# 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
from typing import Union
import numpy as np
__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']
[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: _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()
with open(datafile) as fd:
_read_datafile(self, spacegroup, setting, fd)
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, 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
spg._nsubtrans = int(f.readline().split()[0])
spg._subtrans = np.array(
[
[float(floats.get(t, t)) for t in f.readline().split()]
for _ in range(spg._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._nsymop = nsym
spg._rotations = np.array(symop[:, :9].reshape((nsym, 3, 3)), dtype=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)
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:
_read_datafile_entry(spg, _no, _symbol, _setting, f)
break
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]],
<BLANKLINE>
[[ 0, -1, 0],
[ 1, 0, 0],
[ 0, 0, 1]],
<BLANKLINE>
[[ 0, -1, 0],
[-1, 0, 0],
[ 0, 0, -1]],
<BLANKLINE>
[[ 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)
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
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)