Source code for ase.spacegroup.spacegroup

# Copyright (C) 2010, Jesper Friis
# (see accompanying license files for details).

"""Definition of the Spacegroup class.

This module only depends on NumPy and the space group database.
"""

import os
import warnings
from functools import total_ordering

import numpy as np

__all__ = ['Spacegroup']


class SpacegroupError(Exception):
    """Base exception for the spacegroup module."""
    pass


class SpacegroupNotFoundError(SpacegroupError):
    """Raised when given space group cannot be found in data base."""
    pass


class SpacegroupValueError(SpacegroupError):
    """Raised when arguments have invalid value."""
    pass


[docs]@total_ordering class Spacegroup: """A space group class. The instances of Spacegroup describes the symmetry operations for the given space group. Example: >>> from ase.spacegroup import Spacegroup >>> >>> sg = Spacegroup(225) >>> print('Space group', sg.no, sg.symbol) Space group 225 F m -3 m >>> sg.scaled_primitive_cell array([[ 0. , 0.5, 0.5], [ 0.5, 0. , 0.5], [ 0.5, 0.5, 0. ]]) >>> sites, kinds = sg.equivalent_sites([[0,0,0]]) >>> sites array([[ 0. , 0. , 0. ], [ 0. , 0.5, 0.5], [ 0.5, 0. , 0.5], [ 0.5, 0.5, 0. ]]) """ no = property( lambda self: self._no, doc='Space group number in International Tables of Crystallography.') symbol = property( lambda self: self._symbol, doc='Hermann-Mauguin (or international) symbol for the space group.') setting = property( lambda self: self._setting, doc='Space group setting. Either one or two.') lattice = property( lambda self: self._symbol[0], doc="""Lattice type: P primitive I body centering, h+k+l=2n F face centering, h,k,l all odd or even A,B,C single face centering, k+l=2n, h+l=2n, h+k=2n R rhombohedral centering, -h+k+l=3n (obverse); h-k+l=3n (reverse) """) centrosymmetric = property( lambda self: self._centrosymmetric, doc='Whether a center of symmetry exists.') scaled_primitive_cell = property( lambda self: self._scaled_primitive_cell, doc='Primitive cell in scaled coordinates as a matrix with the ' 'primitive vectors along the rows.') reciprocal_cell = property( lambda self: self._reciprocal_cell, doc='Tree Miller indices that span all kinematically non-forbidden ' 'reflections as a matrix with the Miller indices along the rows.') nsubtrans = property( lambda self: len(self._subtrans), doc='Number of cell-subtranslation vectors.') def _get_nsymop(self): """Returns total number of symmetry operations.""" if self.centrosymmetric: return 2 * len(self._rotations) * len(self._subtrans) else: return len(self._rotations) * len(self._subtrans) nsymop = property(_get_nsymop, doc='Total number of symmetry operations.') subtrans = property( lambda self: self._subtrans, doc='Translations vectors belonging to cell-sub-translations.') rotations = property( lambda self: self._rotations, doc='Symmetry rotation matrices. The invertions are not included ' 'for centrosymmetrical crystals.') translations = property( lambda self: self._translations, doc='Symmetry translations. The invertions are not included ' 'for centrosymmetrical crystals.') def __init__(self, spacegroup, setting=1, datafile=None): """Returns a new Spacegroup instance. Parameters: spacegroup : int | string | Spacegroup instance The space group number in International Tables of Crystallography or its Hermann-Mauguin symbol. E.g. spacegroup=225 and spacegroup='F m -3 m' are equivalent. setting : 1 | 2 Some space groups have more than one setting. `setting` determines Which of these should be used. datafile : None | string Path to database file. If `None`, the the default database will be used. """ if isinstance(spacegroup, Spacegroup): for k, v in spacegroup.__dict__.items(): setattr(self, k, v) return if not datafile: datafile = get_datafile() f = open(datafile, 'r') try: _read_datafile(self, spacegroup, setting, f) finally: f.close() def __repr__(self): return 'Spacegroup(%d, setting=%d)' % (self.no, self.setting) def todict(self): return {'number': self.no, 'setting': self.setting} def __str__(self): """Return a string representation of the space group data in the same format as found the database.""" retval = [] # no, symbol retval.append('%-3d %s\n' % (self.no, self.symbol)) # setting retval.append(' setting %d\n' % (self.setting)) # centrosymmetric retval.append(' centrosymmetric %d\n' % (self.centrosymmetric)) # primitive vectors retval.append(' primitive vectors\n') for i in range(3): retval.append(' ') for j in range(3): retval.append(' %13.10f' % (self.scaled_primitive_cell[i, j])) retval.append('\n') # primitive reciprocal vectors retval.append(' reciprocal vectors\n') for i in range(3): retval.append(' ') for j in range(3): retval.append(' %3d' % (self.reciprocal_cell[i, j])) retval.append('\n') # sublattice retval.append(' %d subtranslations\n' % self.nsubtrans) for i in range(self.nsubtrans): retval.append(' ') for j in range(3): retval.append(' %13.10f' % (self.subtrans[i, j])) retval.append('\n') # symmetry operations nrot = len(self.rotations) retval.append(' %d symmetry operations (rot+trans)\n' % nrot) for i in range(nrot): retval.append(' ') for j in range(3): retval.append(' ') for k in range(3): retval.append(' %2d' % (self.rotations[i, j, k])) retval.append(' ') for j in range(3): retval.append(' %13.10f' % self.translations[i, j]) retval.append('\n') retval.append('\n') return ''.join(retval) def __eq__(self, other): return self.no == other.no and self.setting == other.setting def __ne__(self, other): return not self.__eq__(other) def __lt__(self, other): return self.no < other.no or ( self.no == other.no and self.setting < other.setting) def __index__(self): return self.no __int__ = __index__ def get_symop(self): """Returns all symmetry operations (including inversions and subtranslations) as a sequence of (rotation, translation) tuples.""" symop = [] parities = [1] if self.centrosymmetric: parities.append(-1) for parity in parities: for subtrans in self.subtrans: for rot, trans in zip(self.rotations, self.translations): newtrans = np.mod(trans + subtrans, 1) symop.append((parity * rot, newtrans)) return symop def get_op(self): """Returns all symmetry operations (including inversions and subtranslations), but unlike get_symop(), they are returned as two ndarrays.""" if self.centrosymmetric: rot = np.tile(np.vstack((self.rotations, -self.rotations)), (self.nsubtrans, 1, 1)) trans = np.tile(np.vstack((self.translations, -self.translations)), (self.nsubtrans, 1)) trans += np.repeat(self.subtrans, 2 * len(self.rotations), axis=0) trans = np.mod(trans, 1) else: rot = np.tile(self.rotations, (self.nsubtrans, 1, 1)) trans = np.tile(self.translations, (self.nsubtrans, 1)) trans += np.repeat(self.subtrans, len(self.rotations), axis=0) trans = np.mod(trans, 1) return rot, trans def get_rotations(self): """Return all rotations, including inversions for centrosymmetric crystals.""" if self.centrosymmetric: return np.vstack((self.rotations, -self.rotations)) else: return self.rotations def equivalent_reflections(self, hkl): """Return all equivalent reflections to the list of Miller indices in hkl. Example: >>> from ase.spacegroup import Spacegroup >>> sg = Spacegroup(225) # fcc >>> sg.equivalent_reflections([[0, 0, 2]]) array([[ 0, 0, -2], [ 0, -2, 0], [-2, 0, 0], [ 2, 0, 0], [ 0, 2, 0], [ 0, 0, 2]]) """ hkl = np.array(hkl, dtype='int', ndmin=2) rot = self.get_rotations() n, nrot = len(hkl), len(rot) R = rot.transpose(0, 2, 1).reshape((3 * nrot, 3)).T refl = np.dot(hkl, R).reshape((n * nrot, 3)) ind = np.lexsort(refl.T) refl = refl[ind] diff = np.diff(refl, axis=0) mask = np.any(diff, axis=1) return np.vstack((refl[:-1][mask], refl[-1, :])) def equivalent_lattice_points(self, uvw): """Return all lattice points equivalent to any of the lattice points in `uvw` with respect to rotations only. Only equivalent lattice points that conserves the distance to origo are included in the output (making this a kind of real space version of the equivalent_reflections() method). Example: >>> from ase.spacegroup import Spacegroup >>> sg = Spacegroup(225) # fcc >>> sg.equivalent_lattice_points([[0, 0, 2]]) array([[ 0, 0, -2], [ 0, -2, 0], [-2, 0, 0], [ 2, 0, 0], [ 0, 2, 0], [ 0, 0, 2]]) """ uvw = np.array(uvw, ndmin=2) rot = self.get_rotations() n, nrot = len(uvw), len(rot) directions = np.dot(uvw, rot).reshape((n * nrot, 3)) ind = np.lexsort(directions.T) directions = directions[ind] diff = np.diff(directions, axis=0) mask = np.any(diff, axis=1) return np.vstack((directions[:-1][mask], directions[-1:])) def symmetry_normalised_reflections(self, hkl): """Returns an array of same size as *hkl*, containing the corresponding symmetry-equivalent reflections of lowest indices. Example: >>> from ase.spacegroup import Spacegroup >>> sg = Spacegroup(225) # fcc >>> sg.symmetry_normalised_reflections([[2, 0, 0], [0, 2, 0]]) array([[ 0, 0, -2], [ 0, 0, -2]]) """ hkl = np.array(hkl, dtype=int, ndmin=2) normalised = np.empty(hkl.shape, int) R = self.get_rotations().transpose(0, 2, 1) for i, g in enumerate(hkl): gsym = np.dot(R, g) j = np.lexsort(gsym.T)[0] normalised[i, :] = gsym[j] return normalised def unique_reflections(self, hkl): """Returns a subset *hkl* containing only the symmetry-unique reflections. Example: >>> from ase.spacegroup import Spacegroup >>> sg = Spacegroup(225) # fcc >>> sg.unique_reflections([[ 2, 0, 0], ... [ 0, -2, 0], ... [ 2, 2, 0], ... [ 0, -2, -2]]) array([[2, 0, 0], [2, 2, 0]]) """ hkl = np.array(hkl, dtype=int, ndmin=2) hklnorm = self.symmetry_normalised_reflections(hkl) perm = np.lexsort(hklnorm.T) iperm = perm.argsort() xmask = np.abs(np.diff(hklnorm[perm], axis=0)).any(axis=1) mask = np.concatenate(([True], xmask)) imask = mask[iperm] return hkl[imask] def equivalent_sites(self, scaled_positions, onduplicates='error', symprec=1e-3, occupancies=None): """Returns the scaled positions and all their equivalent sites. Parameters: scaled_positions: list | array List of non-equivalent sites given in unit cell coordinates. occupancies: list | array, optional (default=None) List of occupancies corresponding to the respective sites. onduplicates : 'keep' | 'replace' | 'warn' | 'error' Action if `scaled_positions` contain symmetry-equivalent positions of full occupancy: 'keep' ignore additional symmetry-equivalent positions 'replace' replace 'warn' like 'keep', but issue an UserWarning 'error' raises a SpacegroupValueError symprec: float Minimum "distance" betweed two sites in scaled coordinates before they are counted as the same site. Returns: sites: array A NumPy array of equivalent sites. kinds: list A list of integer indices specifying which input site is equivalent to the corresponding returned site. Example: >>> from ase.spacegroup import Spacegroup >>> sg = Spacegroup(225) # fcc >>> sites, kinds = sg.equivalent_sites([[0, 0, 0], [0.5, 0.0, 0.0]]) >>> sites array([[ 0. , 0. , 0. ], [ 0. , 0.5, 0.5], [ 0.5, 0. , 0.5], [ 0.5, 0.5, 0. ], [ 0.5, 0. , 0. ], [ 0. , 0.5, 0. ], [ 0. , 0. , 0.5], [ 0.5, 0.5, 0.5]]) >>> kinds [0, 0, 0, 0, 1, 1, 1, 1] """ kinds = [] sites = [] scaled = np.array(scaled_positions, ndmin=2) for kind, pos in enumerate(scaled): for rot, trans in self.get_symop(): site = np.mod(np.dot(rot, pos) + trans, 1.) if not sites: sites.append(site) kinds.append(kind) continue t = site - sites mask = np.all((abs(t) < symprec) | (abs(abs(t) - 1.0) < symprec), axis=1) if np.any(mask): inds = np.argwhere(mask).flatten() for ind in inds: # then we would just add the same thing again -> skip if kinds[ind] == kind: pass elif onduplicates == 'keep': pass elif onduplicates == 'replace': kinds[ind] = kind elif onduplicates == 'warn': warnings.warn('scaled_positions %d and %d ' 'are equivalent' % (kinds[ind], kind)) elif onduplicates == 'error': raise SpacegroupValueError( 'scaled_positions %d and %d are equivalent' % ( kinds[ind], kind)) else: raise SpacegroupValueError( 'Argument "onduplicates" must be one of: ' '"keep", "replace", "warn" or "error".') else: sites.append(site) kinds.append(kind) return np.array(sites), kinds def symmetry_normalised_sites(self, scaled_positions, map_to_unitcell=True): """Returns an array of same size as *scaled_positions*, containing the corresponding symmetry-equivalent sites of lowest indices. If *map_to_unitcell* is true, the returned positions are all mapped into the unit cell, i.e. lattice translations are included as symmetry operator. Example: >>> from ase.spacegroup import Spacegroup >>> sg = Spacegroup(225) # fcc >>> sg.symmetry_normalised_sites([[0.0, 0.5, 0.5], [1.0, 1.0, 0.0]]) array([[ 0., 0., 0.], [ 0., 0., 0.]]) """ scaled = np.array(scaled_positions, ndmin=2) normalised = np.empty(scaled.shape, np.float) rot, trans = self.get_op() for i, pos in enumerate(scaled): sympos = np.dot(rot, pos) + trans if map_to_unitcell: # Must be done twice, see the scaled_positions.py test sympos %= 1.0 sympos %= 1.0 j = np.lexsort(sympos.T)[0] normalised[i, :] = sympos[j] return normalised def unique_sites(self, scaled_positions, symprec=1e-3, output_mask=False, map_to_unitcell=True): """Returns a subset of *scaled_positions* containing only the symmetry-unique positions. If *output_mask* is True, a boolean array masking the subset is also returned. If *map_to_unitcell* is true, all sites are first mapped into the unit cell making e.g. [0, 0, 0] and [1, 0, 0] equivalent. Example: >>> from ase.spacegroup import Spacegroup >>> sg = Spacegroup(225) # fcc >>> sg.unique_sites([[0.0, 0.0, 0.0], ... [0.5, 0.5, 0.0], ... [1.0, 0.0, 0.0], ... [0.5, 0.0, 0.0]]) array([[ 0. , 0. , 0. ], [ 0.5, 0. , 0. ]]) """ scaled = np.array(scaled_positions, ndmin=2) symnorm = self.symmetry_normalised_sites(scaled, map_to_unitcell) perm = np.lexsort(symnorm.T) iperm = perm.argsort() xmask = np.abs(np.diff(symnorm[perm], axis=0)).max(axis=1) > symprec mask = np.concatenate(([True], xmask)) imask = mask[iperm] if output_mask: return scaled[imask], imask else: return scaled[imask] def tag_sites(self, scaled_positions, symprec=1e-3): """Returns an integer array of the same length as *scaled_positions*, tagging all equivalent atoms with the same index. Example: >>> from ase.spacegroup import Spacegroup >>> sg = Spacegroup(225) # fcc >>> sg.tag_sites([[0.0, 0.0, 0.0], ... [0.5, 0.5, 0.0], ... [1.0, 0.0, 0.0], ... [0.5, 0.0, 0.0]]) array([0, 0, 0, 1]) """ scaled = np.array(scaled_positions, ndmin=2) scaled %= 1.0 scaled %= 1.0 tags = -np.ones((len(scaled), ), dtype=int) mask = np.ones((len(scaled), ), dtype=np.bool) rot, trans = self.get_op() i = 0 while mask.any(): pos = scaled[mask][0] sympos = np.dot(rot, pos) + trans # Must be done twice, see the scaled_positions.py test sympos %= 1.0 sympos %= 1.0 m = ~np.all(np.any(np.abs(scaled[np.newaxis, :, :] - sympos[:, np.newaxis, :]) > symprec, axis=2), axis=0) assert not np.any((~mask) & m) tags[m] = i mask &= ~m i += 1 return tags
def get_datafile(): """Return default path to datafile.""" return os.path.join(os.path.dirname(__file__), 'spacegroup.dat') def format_symbol(symbol): """Returns well formatted Hermann-Mauguin symbol as extected by the database, by correcting the case and adding missing or removing dublicated spaces.""" fixed = [] s = symbol.strip() s = s[0].upper() + s[1:].lower() for c in s: if c.isalpha(): if len(fixed) and fixed[-1] == '/': fixed.append(c) else: fixed.append(' ' + c + ' ') elif c.isspace(): fixed.append(' ') elif c.isdigit(): fixed.append(c) elif c == '-': fixed.append(' ' + c) elif c == '/': fixed.append(c) s = ''.join(fixed).strip() return ' '.join(s.split()) # Functions for parsing the database. They are moved outside the # Spacegroup class in order to make it easier to later implement # caching to avoid reading the database each time a new Spacegroup # instance is created. def _skip_to_blank(f, spacegroup, setting): """Read lines from f until a blank line is encountered.""" while True: line = f.readline() if not line: raise SpacegroupNotFoundError( 'invalid spacegroup `%s`, setting `%s` not found in data base' % (spacegroup, setting)) if not line.strip(): break def _skip_to_nonblank(f, spacegroup, setting): """Read lines from f until a nonblank line not starting with a hash (#) is encountered and returns this and the next line.""" while True: line1 = f.readline() if not line1: raise SpacegroupNotFoundError( 'invalid spacegroup %s, setting %i not found in data base' % (spacegroup, setting)) line1.strip() if line1 and not line1.startswith('#'): line2 = f.readline() break return line1, line2 def _read_datafile_entry(spg, no, symbol, setting, f): """Read space group data from f to spg.""" floats = {'0.0': 0.0, '1.0': 1.0, '0': 0.0, '1': 1.0, '-1': -1.0} for n, d in [(1, 2), (1, 3), (2, 3), (1, 4), (3, 4), (1, 6), (5, 6)]: floats['{0}/{1}'.format(n, d)] = n / d floats['-{0}/{1}'.format(n, d)] = -n / d spg._no = no spg._symbol = symbol.strip() spg._setting = setting spg._centrosymmetric = bool(int(f.readline().split()[1])) # primitive vectors f.readline() spg._scaled_primitive_cell = np.array([[float(floats.get(s, s)) for s in f.readline().split()] for i in range(3)], dtype=np.float) # primitive reciprocal vectors f.readline() spg._reciprocal_cell = np.array([[int(i) for i in f.readline().split()] for i in range(3)], dtype=np.int) # subtranslations spg._nsubtrans = int(f.readline().split()[0]) spg._subtrans = np.array([[float(floats.get(t, t)) for t in f.readline().split()] for i in range(spg._nsubtrans)], dtype=np.float) # symmetry operations nsym = int(f.readline().split()[0]) symop = np.array([[float(floats.get(s, s)) for s in f.readline().split()] for i in range(nsym)], dtype=np.float) spg._nsymop = nsym spg._rotations = np.array(symop[:, :9].reshape((nsym, 3, 3)), dtype=np.int) spg._translations = symop[:, 9:] def _read_datafile(spg, spacegroup, setting, f): if isinstance(spacegroup, int): pass elif isinstance(spacegroup, str): spacegroup = ' '.join(spacegroup.strip().split()) compact_spacegroup = ''.join(spacegroup.split()) else: raise SpacegroupValueError('`spacegroup` must be of type int or str') while True: line1, line2 = _skip_to_nonblank(f, spacegroup, setting) _no, _symbol = line1.strip().split(None, 1) _symbol = format_symbol(_symbol) compact_symbol = ''.join(_symbol.split()) _setting = int(line2.strip().split()[1]) _no = int(_no) if ((isinstance(spacegroup, int) and _no == spacegroup and _setting == setting) or (isinstance(spacegroup, str) and compact_symbol == compact_spacegroup) and _setting == setting): _read_datafile_entry(spg, _no, _symbol, _setting, f) break else: _skip_to_blank(f, spacegroup, setting) def parse_sitesym(symlist, sep=','): """Parses a sequence of site symmetries in the form used by International Tables and returns corresponding rotation and translation arrays. Example: >>> symlist = [ ... 'x,y,z', ... '-y+1/2,x+1/2,z', ... '-y,-x,-z', ... ] >>> rot, trans = parse_sitesym(symlist) >>> rot array([[[ 1, 0, 0], [ 0, 1, 0], [ 0, 0, 1]], <BLANKLINE> [[ 0, -1, 0], [ 1, 0, 0], [ 0, 0, 1]], <BLANKLINE> [[ 0, -1, 0], [-1, 0, 0], [ 0, 0, -1]]]) >>> trans array([[ 0. , 0. , 0. ], [ 0.5, 0.5, 0. ], [ 0. , 0. , 0. ]]) """ nsym = len(symlist) rot = np.zeros((nsym, 3, 3), dtype='int') trans = np.zeros((nsym, 3)) for i, sym in enumerate(symlist): for j, s in enumerate(sym.split(sep)): s = s.lower().strip() while s: sign = 1 if s[0] in '+-': if s[0] == '-': sign = -1 s = s[1:].lstrip() if s[0] in 'xyz': k = ord(s[0]) - ord('x') rot[i, j, k] = sign s = s[1:].lstrip() elif s[0].isdigit() or s[0] == '.': n = 0 while n < len(s) and (s[n].isdigit() or s[n] in '/.'): n += 1 t = s[:n] s = s[n:].lstrip() if '/' in t: q, r = t.split('/') trans[i, j] = float(q) / float(r) else: trans[i, j] = float(t) else: raise SpacegroupValueError( 'Error parsing %r. Invalid site symmetry: %s' % (s, sym)) return rot, trans def spacegroup_from_data(no=None, symbol=None, setting=None, centrosymmetric=None, scaled_primitive_cell=None, reciprocal_cell=None, subtrans=None, sitesym=None, rotations=None, translations=None, datafile=None): """Manually create a new space group instance. This might be useful when reading crystal data with its own spacegroup definitions.""" if no is not None and setting is not None: spg = Spacegroup(no, setting, datafile) elif symbol is not None: spg = Spacegroup(symbol, None, datafile) else: raise SpacegroupValueError('either *no* and *setting* ' 'or *symbol* must be given') if not isinstance(sitesym, list): raise TypeError('sitesym must be a list') have_sym = False if centrosymmetric is not None: spg._centrosymmetric = bool(centrosymmetric) if scaled_primitive_cell is not None: spg._scaled_primitive_cell = np.array(scaled_primitive_cell) if reciprocal_cell is not None: spg._reciprocal_cell = np.array(reciprocal_cell) if subtrans is not None: spg._subtrans = np.atleast_2d(subtrans) spg._nsubtrans = spg._subtrans.shape[0] if sitesym is not None: spg._rotations, spg._translations = parse_sitesym(sitesym) have_sym = True if rotations is not None: spg._rotations = np.atleast_3d(rotations) have_sym = True if translations is not None: spg._translations = np.atleast_2d(translations) have_sym = True if have_sym: if spg._rotations.shape[0] != spg._translations.shape[0]: raise SpacegroupValueError('inconsistent number of rotations and ' 'translations') spg._nsymop = spg._rotations.shape[0] return spg
[docs]def get_spacegroup(atoms, symprec=1e-5): """Determine the spacegroup to which belongs the Atoms object. This requires spglib: https://atztogo.github.io/spglib/ . Parameters: atoms: Atoms object Types, positions and unit-cell. symprec: float Symmetry tolerance, i.e. distance tolerance in Cartesian coordinates to find crystal symmetry. The Spacegroup object is returned. """ # Example: # (We don't include the example in docstring to appease doctests # when import fails) # >>> from ase.build import bulk # >>> atoms = bulk("Cu", "fcc", a=3.6, cubic=True) # >>> sg = get_spacegroup(atoms) # >>> sg # Spacegroup(225, setting=1) # >>> sg.no # 225 try: import spglib # For version 1.9 or later except ImportError: from pyspglib import spglib # For versions 1.8.x or before sg = spglib.get_spacegroup((atoms.get_cell(), atoms.get_scaled_positions(), atoms.get_atomic_numbers()), symprec=symprec) if sg is None: raise RuntimeError('Spacegroup not found') sg_no = int(sg[sg.find('(') + 1:sg.find(')')]) return Spacegroup(sg_no)
# no spglib, we use our own spacegroup finder. Not as fast as spglib. # we center the Atoms positions on each atom in the cell, and find the # spacegroup of highest symmetry # # XXX That function is not finished. # found = None # for kind, pos in enumerate(atoms.get_scaled_positions()): # sg = _get_spacegroup(atoms, symprec=symprec, center=kind) # if found is None or sg.no > found.no: # found = sg # return found def _get_spacegroup(atoms, symprec=1e-5, center=None): """ASE implementation of get_spacegroup, pure python.""" raise NotImplementedError('get_spacegroup() is not finished') # we try all available spacegroups from 230 to 1, backwards # a Space group is the collection of all symmetry operations which lets the # unit cell invariant. found = None positions = atoms.get_scaled_positions(wrap=True) # in the lattice frame # make sure we are insensitive to translation. this choice is arbitrary and # could lead to a 'slightly' wrong guess for the Space group, e.g. do not # guess centro-symmetry. if center is not None: try: positions -= positions[center] except IndexError: pass # search space groups from the highest symmetry to the lowest # retain the first match for nb in range(230, 0, -1): sg = Spacegroup(nb) # # now we scan all atoms in the cell and look for equivalent sites sites, kinds = sg.equivalent_sites(positions, onduplicates='keep', symprec=symprec) # the equivalent sites should match all other atom locations in the # cell as the spacegroup transforms the unit cell in itself # we test on the number of equivalent sites if len(sites) == len(positions): # store the space group into the list found = sg break return found