code: # coding: utf-8
  # Copyright (c) Pymatgen Development Team.
  # Distributed under the terms of the MIT License.
  
  from __future__ import division, unicode_literals
  
  import warnings
  import ruamel.yaml as yaml
  import os
  
  """
  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"
  
  
  from math import pi, acos
  import numpy as np
  import itertools
  import collections
  
  from monty.dev import deprecated
  
  from warnings import warn
  from scipy.spatial import Voronoi
  from pymatgen import PeriodicSite
  from pymatgen import Element, Specie, Composition
  from pymatgen.util.num import abs_cap
  from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
  from pymatgen.core.surface import SlabGenerator
  from pymatgen.analysis.local_env import VoronoiNN, JmolNN
  
  
  def average_coordination_number(structures, freq=10):
      """
      Calculates the ensemble averaged Voronoi coordination numbers
      of a list of Structures using VoronoiNN.
      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 spec in structures[0].composition.as_dict().keys():
          coordination_numbers[spec] = 0.0
      count = 0
      for t in range(len(structures)):
          if t % freq != 0:
              continue
          count += 1
          vnn = VoronoiNN()
          for atom in range(len(structures[0])):
              cn = vnn.get_cn(structures[t], atom, use_weights=True)
              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 * 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(acos(abs_cap(v)))
      phi = sum(vals)
      return phi + (3 - len(r)) * pi
  
  
  def get_max_bond_lengths(structure, el_radius_updates=None):
      """
      Provides max bond length estimates for a structure based on the JMol
      table and algorithms.
      
      Args:
          structure: (structure)
          el_radius_updates: (dict) symbol->float to update atomic radii
      
      Returns: (dict) - (Element1, Element2) -> float. The two elements are 
          ordered by Z.
      """
      #jmc = JMolCoordFinder(el_radius_updates)
      jmnn = JmolNN(el_radius_updates=el_radius_updates)
  
      bonds_lens = {}
      els = sorted(structure.composition.elements, key=lambda x: x.Z)
  
      for i1 in range(len(els)):
          for i2 in range(len(els) - i1):
              bonds_lens[els[i1], els[i1 + i2]] = jmnn.get_max_bond_distance(
                  els[i1].symbol, els[i1 + i2].symbol)
  
      return bonds_lens
  
  
  @deprecated(message=("find_dimension has been moved to"
                       "pymatgen.analysis.dimensionality.get_dimensionality_gorai"
                       " this method will be removed in pymatgen v2019.1.1."))
  def get_dimensionality(structure, max_hkl=2, el_radius_updates=None,
                         min_slab_size=5, min_vacuum_size=5,
                         standardize=True, bonds=None):
      """
      This method returns whether a structure is 3D, 2D (layered), or 1D (linear
      chains or molecules) according to the algorithm published in Gorai, P.,
      Toberer, E. & Stevanovic, V. Computational Identification of Promising
      Thermoelectric Materials Among Known Quasi-2D Binary Compounds. J. Mater.
      Chem. A 2, 4136 (2016).
  
      Note that a 1D structure detection might indicate problems in the bonding
      algorithm, particularly for ionic crystals (e.g., NaCl)
  
      Users can change the behavior of bonds detection by passing either
      el_radius_updates to update atomic radii for auto-detection of max bond
      distances, or bonds to explicitly specify max bond distances for atom pairs.
      Note that if you pass both, el_radius_updates are ignored.
  
      Args:
          structure: (Structure) structure to analyze dimensionality for
          max_hkl: (int) max index of planes to look for layers
          el_radius_updates: (dict) symbol->float to update atomic radii
          min_slab_size: (float) internal surface construction parameter
          min_vacuum_size: (float) internal surface construction parameter
          standardize (bool): whether to standardize the structure before
              analysis. Set to False only if you already have the structure in a
              convention where layers / chains will be along low <hkl> indexes.
          bonds ({(specie1, specie2): max_bond_dist}: bonds are
                  specified as a dict of tuples: float of specie1, specie2
                  and the max bonding distance. For example, PO4 groups may be
                  defined as {("P", "O"): 3}.
  
      Returns: (int) the dimensionality of the structure - 1 (molecules/chains),
          2 (layered), or 3 (3D)
  
      """
      if standardize:
          structure = SpacegroupAnalyzer(structure). \
              get_conventional_standard_structure()
  
      if not bonds:
          bonds = get_max_bond_lengths(structure, el_radius_updates)
  
      num_surfaces = 0
      for h in range(max_hkl):
          for k in range(max_hkl):
              for l in range(max_hkl):
                  if max([h, k, l]) > 0 and num_surfaces < 2:
                      sg = SlabGenerator(structure, (h, k, l),
                                         min_slab_size=min_slab_size,
                                         min_vacuum_size=min_vacuum_size)
                      slabs = sg.get_slabs(bonds)
                      for _ in slabs:
                          num_surfaces += 1
  
      return 3 - min(num_surfaces, 2)
  
  
  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"
  
  
  
apis: numpy.sum numpy.any numpy.cross numpy.fill_diagonal scipy.spatial.Voronoi matplotlib.pyplot.figure numpy.reshape matplotlib.pyplot.title matplotlib.pyplot.barh numpy.where numpy.mean numpy.ceil numpy.zeros numpy.max numpy.linalg.norm matplotlib.pyplot.grid numpy.array numpy.dot matplotlib.pyplot.yticks matplotlib.pyplot.xlabel