]
      r.append(r[0])
      n = [np.cross(r[i + 1], r[i]) for i in range(len(r) - 1)]
      n.append(np.cross(r[1], r[0]))
      vals = []
      for i in range(len(n) - 1):
          v = -np.dot(n[i], n[i + 1]) \
              / (np.linalg.norm(n[i]) * np.linalg.norm(n[i + 1]))
          vals.append(math.acos(abs_cap(v)))
      phi = sum(vals)
      return phi + (3 - len(r)) * math.pi
  
  
  def contains_peroxide(structure, relative_cutoff=1.1):
      """
      Determines if a structure contains peroxide anions.
  
      Args:
          structure (Structure): Input structure.
          relative_cutoff: The peroxide bond distance is 1.49 Angstrom.
              Relative_cutoff * 1.49 stipulates the maximum distance two O
              atoms must be to each other to be considered a peroxide.
  
      Returns:
          Boolean indicating if structure contains a peroxide anion.
      """
      ox_type = oxide_type(structure, relative_cutoff)
      if ox_type == "peroxide":
          return True
      else:
          return False
  
  
  class OxideType(object):
      """
      Separate class for determining oxide type.
  
      Args:
          structure: Input structure.
          relative_cutoff: Relative_cutoff * act. cutoff stipulates the max.
              distance two O atoms must be from each other. Default value is
              1.1. At most 1.1 is recommended, nothing larger, otherwise the
              script cannot distinguish between superoxides and peroxides.
      """
  
      def __init__(self, structure, relative_cutoff=1.1):
          self.structure = structure
          self.relative_cutoff = relative_cutoff
          self.oxide_type, self.nbonds = self.parse_oxide()
  
      def parse_oxide(self):
          """
          Determines if an oxide is a peroxide/superoxide/ozonide/normal oxide.
  
          Returns:
              oxide_type (str): Type of oxide
              ozonide/peroxide/superoxide/hydroxide/None.
              nbonds (int): Number of peroxide/superoxide/hydroxide bonds in
              structure.
          """
          structure = self.structure
          relative_cutoff = self.relative_cutoff
          o_sites_frac_coords = []
          h_sites_frac_coords = []
          lattice = structure.lattice
  
          if isinstance(structure.composition.elements[0], Element):
              comp = structure.composition
          elif isinstance(structure.composition.elements[0], Specie):
              elmap = collections.defaultdict(float)
              for site in structure:
                  for species, occu in site.species_and_occu.items():
                      elmap[species.element] += occu
              comp = Composition(elmap)
          if Element("O") not in comp or comp.is_element:
              return "None", 0
  
          for site in structure:
              syms = [sp.symbol for sp in site.species_and_occu.keys()]
              if "O" in syms:
                  o_sites_frac_coords.append(site.frac_coords)
              if "H" in syms:
                  h_sites_frac_coords.append(site.frac_coords)
  
          if h_sites_frac_coords:
              dist_matrix = lattice.get_all_distances(o_sites_frac_coords,
                                                      h_sites_frac_coords)
              if np.any(dist_matrix < relative_cutoff * 0.93):
                  return "hydroxide", len(
                      np.where(dist_matrix < relative_cutoff * 0.93)[0]) / 2.0
          dist_matrix = lattice.get_all_distances(o_sites_frac_coords,
                                                  o_sites_frac_coords)
          np.fill_diagonal(dist_matrix, 1000)
          is_superoxide = False
          is_peroxide = False
          is_ozonide = False
          if np.any(dist_matrix < relative_cutoff * 1.35):
              bond_atoms = np.where(dist_matrix < relative_cutoff * 1.35)[0]
              is_superoxide = True
          elif np.any(dist_matrix < relative_cutoff * 1.49):
              is_peroxide = True
              bond_atoms = np.where(dist_matrix < relative_cutoff * 1.49)[0]
          if is_superoxide:
              if len(bond_atoms) > len(set(bond_atoms)):
                  is_superoxide = False
                  is_ozonide = True
          try:
              nbonds = len(set(bond_atoms))
          except UnboundLocalError:
              nbonds = 0.0
          if is_ozonide:
              str_oxide = "ozonide"
          elif is_superoxide:
              str_oxide = "superoxide"
          elif is_peroxide:
              str_oxide = "peroxide"
          else:
              str_oxide = "oxide"
          if str_oxide == "oxide":
              nbonds = comp["O"]
          return str_oxide, nbonds
  
  
  def oxide_type(structure, relative_cutoff=1.1, return_nbonds=False):
      """
      Determines if an oxide is a peroxide/superoxide/ozonide/normal oxide
  
      Args:
          structure (Structure): Input structure.
          relative_cutoff (float): Relative_cutoff * act. cutoff stipulates the
              max distance two O atoms must be from each other.
          return_nbonds (bool): Should number of bonds be requested?
      """
  
      ox_obj = OxideType(structure, relative_cutoff)
      if return_nbonds:
          return ox_obj.oxide_type, ox_obj.nbonds
      else:
          return ox_obj.oxide_type
  
  
  def sulfide_type(structure):
      """
      Determines if a structure is a sulfide/polysulfide
  
      Args:
          structure (Structure): Input structure.
  
      Returns:
          (str) sulfide/polysulfide/sulfate
      """
      structure = structure.copy()
      structure.remove_oxidation_states()
      s = Element("S")
      comp = structure.composition
      if comp.is_element or s not in comp:
          return None
  
      finder = SpacegroupAnalyzer(structure, symprec=0.1)
      symm_structure = finder.get_symmetrized_structure()
      s_sites = [sites[0] for sites in symm_structure.equivalent_sites if sites[0].specie == s]
  
      def process_site(site):
          neighbors = structure.get_neighbors(site, 4)
          neighbors = sorted(neighbors, key=lambda n: n[1])
          nn, dist = neighbors[0]
          coord_elements = [site.specie for site, d in neighbors
                            if d < dist + 0.4][:4]
          avg_electroneg = np.mean([e.X for e in coord_elements])
          if avg_electroneg > s.X:
              return "sulfate"
          elif avg_electroneg == s.X and s in coord_elements:
              return "polysulfide"
          else:
              return "sulfide"
  
      types = set([process_site(site) for site in s_sites])
      if "sulfate" in types:
          return None
      elif "polysulfide" in types:
          return "polysulfide"
      else:
          return "sulfide"
  
  
  def gramschmidt(vin, uin):
      """
      Returns that part of the first input vector
      that is orthogonal to the second input vector.
      The output vector is not normalized.
  
      Args:
          vin (numpy array):
              first input vector
          uin (numpy array):
              second input vector
      """
  
      vin_uin = np.inner(vin, uin)
      uin_uin = np.inner(uin, uin)
      if uin_uin <= 0.0:
          raise ValueError("Zero or negative inner product!")
      return vin - (vin_uin / uin_uin) * uin
  
  
  class OrderParameters(object):
      """
      This class permits the calculation of various types of local order
      parameters.
      """
  
      __supported_types = ("cn", "tet", "oct", "bcc", "q2", "q4", "q6")
  
      def __init__(self, types, parameters=None, cutoff=-10.0):
          """
          Create an OrderParameter analyzer instance.
  
          Args:
              types ([string]):
                  List of strings representing the types of order parameters
                  to be calculated. Note that multiple mentions of the
                  same type may occur. Currently available types are
                  "cn"  (simple coordination number---normalized,
                        if desired),
                  "tet" [Shetty--Peters style OP recognizing tetrahedral
                        coordination (Zimmermann et al.,
                        J. Am. Chem. Soc., 137, 13352-13361, 2015)],
                  "oct" [Shetty--Peters style OP recognizing octahedral
                        coordination (Zimmermann et al.,
                        J. Am. Chem. Soc., 137, 13352-13361, 2015)],
                  "bcc" [Shetty--Peters style OP recognizing local
                        body-centered cubic environment (Peters,
                        J. Chem. Phys., 131, 244103, 2009)],
                  "q2"  [Bond orientational order parameter (BOOP)
                        of weight l=2 (Steinhardt et al., Phys. Rev. B,
                        28, 784-805, 1983)],
                  "q4"  (BOOP of weight l=4),
                  "q6"  (BOOP of weight l=6).
              parameters ([[float]]):
                  2D list of floating point numbers that store
                  parameters associated with the different order parameters
                  that are to be calculated (1st dimension = length of
                  types tuple; any 2nd dimension may be zero, in which case
                  default values are used). In the following, those order
                  parameters q_i are listed that require further parameters
                  for their computation (values in brackets denote default
                  values):
                    "cn":  normalizing constant (1);
                    "tet": Gaussian width in fractions of pi (180 degrees)
                           reflecting the "speed of
                           penalizing" deviations away from the perfect
                           tetrahedral angle of any individual
                           neighbor1-center-neighbor2 configuration (0.0667);
                    "oct": threshold angle in degrees distinguishing a second
                           neighbor to be either close to the south pole or
                           close to the equator (160.0);
                           Gaussian width for penalizing deviations away
                           from south pole (0.0667);
                           Gaussian width for penalizing deviations away
                           from equator (0.0556);
                           constant for shifting q_oct toward smaller
                           values, which can be helpful when trying to fine-
                           tune the capabilities of distinguishing between
                           different environments (e.g., tet vs oct)
                           given a single mutual threshold q_thresh;
                    "bcc": south-pole threshold angle as for "oct" (160.0);
                           south-pole Gaussian width as for "oct" (0.0667).
              cutoff (float):
                  Cutoff radius to determine which nearest neighbors are
                  supposed to contribute to the order parameters.
                  If the value is negative the neighboring sites found by
                  distance and cutoff radius are further
                  pruned using the get_coordinated_sites method from the
                  VoronoiCoordFinder class.
          """
          if len(types) == 0:
              raise ValueError("Empty types list!")
          for t in types:
              if t not in OrderParameters.__supported_types:
                  raise ValueError("Unknown order parameter type (" + \
                                   t + ")!")
          if parameters:
              if len(types) != len(parameters):
                  raise ValueError("1st dimension of parameters array is not"
                                   " consistent with types list!")
              for lp in parameters:
                  if len(lp) > 0:
                      for p in lp:
                          if type(p) != float and type(p) != int:
                              raise AttributeError("Expected only float and"
                                                   " integer type parameters!")
              loc_parameters = list(parameters)
          else:
              loc_parameters = [[] for t in types]
          self._types = tuple(types)
          tmpparas = []
          self._computerijs = self._geomops = self._boops = False
          self._max_trig_order = -1
          for i, t in enumerate(self._types):
              # add here any additional parameter checking and
              #     default value assignment
              tmpparas.append([])
              if t == "cn":
                  if len(loc_parameters[i]) == 0:
                      tmpparas[i].append(1.0)
                  else:
                      if loc_parameters[i][0] == 0.0:
                          raise ValueError("Normalizing constant for"
                                           " coordination-number based order"
                                           " parameter is zero!")
                      else:
                          tmpparas[i].append(loc_parameters[i][0])
              elif t == "tet":
                  if len(loc_parameters[i]) == 0:
                      tmpparas[i].append(1.0 / 0.0667)
                  else:
                      if loc_parameters[i][0] == 0.0:
                          raise ValueError("Gaussian width for"
                                           " tetrahedral order"
                                           " parameter is zero!")
                      else:
                          tmpparas[i].append(1.0 / loc_parameters[i][0])
              elif t == "oct":
                  if len(loc_parameters[i]) < 4:
                      tmpparas[i].append(8.0 * pi / 9.0)
                      tmpparas[i].append(1.0 / 0.0667)
                      tmpparas[i].append(1.0 / 0.0556)
                      tmpparas[i].append(0.25)
                      tmpparas[i].append(4.0 / 3.0)
                  else:
                      if loc_parameters[i][0] <= 0.0 or loc_parameters[i][
                          0] >= 180.0:
                          warn("Threshold value for south pole"
                               " configurations in octahedral order"
                               " parameter outside ]0,180[")
                      tmpparas[i].append(loc_parameters[i][0] * pi / 180.0)
                      if loc_parameters[i][1] == 0.0:
                          raise ValueError("Gaussian width for south pole"
                                           " configurations in octahedral"
                                           " order parameter is zero!")
                      else:
                          tmpparas[i].append(1.0 / loc_parameters[i][1])
                      if loc_parameters[i][2] == 0.0:
                          raise ValueError("Gaussian width for equatorial"
                                           " configurations in octahedral"
                                           " order parameter is zero!")
                      else:
                          tmpparas[i].append(1.0 / loc_parameters[i][2])
                      if loc_parameters[i][3] - 1.0 == 0.0:
                          raise ValueError("Shift constant may not be"
                                           " unity!")
                      if loc_parameters[i][3] < 0.0 or loc_parameters[i][3] > 1.0:
                          warn("Shift constant outside [0,1[.")
                      tmpparas[i].append(loc_parameters[i][3])
                      tmpparas[i].append(1.0 / (1.0 - loc_parameters[i][3]))
              elif t == "bcc":
                  if len(loc_parameters[i]) < 2:
                      tmpparas[i].append(8.0 * pi / 9.0)
                      tmpparas[i].append(1.0 / 0.0667)
                  else:
                      if loc_parameters[i][0] <= 0.0 or loc_parameters[i][
                          0] >= 180.0:
                          warn("Threshold value for south pole"
                               " configurations in bcc order"
                               " parameter outside ]0,180[")
                      tmpparas[i].append(loc_parameters[i][0] * pi / 180.0)
                      if loc_parameters[i][1] == 0.0:
                          raise ValueError("Gaussian width for south pole"
                                           " configurations in bcc"
                                           " order parameter is zero!")
                      else:
                          tmpparas[i].append(1.0 / loc_parameters[i][1])
              # All following types should be well-defined/-implemented,
              # and they should not require parameters.
              elif t != "q2" and t != "q4" and t != "q6":
                  raise ValueError("unknown order-parameter type \"" + t + "\"")
  
              # Add here any additional flags to be used during calculation.
              if t == "tet" or t == "oct" or t == "bcc":
                  self._computerijs = self._geomops = True
              if t == "q2" or t == "q4" or t == "q6":
                  self._computerijs = self._boops = True
              if t == "q2" and self._max_trig_order < 2:
                  self._max_trig_order = 2
              if t == "q4" and self._max_trig_order < 4:
                  self._max_trig_order = 4
              if t == "q6" and self._max_trig_order < 6:
                  self._max_trig_order = 6
  
          # Finish parameter treatment.
          self._paras = list(tmpparas)
          if cutoff < 0.0:
              self._cutoff = -cutoff
              self._voroneigh = True
          elif cutoff > 0.0:
              self._cutoff = cutoff
              self._voroneigh = False
          else:
              raise ValueError("Cutoff radius is zero!")
  
          # Further variable definitions.
          self._last_nneigh = -1
          self._pow_sin_t = {}
          self._pow_cos_t = {}
          self._sin_n_p = {}
          self._cos_n_p = {}
  
      @property
      def num_ops(self):
  
          """"
          Returns the number of different order parameters that are targeted
          to be calculated.
          """
  
          return len(self._types)
  
      @property
      def last_nneigh(self):
  
          """"
          Returns the number of neighbors encountered during the most
          recent order-parameter calculation. A value of -1 indicates that
          no such calculation has yet been performed for this instance.
          """
  
          return len(self._last_nneigh)
  
      def compute_trigonometric_terms(self, thetas=[], phis=[]):
  
          """"
          Computes trigonometric terms that are required to
          calculate bond orientational order parameters.
  
          Args:
              thetas ([float]):
                  polar angles of all neighbors in radians.
              phis ([float]):
                  azimuth angles of all neighbors in radians.  The list of
                  azimuth angles is expected to have the same size as the list
                  of polar angles; otherwise, a ValueError is raised.  Also,
                  the two lists of angles have to be coherent in order. That
                  is, it is expected that the order in the list of azimuth
                  angles corresponds to a distinct sequence of neighbors.
                  And, this sequence has to equal the sequence
                  of neighbors in the list of polar angles.
  
          """
  
          if not thetas or not phis:
              raise ValueError("No entries in list/s of polar and/or azimuthal" \
                               " angles!")
          if len(thetas) != len(phis):
              raise ValueError("List of polar and azimuthal angles have to be"
                               " equal!")
  
          self._pow_sin_t.clear()
          self._pow_cos_t.clear()
          self._sin_n_p.clear()
          self._cos_n_p.clear()
  
          self._pow_sin_t[1] = [math.sin(float(t)) for t in thetas]
          self._pow_cos_t[1] = [math.cos(float(t)) for t in thetas]
          self._sin_n_p[1] = [math.sin(float(p)) for p in phis]
          self._cos_n_p[1] = [math.cos(float(p)) for p in phis]
  
          for i in range(2, self._max_trig_order + 1):
              self._pow_sin_t[i] = [e[0] * e[1] for e in zip(
                  self._pow_sin_t[i - 1], self._pow_sin_t[1])]
              self._pow_cos_t[i] = [e[0] * e[1] for e in zip(
                  self._pow_cos_t[i - 1], self._pow_cos_t[1])]
              self._sin_n_p[i] = [math.sin(float(i) * float(p)) \
                                  for p in phis]
              self._cos_n_p[i] = [math.cos(float(i) * float(p)) \
                                  for p in phis]
  
      def get_q2(self, thetas=[], phis=[]):
  
          """
          Calculates the value of the bond orientational order parameter of
          weight l=2.  If the function is called with non-empty lists of
          polar and azimuthal angles the corresponding trigonometric terms
          are computed afresh.  Otherwise, it is expected that the
          compute_trigonometric_terms function has been just called.
  
          Args:
              thetas ([float]):
                  polar angles of all neighbors in radians.
              phis ([float]):
                  azimuth angles of all neighbors in radians.
  
          Return:
              q2 (float): bond orientational order parameter of weight l=2
                  corresponding to the input angles thetas and phis.
          """
  
          if thetas and phis:
              self.compute_trigonometric_terms(thetas, phis)
          nnn = len(self._pow_sin_t[1])
          nnn_range = range(nnn)
  
          sqrt_15_2pi = math.sqrt(15.0 / (2.0 * pi))
          sqrt_5_pi = math.sqrt(5.0 / pi)
  
          pre_y_2_2 = [0.25 * sqrt_15_2pi * val for val in self._pow_sin_t[2]]
          pre_y_2_1 = [0.5 * sqrt_15_2pi * val[0] * val[1]
                       for val in zip(self._pow_sin_t[1], self._pow_cos_t[1])]
  
          acc = 0.0
  
          # Y_2_-2
          real = imag = 0.0
          for i in nnn_range:
              real += pre_y_2_2[i] * self._cos_n_p[2][i]
              imag -= pre_y_2_2[i] * self._sin_n_p[2][i]
          acc += (real * real + imag * imag)
  
          # Y_2_-1
          real = imag = 0.0
          for i in nnn_range:
              real += pre_y_2_1[i] * self._cos_n_p[1][i]
              imag -= pre_y_2_1[i] * self._sin_n_p[1][i]
          acc += (real * real + imag * imag)
  
          # Y_2_0
          real = imag = 0.0
          for i in nnn_range:
              real += 0.25 * sqrt_5_pi * (3.0 * self._pow_cos_t[2][i] - 1.0)
          acc += (real * real)
  
          # Y_2_1
          real = imag = 0.0
          for i in nnn_range:
              real -= pre_y_2_1[i] * self._cos_n_p[1][i]
              imag -= pre_y_2_1[i] * self._sin_n_p[1][i]
          acc += (real * real + imag * imag)
  
          # Y_2_2
          real = imag = 0.0
          for i in nnn_range:
              real += pre_y_2_2[i] * self._cos_n_p[2][i]
              imag += pre_y_2_2[i] * self._sin_n_p[2][i]
          acc += (real * real + imag * imag)
  
          q2 = math.sqrt(4.0 * pi * acc / (5.0 * float(nnn * nnn)))
          return q2
  
      def get_q4(self, thetas=[], phis=[]):
  
          """
          Calculates the value of the bond orientational order parameter of
          weight l=4.  If the function is called with non-empty lists of
          polar and azimuthal angles the corresponding trigonometric terms
          are computed afresh.  Otherwise, it is expected that the
          compute_trigonometric_terms function has been just called.
  
          Args:
              thetas ([float]):
                  polar angles of all neighbors in radians.
              phis ([float]):
                  azimuth angles of all neighbors in radians.
  
          Return:
              q4 (float): bond orientational order parameter of weight l=4
                  corresponding to the input angles thetas and phis.
          """
  
          if thetas and phis:
              self.compute_trigonometric_terms(thetas, phis)
          nnn = len(self._pow_sin_t[1])
          nnn_range = range(nnn)
  
          i16_3 = 3.0 / 16.0
          i8_3 = 3.0 / 8.0
  
          sqrt_35_pi = math.sqrt(35.0 / pi)
          sqrt_35_2pi = math.sqrt(35.0 / (2.0 * pi))
          sqrt_5_pi = math.sqrt(5.0 / pi)
          sqrt_5_2pi = math.sqrt(5.0 / (2.0 * pi))
          sqrt_1_pi = math.sqrt(1.0 / pi)
  
          pre_y_4_4 = [i16_3 * sqrt_35_2pi * val for val in self._pow_sin_t[4]]
          pre_y_4_3 = [i8_3 * sqrt_35_pi * val[0] * val[1] \
                       for val in zip(self._pow_sin_t[3], self._pow_cos_t[1])]
          pre_y_4_2 = [i8_3 * sqrt_5_2pi * val[0] * (7.0 * val[1] - 1.0) \
                       for val in zip(self._pow_sin_t[2], self._pow_cos_t[2])]
          pre_y_4_1 = [i8_3 * sqrt_5_pi * val[0] * (7.0 * val[1] - 3.0 * val[2]) \
                       for val in zip(self._pow_sin_t[1], self._pow_cos_t[3], \
                                      self._pow_cos_t[1])]
  
          acc = 0.0
  
          # Y_4_-4
          real = imag = 0.0
          for i in nnn_range:
              real += pre_y_4_4[i] * self._cos_n_p[4][i]
              imag -= pre_y_4_4[i] * self._sin_n_p[4][i]
          acc += (real * real + imag * imag)
  
          # Y_4_-3
          real = imag = 0.0
          for i in nnn_range:
              real += pre_y_4_3[i] * self._cos_n_p[3][i]
              imag -= pre_y_4_3[i] * self._sin_n_p[3][i]
          acc += (real * real + imag * imag)
  
          # Y_4_-2
          real = imag = 0.0
          for i in nnn_range:
              real += pre_y_4_2[i] * self._cos_n_p[2][i]
              imag -= pre_y_4_2[i] * self._sin_n_p[2][i]
          acc += (real * real + imag * imag)
  
          # Y_4_-1
          real = imag = 0.0
          for i in nnn_range:
              real += pre_y_4_1[i] * self._cos_n_p[1][i]
              imag -= pre_y_4_1[i] * self._sin_n_p[1][i]
          acc += (real * real + imag * imag)
  
          # Y_4_0
          real = imag = 0.0
          for i in nnn_range:
              real += i16_3 * sqrt_1_pi * (35.0 * self._pow_cos_t[4][i] - \
                                           30.0 * self._pow_cos_t[2][i] + 3.0)
          acc += (real * real)
  
          # Y_4_1
          real = imag = 0.0
          for i in nnn_range:
              real -= pre_y_4_1[i] * self._cos_n_p[1][i]
              imag -= pre_y_4_1[i] * self._sin_n_p[1][i]
          acc += (real * real + imag * imag)
  
          # Y_4_2
          real = imag = 0.0
          for i in nnn_range:
              real += pre_y_4_2[i] * self._cos_n_p[2][i]
              imag += pre_y_4_2[i] * self._sin_n_p[2][i]
          acc += (real * real + imag * imag)
  
          # Y_4_3
          real = imag = 0.0
          for i in nnn_range:
              real -= pre_y_4_3[i] * self._cos_n_p[3][i]
              imag -= pre_y_4_3[i] * self._sin_n_p[3][i]
          acc += (real * real + imag * imag)
  
          # Y_4_4
          real = imag = 0.0
          for i in nnn_range:
              real += pre_y_4_4[i] * self._cos_n_p[4][i]
              imag += pre_y_4_4[i] * self._sin_n_p[4][i]
          acc += (real * real + imag * imag)
  
          q4 = math.sqrt(4.0 * pi * acc / (9.0 * float(nnn * nnn)))
          return q4
  
      def get_q6(self, thetas=[], phis=[]):
  
          """
          Calculates the value of the bond orientational order parameter of
          weight l=6.  If the function is called with non-empty lists of
          polar and azimuthal angles the corresponding trigonometric terms
          are computed afresh.  Otherwise, it is expected that the
          compute_trigonometric_terms function has been just called.
  
          Args:
              thetas ([float]):
                  polar angles of all neighbors in radians.
              phis ([float]):
                  azimuth angles of all neighbors in radians.
  
          Return:
              q6 (float): bond orientational order parameter of weight l=6
                  corresponding to the input angles thetas and phis.
          """
  
          if thetas and phis:
              self.compute_trigonometric_terms(thetas, phis)
          nnn = len(self._pow_sin_t[1])
          nnn_range = range(nnn)
  
          i64 = 1.0 / 64.0
          i32 = 1.0 / 32.0
          i32_3 = 3.0 / 32.0
          i16 = 1.0 / 16.0
  
          sqrt_3003_pi = math.sqrt(3003.0 / pi)
          sqrt_1001_pi = math.sqrt(1001.0 / pi)
          sqrt_91_2pi = math.sqrt(91.0 / (2.0 * pi))
          sqrt_1365_pi = math.sqrt(1365.0 / pi)
          sqrt_273_2pi = math.sqrt(273.0 / (2.0 * pi))
          sqrt_13_pi = math.sqrt(13.0 / pi)
  
          pre_y_6_6 = [i64 * sqrt_3003_pi * val for val in self._pow_sin_t[6]]
          pre_y_6_5 = [i32_3 * sqrt_1001_pi * val[0] * val[1] \
                       for val in zip(self._pow_sin_t[5], self._pow_cos_t[1])]
          pre_y_6_4 = [i32_3 * sqrt_91_2pi * val[0] * (11.0 * val[1] - 1.0) \
                       for val in zip(self._pow_sin_t[4], self._pow_cos_t[2])]
          pre_y_6_3 = [
              i32 * sqrt_1365_pi * val[0] * (11.0 * val[1] - 3.0 * val[2]) \
              for val in zip(self._pow_sin_t[3], self._pow_cos_t[3], \
                             self._pow_cos_t[1])]
          pre_y_6_2 = [i64 * sqrt_1365_pi * val[0] * (33.0 * val[1] - \
                                                      18.0 * val[2] + 1.0) for val
                       in zip(self._pow_sin_t[2], \
                              self._pow_cos_t[4], self._pow_cos_t[2])]
          pre_y_6_1 = [i16 * sqrt_273_2pi * val[0] * (33.0 * val[1] - \
                                                      30.0 * val[2] + 5.0 * val[
                                                          3]) for val in
                       zip(self._pow_sin_t[1], \
                           self._pow_cos_t[5], self._pow_cos_t[3],
                           self._pow_cos_t[1])]
  
          acc = 0.0
  
          # Y_6_-6
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real += pre_y_6_6[i] * self._cos_n_p[6][i]  # cos(x) =  cos(-x)
              imag -= pre_y_6_6[i] * self._sin_n_p[6][i]  # sin(x) = -sin(-x)
          acc += (real * real + imag * imag)
  
          # Y_6_-5
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real += pre_y_6_5[i] * self._cos_n_p[5][i]
              imag -= pre_y_6_5[i] * self._sin_n_p[5][i]
          acc += (real * real + imag * imag)
  
          # Y_6_-4
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real += pre_y_6_4[i] * self._cos_n_p[4][i]
              imag -= pre_y_6_4[i] * self._sin_n_p[4][i]
          acc += (real * real + imag * imag)
  
          # Y_6_-3
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real += pre_y_6_3[i] * self._cos_n_p[3][i]
              imag -= pre_y_6_3[i] * self._sin_n_p[3][i]
          acc += (real * real + imag * imag)
  
          # Y_6_-2
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real += pre_y_6_2[i] * self._cos_n_p[2][i]
              imag -= pre_y_6_2[i] * self._sin_n_p[2][i]
          acc += (real * real + imag * imag)
  
          # Y_6_-1
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real += pre_y_6_1[i] * self._cos_n_p[1][i]
              imag -= pre_y_6_1[i] * self._sin_n_p[1][i]
          acc += (real * real + imag * imag)
  
          # Y_6_0
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real += i32 * sqrt_13_pi * (231.0 * self._pow_cos_t[6][i] - \
                                          315.0 * self._pow_cos_t[4][i] + 105.0 *
                                          self._pow_cos_t[2][i] - 5.0)
          acc += (real * real)
  
          # Y_6_1
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real -= pre_y_6_1[i] * self._cos_n_p[1][i]
              imag -= pre_y_6_1[i] * self._sin_n_p[1][i]
          acc += (real * real + imag * imag)
  
          # Y_6_2
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real += pre_y_6_2[i] * self._cos_n_p[2][i]
              imag += pre_y_6_2[i] * self._sin_n_p[2][i]
          acc += (real * real + imag * imag)
  
          # Y_6_3
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real -= pre_y_6_3[i] * self._cos_n_p[3][i]
              imag -= pre_y_6_3[i] * self._sin_n_p[3][i]
          acc += (real * real + imag * imag)
  
          # Y_6_4
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real += pre_y_6_4[i] * self._cos_n_p[4][i]
              imag += pre_y_6_4[i] * self._sin_n_p[4][i]
          acc += (real * real + imag * imag)
  
          # Y_6_5
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real -= pre_y_6_5[i] * self._cos_n_p[5][i]
              imag -= pre_y_6_5[i] * self._sin_n_p[5][i]
          acc += (real * real + imag * imag)
  
          # Y_6_6
          real = imag = 0.0
          real = 0.0
          imag = 0.0
          for i in nnn_range:
              real += pre_y_6_6[i] * self._cos_n_p[6][i]
              imag += pre_y_6_6[i] * self._sin_n_p[6][i]
          acc += (real * real + imag * imag)
  
          q6 = math.sqrt(4.0 * pi * acc / (13.0 * float(nnn * nnn)))
          return q6
  
      def get_type(self, index):
  
          """
          Return type of order-parameter at the index provided and
          represented by a short string.
  
          Args:
              index (int):
                  index of order-parameter for which type is to be returned
          """
          if index < 0 or index >= len(self._types):
              raise ValueError("Index for getting order-parameter type"
                               " out-of-bounds!")
          return self._types[index]
  
      def get_parameters(self, index):
  
          """
          Returns list of floats that represents
          the parameters associated with calculation of the order
          parameter that was defined at the index provided.
          Attention: the parameters do not need to equal those originally
          inputted because of processing out of efficiency reasons.
  
          Args:
              index (int):
                  index of order-parameter for which associated parameters
                  are to be returned
          """
          if index < 0 or index >= len(self._types):
              raise ValueError("Index for getting parameters associated with"
                               " order-parameter calculation out-of-bounds!")
          return self._paras[index]
  
      def get_order_parameters(self, structure, n, indeces_neighs=[], \
                               tol=0.0, target_spec=None):
  
          """
          Compute all order parameters of site n.
  
          Args:
              structure (Structure):
                  input structure.
              n (int):
                  index of site in input structure, for which OPs are to be
                  calculated.  Note that we do not use the sites iterator
                  here, but directly access sites via struct[index].
              indeces_neighs ([int]):
                  list of indeces of those neighbors in Structure object
                  structure that are to be considered for OP computation.
                  This optional argument overwrites the way neighbors are
                  to be determined as defined in the constructor (i.e.,
                  Voronoi coordination finder via negative cutoff radius
                  vs constant cutoff radius if cutoff was positive).
                  We do not use information about the underlying
                  structure lattice if the neighbor indeces are explicitly
                  provided.  This has two important consequences.  First,
                  the input Structure object can, in fact, be a
                  simple list of Site objects.  Second, no nearest images
                  of neighbors are determined when providing an index list.
                  Note furthermore that this neighbor
                  determination type ignores the optional target_spec
                  argument.
              tol (float):
                  threshold of weight (= solid angle / maximal solid angle)
                  to determine if a particular pair is
                  considered neighbors; this is relevant only in the case
                  when Voronoi polyhedra are used to determine coordination
              target_spec (Specie):
                  target specie to be considered when calculating the order
                  parameters of site n; None includes all species of input
                  structure.
  
          Returns:
              list of floats representing order parameters.  Should it not be
              possible to compute a given OP for a conceptual reason, the
              corresponding entry is None instead of a float.  For Steinhardt
              et al.'s bond orientational OPs and the other geometric OPs
              ("tet", "oct", "bcc"), this can happen if there is a single
              neighbor around site n in the structure because that, obviously,
              does not permit calculation of angles between multiple
              neighbors.
          """
  
          # Do error-checking and initialization.
          if n < 0:
              raise ValueError("Site index smaller zero!")
          if n >= len(structure):
              raise ValueError("Site index beyond maximum!")
          if indeces_neighs:
              for index in indeces_neighs:
                  if index >= len(structure):
                      raise ValueError("Neighbor site index beyond maximum!")
          if tol < 0.0:
              raise ValueError("Negative tolerance for weighted solid angle!")
  
          left_of_unity = 1.0 - 1.0e-12
          # The following threshold has to be adapted to non-Angstrom units.
          very_small = 1.0e-12
  
          # Find central site and its neighbors.
          # Note that we adopt the same way of accessing sites here as in
          # VoronoiCoordFinder; that is, not via the sites iterator.
          centsite = structure[n]
          if indeces_neighs:
              neighsites = [structure[index] for index in indeces_neighs]
          elif self._voroneigh:
              vorocf = VoronoiCoordFinder(structure)
              neighsites = vorocf.get_coordinated_sites(n, tol, target_spec)
          else:
              # Structure.get_sites_in_sphere --> also other periodic images
              neighsitestmp = [i[0] for i in structure.get_sites_in_sphere(
                  centsite.coords, self._cutoff)]
              neighsites = []
              if centsite not in neighsitestmp:
                  raise ValueError("Could not find center site!")
              else:
                  neighsitestmp.remove(centsite)
              if target_spec is None:
                  neighsites = list(neighsitestmp)
              else:
                  neighsites[:] = [site for site in neighsitestmp \
                                   if site.specie.symbol == target_spec]
          nneigh = len(neighsites)
          self._last_nneigh = nneigh
  
          # Prepare angle calculations, if applicable.
          rij = []
          rijnorm = []
          dist = []
          centvec = centsite.coords
          if self._computerijs:
              for j, neigh in enumerate(neighsites):
                  rij.append((neigh.coords - centvec))
                  dist.append(np.linalg.norm(rij[j]))
                  rijnorm.append((rij[j] / dist[j]))
  
          # Initialize OP list and, then, calculate OPs.
          ops = [0.0 for t in self._types]
  
          # First, coordination number-based OPs.
          for i, t in enumerate(self._types):
              if t == "cn":
                  ops[i] = nneigh / self._paras[i][0]
  
          # Then, bond orientational OPs based on spherical harmonics
          # according to Steinhardt et al., Phys. Rev. B, 28, 784-805, 1983.
          if self._boops:
              thetas = []
              phis = []
              for j, vec in enumerate(rijnorm):
  
                  # z is North pole --> theta between vec and (0, 0, 1)^T.
                  # Because vec is normalized, dot product is simply vec[2].
                  thetas.append(math.acos(max(-1.0, min(vec[2], 1.0))))
                  tmpphi = 0.0
  
                  # Compute phi only if it is not (almost) perfectly
                  # aligned with z-axis.
                  if vec[2] < left_of_unity and vec[2] > - (left_of_unity):
                      # x is prime meridian --> phi between projection of vec
                      # into x-y plane and (1, 0, 0)^T
                      tmpphi = math.acos(max(
                          -1.0,
                          min(vec[0] / (math.sqrt(
                              vec[0] * vec[0] + vec[1] * vec[1])),
                              1.0)))
                      if vec[1] < 0.0:
                          tmpphi = -tmpphi
                  phis.append(tmpphi)
  
              # Note that None flags that we have too few neighbors
              # for calculating BOOPS.
              for i, t in enumerate(self._types):
                  if t == "q2":
                      ops[i] = self.get_q2(thetas, phis) if len(
                          thetas) > 0 else None
                  elif t == "q4":
                      ops[i] = self.get_q4(thetas, phis) if len(
                          thetas) > 0 else None
                  elif t == "q6":
                      ops[i] = self.get_q6(thetas, phis) if len(
                          thetas) > 0 else None
  
          # Then, deal with the Shetty--Peters style OPs that are tailor-made
          # to recognize common structural motifs
          # (Shetty et al., J. Chem. Phys., 117, 4000-4009, 2002;
          #  Peters, J. Chem. Phys., 131, 244103, 2009;
          #  Zimmermann et al., J. Am. Chem. Soc., under revision, 2015).
          if self._geomops:
              gaussthetak = [0.0 for t in self._types]  # not used by all OPs
              ipi = 1.0 / pi
              piover2 = pi / 2.0
              tetangoverpi = math.acos(-1.0 / 3.0) * ipi
              itetangminuspihalfoverpi = 1.0 / (tetangoverpi - 0.5)
  
              for j in range(nneigh):  # Neighbor j is put to the North pole.
                  zaxis = rijnorm[j]
  
                  for k in range(nneigh):  # From neighbor k, we construct
                      if j != k:  # the prime meridian.
                          tmp = max(
                              -1.0, min(np.inner(zaxis, rijnorm[k]), 1.0))
                          thetak = math.acos(tmp)
                          xaxistmp = gramschmidt(rijnorm[k], zaxis)
                          if np.linalg.norm(xaxistmp) < very_small:
                              flag_xaxis = True
                          else:
                              xaxis = xaxistmp / np.linalg.norm(xaxistmp)
                              flag_xaxis = False
  
                          # Contributions of j-i-k angles, where i represents the central atom
                          # and j and k two of the neighbors.
                          for i, t in enumerate(self._types):
                              if t == "tet":
                                  tmp = self._paras[i][0] * (
                                      thetak * ipi - tetangoverpi)
                                  gaussthetak[i] = math.exp(-0.5 * tmp * tmp)
                              elif t == "oct":
                                  if thetak >= self._paras[i][0]:
                                      # k is south pole to j
                                      tmp = self._paras[i][1] * (
                                          thetak * ipi - 1.0)
                                      ops[i] += 3.0 * math.exp(-0.5 * tmp * tmp)
                              elif t == "bcc" and j < k:
                                  if thetak >= self._paras[i][0]:
                                      # k is south pole to j
                                      tmp = self._paras[i][1] * (
                                          thetak * ipi - 1.0)
                                      ops[i] += 6.0 * math.exp(-0.5 * tmp * tmp)
  
                          for m in range(nneigh):
                              if (m != j) and (m != k) and (not flag_xaxis):
                                  tmp = max(
                                      -1.0, min(np.inner(zaxis, rijnorm[m]), 1.0))
                                  thetam = math.acos(tmp)
                                  xtwoaxistmp = gramschmidt(rijnorm[m], zaxis)
                                  l = np.linalg.norm(xtwoaxistmp)
                                  if l < very_small:
                                      flag_xtwoaxis = True
                                  else:
                                      xtwoaxis = xtwoaxistmp / l
                                      phi = math.acos(max(
                                          -1.0,
                                          min(np.inner(xtwoaxis, xaxis), 1.0)))
                                      flag_xtwoaxis = False
  
                                  # Contributions of j-i-m angle and
                                  # angles between plane j-i-k and i-m vector.
                                  if not flag_xaxis and not flag_xtwoaxis:
                                      for i, t in enumerate(self._types):
                                          if t == "tet":
                                              tmp = self._paras[i][0] * (
                                                  thetam * ipi - tetangoverpi)
                                              ops[i] += gaussthetak[i] * math.exp(
                                                  -0.5 * tmp * tmp) * math.cos(
                                                  3.0 * phi)
                                          elif t == "oct":
                                              if thetak < self._paras[i][0] and \
                                                              thetam < \
                                                              self._paras[i][0]:
                                                  tmp = math.cos(2.0 * phi)
                                                  tmp2 = self._paras[i][2] * (
                                                      thetam * ipi - 0.5)
                                                  ops[i] += tmp * tmp * \
                                                            self._paras[i][4] * (
                                                                math.exp(
                                                                    -0.5 * tmp2 * tmp2) - \
                                                                self._paras[i][3])
                                          elif t == "bcc" and j < k:
                                              if thetak < self._paras[i][0]:
                                                  if thetak > piover2:
                                                      fac = 1.0
                                                  else:
                                                      fac = -1.0
                                                  tmp = (thetam - piover2) / (
                                                      19.47 * pi / 180.0)
                                                  ops[i] += fac * math.cos(
                                                      3.0 * phi) * \
                                                            1.6 * tmp * \
                                                            math.exp(
                                                                -0.5 * tmp * tmp)
  
              # Normalize Shetty--Peters style OPs.
              for i, t in enumerate(self._types):
                  if t == "tet":
                      ops[i] = ops[i] / 24.0 if nneigh > 2 else None
  
                  elif t == "oct":
                      ops[i] = ops[i] / 90.0 if nneigh > 2 else None
  
                  elif t == "bcc":
                      # Reassured 144 by pen-and-paper for perfect bcc
                      # structure (24 from i-j-k South pole contributions
                      # and 4 * 6 * 5 = 120 from i-j-k-m non-South
                      # pole-containing quadruples.
                      # Because qbcc has a separate South pole contribution
                      # as summand, it is sufficient to have 2 neighbors to
                      # obtain a configuration that is well-defined by
                      # yielding a contribution to qbcc via thetak alone:
                      # ==> nneigh > 1.
                      ops[i] = ops[i] / 144.0 if nneigh > 1 else None
  
          return ops
  