text: # coding: utf-8
  # Copyright (c) Pymatgen Development Team.
  # Distributed under the terms of the MIT License.
  
  """
  This module provides classes to define a phonon band structure.
  """
  
  import collections
  import numpy as np
  
  from monty.json import MSONable
  from pymatgen.core.structure import Structure
  from pymatgen.core.lattice import Lattice
  from pymatgen.electronic_structure.bandstructure import Kpoint
  
  
  def get_reasonable_repetitions(natoms):
      """
      Choose the number of repetitions
      according to the number of atoms in the system
      """
      if natoms < 4:
          return [3, 3, 3]
      if 4 <= natoms < 15:
          return [2, 2, 2]
      if 15 <= natoms < 50:
          return [2, 2, 1]
  
      return [1, 1, 1]
  
  
  def eigenvectors_from_displacements(disp, masses):
      """
      Calculate the eigenvectors from the atomic displacements
      """
      nphonons, natoms, ndirections = disp.shape
      sqrt_masses = np.sqrt(masses)
      return np.einsum("nax,a->nax", disp, sqrt_masses)
  
  
  def estimate_band_connection(prev_eigvecs, eigvecs, prev_band_order):
      """
      A function to order the phonon eigenvectors taken from phonopy
      """
      metric = np.abs(np.dot(prev_eigvecs.conjugate().T, eigvecs))
      connection_order = []
      for overlaps in metric:
          maxval = 0
          for i in reversed(range(len(metric))):
              val = overlaps[i]
              if i in connection_order:
                  continue
              if val > maxval:
                  maxval = val
                  maxindex = i
          connection_order.append(maxindex)
  
      band_order = [connection_order[x] for x in prev_band_order]
  
      return band_order
  
  
  class PhononBandStructure(MSONable):
      """
      This is the most generic phonon band structure data possible
      it's defined by a list of qpoints + frequencies for each of them.
      Additional information may be given for frequencies at Gamma, where
      non-analytical contribution may be taken into account.
      """
  
      def __init__(self, qpoints, frequencies, lattice, nac_frequencies=None,
                   eigendisplacements=None, nac_eigendisplacements=None,
                   labels_dict=None, coords_are_cartesian=False,
                   structure=None):
          """
          Args:
              qpoints: list of qpoint as numpy arrays, in frac_coords of the
                  given lattice by default
              frequencies: list of phonon frequencies in THz as a numpy array with shape
                  (3*len(structure), len(qpoints)). The First index of the array
                  refers to the band and the second to the index of the qpoint.
              lattice: The reciprocal lattice as a pymatgen Lattice object.
                  Pymatgen uses the physics convention of reciprocal lattice vectors
                  WITH a 2*pi coefficient.
              nac_frequencies: Frequencies with non-analytical contributions at Gamma in THz.
                  A list of tuples. The first element of each tuple should be a list
                  defining the direction (not necessarily a versor, will be normalized
                  internally). The second element containing the 3*len(structure)
                  phonon frequencies with non-analytical correction for that direction.
              eigendisplacements: the phonon eigendisplacements associated to the
                  frequencies in cartesian coordinates. A numpy array of complex
                  numbers with shape (3*len(structure), len(qpoints), len(structure), 3).
                  he First index of the array refers to the band, the second to the index
                  of the qpoint, the third to the atom in the structure and the fourth
                  to the cartesian coordinates.
              nac_eigendisplacements: the phonon eigendisplacements associated to the
                  non-analytical frequencies in nac_frequencies in cartesian coordinates.
                  A list of tuples. The first element of each tuple should be a list
                  defining the direction. The second element containing a numpy array of
                  complex numbers with shape (3*len(structure), len(structure), 3).
              labels_dict: (dict) of {} this links a qpoint (in frac coords or
                  cartesian coordinates depending on the coords) to a label.
              coords_are_cartesian: Whether the qpoint coordinates are cartesian.
              structure: The crystal structure (as a pymatgen Structure object)
                  associated with the band structure. This is needed if we
                  provide projections to the band structure
          """
          self.lattice_rec = lattice
          self.qpoints = []
          self.labels_dict = {}
          self.structure = structure
          if eigendisplacements is None:
              eigendisplacements = np.array([])
          self.eigendisplacements = eigendisplacements
          if labels_dict is None:
              labels_dict = {}
  
          for q in qpoints:
              # let see if this qpoint has been assigned a label
              label = None
              for c in labels_dict:
                  if np.linalg.norm(q - np.array(labels_dict[c])) < 0.0001:
                      label = c
                      self.labels_dict[label] = Kpoint(
                          q, lattice, label=label,
                          coords_are_cartesian=coords_are_cartesian)
              self.qpoints.append(
                  Kpoint(q, lattice, label=label,
                         coords_are_cartesian=coords_are_cartesian))
          self.bands = frequencies
          self.nb_bands = len(self.bands)
          self.nb_qpoints = len(self.qpoints)
  
          # normalize directions for nac_frequencies and nac_eigendisplacements
          self.nac_frequencies = []
          self.nac_eigendisplacements = []
          if nac_frequencies is not None:
              for t in nac_frequencies:
                  self.nac_frequencies.append(([i / np.linalg.norm(t[0]) for i in t[0]], t[1]))
          if nac_eigendisplacements is not None:
              for t in nac_eigendisplacements:
                  self.nac_eigendisplacements.append(([i / np.linalg.norm(t[0]) for i in t[0]], t[1]))
  
      def min_freq(self):
          """
          Returns the point where the minimum frequency is reached and its value
          """
          i = np.unravel_index(np.argmin(self.bands), self.bands.shape)
  
          return self.qpoints[i[1]], self.bands[i]
  
      def has_imaginary_freq(self, tol=1e-5):
          """
          True if imaginary frequencies are present in the BS.
          """
  
          return self.min_freq()[1] + tol < 0
  
      @property
      def has_nac(self):
          """
          True if nac_frequencies are present.
          """
          return len(self.nac_frequencies) > 0
  
      @property
      def has_eigendisplacements(self):
          """
          True if eigendisplacements are present.
          """
          return len(self.eigendisplacements) > 0
  
      def get_nac_frequencies_along_dir(self, direction):
          """
          Returns the nac_frequencies for the given direction (not necessarily a versor).
          None if the direction is not present or nac_frequencies has not been calculated.
  
          Args:
              direction: the direction as a list of 3 elements
          Returns:
              the frequencies as a numpy array o(3*len(structure), len(qpoints)).
              None if not found.
          """
          versor = [i / np.linalg.norm(direction) for i in direction]
          for d, f in self.nac_frequencies:
              if np.allclose(versor, d):
                  return f
  
          return None
  
      def get_nac_eigendisplacements_along_dir(self, direction):
          """
          Returns the nac_eigendisplacements for the given direction (not necessarily a versor).
          None if the direction is not present or nac_eigendisplacements has not been calculated.
  
          Args:
              direction: the direction as a list of 3 elements
          Returns:
              the eigendisplacements as a numpy array of complex numbers with shape
              (3*len(structure), len(structure), 3). None if not found.
          """
          versor = [i / np.linalg.norm(direction) for i in direction]
          for d, e in self.nac_eigendisplacements:
              if np.allclose(versor, d):
                  return e
  
          return None
  
      def asr_breaking(self, tol_eigendisplacements=1e-5):
          """
          Returns the breaking of the acoustic sum rule for the three acoustic modes,
          if Gamma is present. None otherwise.
          If eigendisplacements are available they are used to determine the acoustic
          modes: selects the bands corresponding  to the eigendisplacements that
          represent to a translation within tol_eigendisplacements. If these are not
          identified or eigendisplacements are missing the first 3 modes will be used
          (indices [0:3]).
          """
  
          for i in range(self.nb_qpoints):
              if np.allclose(self.qpoints[i].frac_coords, (0, 0, 0)):
  
                  if self.has_eigendisplacements:
                      acoustic_modes_index = []
                      for j in range(self.nb_bands):
                          eig = self.eigendisplacements[j][i]
                          if np.max(np.abs(eig[1:] - eig[:1])) < tol_eigendisplacements:
                              acoustic_modes_index.append(j)
                      # if acoustic modes are not correctly identified return use
                      # the first three modes
                      if len(acoustic_modes_index) != 3:
                          acoustic_modes_index = [0, 1, 2]
                      return self.bands[acoustic_modes_index, i]
  
                  return self.bands[:3, i]
  
          return None
  
      def as_dict(self):
          """
          :return: MSONable dict
          """
          d = {"@module": self.__class__.__module__,
               "@class": self.__class__.__name__,
               "lattice_rec": self.lattice_rec.as_dict(),
               "qpoints": []}
          # qpoints are not Kpoint objects dicts but are frac coords.Tthis makes
          # the dict smaller and avoids the repetition of the lattice
          for q in self.qpoints:
              d["qpoints"].append(q.as_dict()["fcoords"])
          d["bands"] = self.bands.tolist()
          d['labels_dict'] = {}
          for c in self.labels_dict:
              d['labels_dict'][c] = self.labels_dict[c].as_dict()['fcoords']
          # split the eigendisplacements to real and imaginary part for serialization
          d['eigendisplacements'] = dict(real=np.real(self.eigendisplacements).tolist(),
                                         imag=np.imag(self.eigendisplacements).tolist())
          d['nac_eigendisplacements'] = [(direction, dict(real=np.real(e).tolist(), imag=np.imag(e).tolist()))
                                         for direction, e in self.nac_eigendisplacements]
          d['nac_frequencies'] = [(direction, f.tolist()) for direction, f in self.nac_frequencies]
  
          if self.structure:
              d['structure'] = self.structure.as_dict()
  
          return d
  
      @classmethod
      def from_dict(cls, d):
          """
          :param d: Dict representation
          :return: PhononBandStructure
          """
          lattice_rec = Lattice(d['lattice_rec']['matrix'])
          eigendisplacements = np.array(d['eigendisplacements']['real']) + np.array(d['eigendisplacements']['imag']) * 1j
          nac_eigendisplacements = [(direction, np.array(e['real']) + np.array(e['imag']) * 1j)
                                    for direction, e in d['nac_eigendisplacements']]
          nac_frequencies = [(direction, np.array(f)) for direction, f in d['nac_frequencies']]
          structure = Structure.from_dict(d['structure']) if 'structure' in d else None
          return cls(d['qpoints'], np.array(d['bands']), lattice_rec, nac_frequencies, eigendisplacements,
                     nac_eigendisplacements, d['labels_dict'], structure=structure)
  
  
  class PhononBandStructureSymmLine(PhononBandStructure):
      r"""
      This object stores phonon band structures along selected (symmetry) lines in the
      Brillouin zone. We call the different symmetry lines (ex: \\Gamma to Z)
      "branches".
      """
  
      def __init__(self, qpoints, frequencies, lattice, has_nac=False, eigendisplacements=None,
                   labels_dict=None, coords_are_cartesian=False, structure=None):
          """
          Args:
              qpoints: list of qpoints as numpy arrays, in frac_coords of the
                  given lattice by default
              frequencies: list of phonon frequencies in eV as a numpy array with shape
                  (3*len(structure), len(qpoints))
              lattice: The reciprocal lattice as a pymatgen Lattice object.
                  Pymatgen uses the physics convention of reciprocal lattice vectors
                  WITH a 2*pi coefficient
              has_nac: specify if the band structure has been produced taking into account
                  non-analytical corrections at Gamma. If True frequenciens at Gamma from
                  diffent directions will be stored in naf. Default False.
              eigendisplacements: the phonon eigendisplacements associated to the
                  frequencies in cartesian coordinates. A numpy array of complex
                  numbers with shape (3*len(structure), len(qpoints), len(structure), 3).
                  he First index of the array refers to the band, the second to the index
                  of the qpoint, the third to the atom in the structure and the fourth
                  to the cartesian coordinates.
              labels_dict: (dict) of {} this links a qpoint (in frac coords or
                  cartesian coordinates depending on the coords) to a label.
              coords_are_cartesian: Whether the qpoint coordinates are cartesian.
              structure: The crystal structure (as a pymatgen Structure object)
                  associated with the band structure. This is needed if we
                  provide projections to the band structure
          """
  
          super().__init__(
              qpoints, frequencies, lattice, None, eigendisplacements,
              None, labels_dict, coords_are_cartesian, structure)
  
          self.distance = []
          self.branches = []
          one_group = []
          branches_tmp = []
  
          # get labels and distance for each qpoint
          previous_qpoint = self.qpoints[0]
          previous_distance = 0.0
          previous_label = self.qpoints[0].label
          for i in range(self.nb_qpoints):
              label = self.qpoints[i].label
              if label is not None and previous_label is not None:
                  self.distance.append(previous_distance)
              else:
                  self.distance.append(
                      np.linalg.norm(self.qpoints[i].cart_coords -
                                     previous_qpoint.cart_coords) +
                      previous_distance)
              previous_qpoint = self.qpoints[i]
              previous_distance = self.distance[i]
              if label:
                  if previous_label:
                      if len(one_group) != 0:
                          branches_tmp.append(one_group)
                      one_group = []
              previous_label = label
              one_group.append(i)
  
          if len(one_group) != 0:
              branches_tmp.append(one_group)
          for b in branches_tmp:
              self.branches.append(
                  {"start_index": b[0], "end_index": b[-1],
                   "name": str(self.qpoints[b[0]].label) + "-" + str(self.qpoints[b[-1]].label)})
  
          # extract the frequencies with non-analytical contribution at gamma
          if has_nac:
              naf = []
              nac_eigendisplacements = []
              for i in range(self.nb_qpoints):
                  # get directions with nac irrespectively of the label_dict. NB: with labels
                  # the gamma point is expected to appear twice consecutively.
                  if np.allclose(qpoints[i], (0, 0, 0)):
                      if i > 0 and not np.allclose(qpoints[i - 1], (0, 0, 0)):
                          q_dir = self.qpoints[i - 1]
                          direction = q_dir.frac_coords / np.linalg.norm(q_dir.frac_coords)
                          naf.append((direction, frequencies[:, i]))
                          if self.has_eigendisplacements:
                              nac_eigendisplacements.append((direction, eigendisplacements[:, i]))
                      if i < len(qpoints) - 1 and not np.allclose(qpoints[i + 1], (0, 0, 0)):
                          q_dir = self.qpoints[i + 1]
                          direction = q_dir.frac_coords / np.linalg.norm(q_dir.frac_coords)
                          naf.append((direction, frequencies[:, i]))
                          if self.has_eigendisplacements:
                              nac_eigendisplacements.append((direction, eigendisplacements[:, i]))
  
              self.nac_frequencies = np.array(naf)
              self.nac_eigendisplacements = np.array(nac_eigendisplacements)
  
      def get_equivalent_qpoints(self, index):
          """
          Returns the list of qpoint indices equivalent (meaning they are the
          same frac coords) to the given one.
  
          Args:
              index: the qpoint index
  
          Returns:
              a list of equivalent indices
  
          TODO: now it uses the label we might want to use coordinates instead
          (in case there was a mislabel)
          """
          # if the qpoint has no label it can"t have a repetition along the band
          # structure line object
  
          if self.qpoints[index].label is None:
              return [index]
  
          list_index_qpoints = []
          for i in range(self.nb_qpoints):
              if self.qpoints[i].label == self.qpoints[index].label:
                  list_index_qpoints.append(i)
  
          return list_index_qpoints
  
      def get_branch(self, index):
          r"""
          Returns in what branch(es) is the qpoint. There can be several
          branches.
  
          Args:
              index: the qpoint index
  
          Returns:
              A list of dictionaries [{"name","start_index","end_index","index"}]
              indicating all branches in which the qpoint is. It takes into
              account the fact that one qpoint (e.g., \\Gamma) can be in several
              branches
          """
          to_return = []
          for i in self.get_equivalent_qpoints(index):
              for b in self.branches:
                  if b["start_index"] <= i <= b["end_index"]:
                      to_return.append({"name": b["name"],
                                        "start_index": b["start_index"],
                                        "end_index": b["end_index"],
                                        "index": i})
          return to_return
  
      def write_phononwebsite(self, filename):
          """
          Write a json file for the phononwebsite:
          http://henriquemiranda.github.io/phononwebsite
          """
          import json
          with open(filename, 'w') as f:
              json.dump(self.as_phononwebsite(), f)
  
      def as_phononwebsite(self):
          """
          Return a dictionary with the phononwebsite format:
          http://henriquemiranda.github.io/phononwebsite
          """
          d = {}
  
          # define the lattice
          d["lattice"] = self.structure.lattice._matrix.tolist()
  
          # define atoms
          atom_pos_car = []
          atom_pos_red = []
          atom_types = []
          for site in self.structure.sites:
              atom_pos_car.append(site.coords.tolist())
              atom_pos_red.append(site.frac_coords.tolist())
              atom_types.append(site.species_string)
  
          # default for now
          d["repetitions"] = get_reasonable_repetitions(len(atom_pos_car))
  
          d["natoms"] = len(atom_pos_car)
          d["atom_pos_car"] = atom_pos_car
          d["atom_pos_red"] = atom_pos_red
          d["atom_types"] = atom_types
          d["atom_numbers"] = self.structure.atomic_numbers
          d["formula"] = self.structure.formula
          d["name"] = self.structure.formula
  
          # get qpoints
          qpoints = []
          for q in self.qpoints:
              qpoints.append(list(q.frac_coords))
          d["qpoints"] = qpoints
  
          # get labels
          hsq_dict = collections.OrderedDict()
          for nq, q in enumerate(self.qpoints):
              if q.label is not None:
                  hsq_dict[nq] = q.label
  
          # get distances
          dist = 0
          nqstart = 0
          distances = [dist]
          line_breaks = []
          for nq in range(1, len(qpoints)):
              q1 = np.array(qpoints[nq])
              q2 = np.array(qpoints[nq - 1])
              # detect jumps
              if (nq in hsq_dict) and (nq - 1 in hsq_dict):
                  if hsq_dict[nq] != hsq_dict[nq - 1]:
                      hsq_dict[nq - 1] += "|" + hsq_dict[nq]
                  del hsq_dict[nq]
                  line_breaks.append((nqstart, nq))
                  nqstart = nq
              else:
                  dist += np.linalg.norm(q1 - q2)
              distances.append(dist)
          line_breaks.append((nqstart, len(qpoints)))
          d["distances"] = distances
          d["line_breaks"] = line_breaks
          d["highsym_qpts"] = list(hsq_dict.items())
  
          # eigenvalues
          thz2cm1 = 33.35641
          bands = self.bands.copy() * thz2cm1
          d["eigenvalues"] = bands.T.tolist()
  
          # eigenvectors
          eigenvectors = self.eigendisplacements.copy()
          eigenvectors /= np.linalg.norm(eigenvectors[0, 0])
          eigenvectors = eigenvectors.swapaxes(0, 1)
          eigenvectors = np.array([eigenvectors.real, eigenvectors.imag])
          eigenvectors = np.rollaxis(eigenvectors, 0, 5)
          d["vectors"] = eigenvectors.tolist()
  
          return d
  
      def band_reorder(self):
          """
          Re-order the eigenvalues according to the similarity of the eigenvectors
          """
          eiv = self.eigendisplacements
          eig = self.bands
  
          nphonons, nqpoints = self.bands.shape
          order = np.zeros([nqpoints, nphonons], dtype=int)
          order[0] = np.array(range(nphonons))
  
          # get the atomic masses
          atomic_masses = [site.specie.atomic_mass for site in self.structure.sites]
  
          # get order
          for nq in range(1, nqpoints):
              old_eiv = eigenvectors_from_displacements(eiv[:, nq - 1], atomic_masses)
              new_eiv = eigenvectors_from_displacements(eiv[:, nq], atomic_masses)
              order[nq] = estimate_band_connection(old_eiv.reshape([nphonons, nphonons]).T,
                                                   new_eiv.reshape([nphonons, nphonons]).T,
                                                   order[nq - 1])
  
          # reorder
          for nq in range(1, nqpoints):
              eivq = eiv[:, nq]
              eigq = eig[:, nq]
              eiv[:, nq] = eivq[order[nq]]
              eig[:, nq] = eigq[order[nq]]
  
      def as_dict(self):
          """
          :return: MSONable dict
          """
          d = super().as_dict()
          # remove nac_frequencies and nac_eigendisplacements as they are reconstructed
          # in the __init__ when the dict is deserialized
          nac_frequencies = d.pop('nac_frequencies')
          d.pop('nac_eigendisplacements')
          d['has_nac'] = len(nac_frequencies) > 0
          return d
  
      @classmethod
      def from_dict(cls, d):
          """
          :param d: Dict representation
          :return: PhononBandStructureSummLine
          """
          lattice_rec = Lattice(d['lattice_rec']['matrix'])
          eigendisplacements = np.array(d['eigendisplacements']['real']) + np.array(d['eigendisplacements']['imag']) * 1j
          structure = Structure.from_dict(d['structure']) if 'structure' in d else None
          return cls(d['qpoints'], np.array(d['bands']), lattice_rec, d['has_nac'], eigendisplacements,
                     d['labels_dict'], structure=structure)
  