# 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 lru_cache, total_ordering from types import SimpleNamespace from typing import Union import numpy as np from ase.utils import deprecated __all__ = ['Spacegroup'] class SpacegroupError(Exception): """Base exception for the spacegroup module.""" class SpacegroupNotFoundError(SpacegroupError): """Raised when given space group cannot be found in data base.""" class SpacegroupValueError(SpacegroupError): """Raised when arguments have invalid value.""" # Type alias _SPACEGROUP = Union[int, str, 'Spacegroup'] @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. ]]) """ @property def no(self): """Space group number in International Tables of Crystallography.""" return self._no @property def symbol(self): """Hermann-Mauguin (or international) symbol for the space group.""" return self._symbol @property def setting(self): """Space group setting. Either one or two.""" return self._setting @property def lattice(self): """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) """ return self._symbol[0] @property def centrosymmetric(self): """Whether a center of symmetry exists.""" return self._centrosymmetric @property def scaled_primitive_cell(self): """Primitive cell in scaled coordinates. Matrix with the primitive vectors along the rows. """ return self._scaled_primitive_cell @property def reciprocal_cell(self): """ Tree Miller indices that span all kinematically non-forbidden reflections as a matrix with the Miller indices along the rows. """ return self._reciprocal_cell @property def nsubtrans(self): """Number of cell-subtranslation vectors.""" return len(self._subtrans) @property def nsymop(self): """Total number of symmetry operations.""" scale = 2 if self.centrosymmetric else 1 return scale * len(self._rotations) * len(self._subtrans) @property def subtrans(self): """Translations vectors belonging to cell-sub-translations.""" return self._subtrans @property def rotations(self): """Symmetry rotation matrices. The invertions are not included for centrosymmetrical crystals. """ return self._rotations @property def translations(self): """Symmetry translations. The invertions are not included for centrosymmetrical crystals. """ return self._translations def __init__(self, spacegroup: _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() namespace = _read_datafile(spacegroup, setting, datafile) self._no = namespace._no self._symbol = namespace._symbol self._setting = namespace._setting self._centrosymmetric = namespace._centrosymmetric self._scaled_primitive_cell = namespace._scaled_primitive_cell self._reciprocal_cell = namespace._reciprocal_cell self._subtrans = namespace._subtrans self._rotations = namespace._rotations self._translations = namespace._translations 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] """ if onduplicates not in ('keep', 'replace', 'warn', 'error'): raise SpacegroupValueError( 'Argument "onduplicates" must be one of: ' '"keep", "replace", "warn" or "error".' ) scaled = np.array(scaled_positions, ndmin=2) rotations, translations = zip(*self.get_symop()) rotations = np.array(rotations) translations = np.array(translations) def find_orbit(point: np.ndarray) -> np.ndarray: """Find crystallographic orbit of the given point.""" candidates = ((rotations @ point) + translations % 1.0) % 1.0 orbit = [candidates[0]] for member in candidates[1:]: diff = member - orbit diff -= np.rint(diff) if not np.any(np.all(np.abs(diff) < symprec, axis=1)): orbit.append(member) return np.array(orbit) orbits = [] for kind, pos in enumerate(scaled): for i, (kind0, positions0) in enumerate(orbits): diff = pos - positions0 diff -= np.rint(diff) if np.any(np.all(np.abs(diff) < symprec, axis=1)): if onduplicates == 'keep': pass elif onduplicates == 'replace': orbits[i] = (kind, positions0) elif onduplicates == 'warn': warnings.warn( 'scaled_positions %d and %d are equivalent' % (kind0, kind)) elif onduplicates == 'error': raise SpacegroupValueError( 'scaled_positions %d and %d are equivalent' % (kind0, kind)) break else: orbits.append((kind, find_orbit(pos))) kinds = [] sites = [] for kind, orbit in orbits: kinds.extend(len(orbit) * [kind]) sites.append(orbit) return np.concatenate(sites, axis=0), 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, 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=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( f'invalid spacegroup `{spacegroup}`, setting `{setting}` not ' 'found in data base') 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[f'{n}/{d}'] = n / d floats[f'-{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 _ in range(3) ], dtype=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=int) # subtranslations nsubtrans = int(f.readline().split()[0]) spg._subtrans = np.array( [ [float(floats.get(t, t)) for t in f.readline().split()] for _ in range(nsubtrans) ], dtype=float, ) # symmetry operations nsym = int(f.readline().split()[0]) symop = np.array( [ [float(floats.get(s, s)) for s in f.readline().split()] for _ in range(nsym) ], dtype=float, ) spg._rotations = np.array(symop[:, :9].reshape((nsym, 3, 3)), dtype=int) spg._translations = symop[:, 9:] @lru_cache def _read_datafile(spacegroup, setting, datafile): with open(datafile, encoding='utf-8') as fd: return _read_f(spacegroup, setting, fd) def _read_f(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) condition = ( (isinstance(spacegroup, int) and _no == spacegroup and _setting == setting) or (isinstance(spacegroup, str) and compact_symbol == compact_spacegroup) and (setting is None or _setting == setting)) if condition: namespace = SimpleNamespace() _read_datafile_entry(namespace, _no, _symbol, _setting, f) return namespace else: _skip_to_blank(f, spacegroup, setting) def parse_sitesym_element(element): """Parses one element from a single site symmetry in the form used by the International Tables. Examples: >>> parse_sitesym_element("x") ([(0, 1)], 0.0) >>> parse_sitesym_element("-1/2-y") ([(1, -1)], -0.5) >>> parse_sitesym_element("z+0.25") ([(2, 1)], 0.25) >>> parse_sitesym_element("x-z+0.5") ([(0, 1), (2, -1)], 0.5) Parameters ---------- element: str Site symmetry like "x" or "-y+1/4" or "0.5+z". Returns ------- list[tuple[int, int]] Rotation information in the form '(index, sign)' where index is 0 for "x", 1 for "y" and 2 for "z" and sign is '1' for a positive entry and '-1' for a negative entry. E.g. "x" is '(0, 1)' and "-z" is (2, -1). float Translation information in fractional space. E.g. "-1/4" is '-0.25' and "1/2" is '0.5' and "0.75" is '0.75'. """ element = element.lower() is_positive = True is_frac = False sng_trans = None fst_trans = [] snd_trans = [] rot = [] for char in element: if char == "+": is_positive = True elif char == "-": is_positive = False elif char == "/": is_frac = True elif char in "xyz": rot.append((ord(char) - ord("x"), 1 if is_positive else -1)) elif char.isdigit() or char == ".": if sng_trans is None: sng_trans = 1.0 if is_positive else -1.0 if is_frac: snd_trans.append(char) else: fst_trans.append(char) trans = 0.0 if not fst_trans else (sng_trans * float("".join(fst_trans))) if is_frac: trans /= float("".join(snd_trans)) return rot, trans def parse_sitesym_single(sym, out_rot, out_trans, sep=",", force_positive_translation=False): """Parses a single site symmetry in the form used by International Tables and overwrites 'out_rot' and 'out_trans' with data. Parameters ---------- sym: str Site symmetry in the form used by International Tables (e.g. "x,y,z", "y-1/2,x,-z"). out_rot: np.array A 3x3-integer array representing rotations (changes are made inplace). out_rot: np.array A 3-float array representing translations (changes are made inplace). sep: str String separator ("," in "x,y,z"). force_positive_translation: bool Forces fractional translations to be between 0 and 1 (otherwise negative values might be accepted). Defaults to 'False'. Returns ------- Nothing is returned: 'out_rot' and 'out_trans' are changed inplace. """ out_rot[:] = 0.0 out_trans[:] = 0.0 for i, element in enumerate(sym.split(sep)): e_rot_list, e_trans = parse_sitesym_element(element) for rot_idx, rot_sgn in e_rot_list: out_rot[i][rot_idx] = rot_sgn out_trans[i] = \ (e_trans % 1.0) if force_positive_translation else e_trans def parse_sitesym(symlist, sep=',', force_positive_translation=False): """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', ... 'x-1/4, y-1/4, -z' ... ] >>> rot, trans = parse_sitesym(symlist) >>> rot array([[[ 1, 0, 0], [ 0, 1, 0], [ 0, 0, 1]], [[ 0, -1, 0], [ 1, 0, 0], [ 0, 0, 1]], [[ 0, -1, 0], [-1, 0, 0], [ 0, 0, -1]], [[ 1, 0, 0], [ 0, 1, 0], [ 0, 0, -1]]]) >>> trans array([[ 0. , 0. , 0. ], [ 0.5 , 0.5 , 0. ], [ 0. , 0. , 0. ], [-0.25, -0.25, 0. ]]) """ nsym = len(symlist) rot = np.zeros((nsym, 3, 3), dtype='int') trans = np.zeros((nsym, 3)) for i, sym in enumerate(symlist): parse_sitesym_single( sym, rot[i], trans[i], sep=sep, force_positive_translation=force_positive_translation) 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) 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') return spg @deprecated( '`get_spacegroup` has been deprecated due to its misleading output. ' 'The returned `Spacegroup` object has symmetry operations for a ' 'standard setting regardress of the given `Atoms` object. ' 'See https://gitlab.com/ase/ase/-/issues/1534 for details. ' 'Please use `ase.spacegroup.symmetrize.check_symmetry` or `spglib` ' 'directly to get the symmetry operations for the given `Atoms` object.' ) def get_spacegroup(atoms, symprec=1e-5): """Determine the spacegroup to which belongs the Atoms object. This requires spglib: https://atztogo.github.io/spglib/ . .. warning:: The returned ``Spacegroup`` object has symmetry operations for a standard setting regardless of the given ``Atoms`` object. See https://gitlab.com/ase/ase/-/issues/1534 for details. .. deprecated:: 3.24.0 Please use ``ase.spacegroup.symmetrize.check_symmetry`` or ``spglib`` directly to get the symmetry operations for the given ``Atoms`` object. 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 import spglib 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)