# File from ASE distribution (GPL)
# 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.
"""
from __future__ import print_function, division
import os
import warnings
from functools import total_ordering
from codecs import decode
import numpy as np
from muesr.core.isstr import isstr
# check if we have access to get_spacegroup from spglib
# https://atztogo.github.io/spglib/
has_spglib = False
try:
import spglib # For version 1.9 or later
has_spglib = True
except ImportError:
try:
from pyspglib import spglib # For versions 1.8.x or before
has_spglib = True
except ImportError:
pass
try:
from StringIO import StringIO
except ImportError:
from io import StringIO
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(object):
"""A space group class.
The instances of Spacegroup describes the symmetry operations for
the given space group.
Example:
>>> from muesr.core.spg 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:
f = StringIO(decode(spacegroupdat,'zlib').decode('utf8'))
else:
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)
[docs] 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
[docs] 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
[docs] 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
[docs] 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
[docs] def equivalent_reflections(self, hkl):
"""Return all equivalent reflections to the list of Miller indices
in hkl.
Example:
>>> from muesr.core.spg 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, :]))
[docs] 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:]))
[docs] 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 muesr.core.spg 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
[docs] def unique_reflections(self, hkl):
"""Returns a subset *hkl* containing only the symmetry-unique
reflections.
Example:
>>> from muesr.core.spg 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]
[docs] def equivalent_sites(self, scaled_positions, onduplicates='error',
symprec=1e-3):
"""Returns the scaled positions and all their equivalent sites.
Parameters:
scaled_positions: list | array
List of non-equivalent sites given in unit cell coordinates.
onduplicates : 'keep' | 'replace' | 'warn' | 'error'
Action if `scaled_positions` contain symmetry-equivalent
positions:
'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 muesr.core.spg 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):
ind = np.argwhere(mask)[0][0]
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
[docs] 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 muesr.core.spg 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
[docs] 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 muesr.core.spg 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]
[docs] 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 muesr.core.spg 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 %i 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 isstr(spacegroup):
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) or
(isstr(spacegroup) 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:]
if s[0] in 'xyz':
k = ord(s[0]) - ord('x')
rot[i, j, k] = sign
s = s[1:]
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:]
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=1,
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:
spg = Spacegroup(no, setting, datafile)
elif symbol is not None:
spg = Spacegroup(symbol, setting, datafile)
else:
raise SpacegroupValueError('either *no* or *symbol* must be given')
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
def get_spacegroup(atoms, symprec=1e-5, method='spglib'):
"""Determine the spacegroup to which belongs the Atoms object.
When PhonoPy/SPGlib is NOT available, a pure ASE python implementation is
used. The pure ASE method is NOT recommended for large systems (SLOW).
Parameters:
atoms: Atoms object
Types, positions and unit-cell.
symprec: float
Symmetry tolerance, i.e. distance tolerance in Cartesian
coordinates to find crystal symmetry.
method: str
'phonopy' or 'spglib' when available, or 'ase' (fallback).
The Spacegroup object is returned.
Example:
>>> 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
"""
# use spglib when it is available (and return)
if has_spglib and method in ['phonopy', 'spglib']:
sg = spglib.get_spacegroup(atoms, symprec=symprec)
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
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."""
# 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
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# Updated 15/2/18
spacegroupdat = 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