import itertools
import numpy as np
import spglib as spg
from . import atoms as atoms_module
from ..input_output.logging_tools import logger
from .utilities import ase_atoms_to_spglib_tuple
logger = logger.getChild('relate_structures')
[docs]def align_supercell(supercell, prim, symprec=None):
"""Rotate and translate a supercell configuration such that it is aligned
with the target primitive cell.
Parameters
----------
sc : ase.Atoms
supercell configuration
prim : ase.Atoms
target primitive configuration
symprec : float
precision parameter forwarded to spglib
Returns
-------
tuple(ase.Atoms, numpy.ndarray, numpy.ndarray)
aligned supercell configuration as well as rotation matrix
(`3x3` array) and translation vector (`3x1` array) that relate
the input to the aligned supercell configuration.
"""
# TODO: Make sure the input is what we expect
# find rotation and translation
R, T = relate_structures(supercell, prim, symprec=symprec)
# Create the aligned system
aligned_supercell = rotate_atoms(supercell, R)
aligned_supercell.translate(T)
aligned_supercell.wrap()
return aligned_supercell, R, T
[docs]def relate_structures(reference, target, symprec=1e-5):
"""Finds rotation and translation operations that align two structures with
periodic boundary conditions.
The rotation and translation in Cartesian coordinates will map the
reference structure onto the target
Aligning reference with target can be achieved via the transformations::
R, T = relate_structures(atoms_ref, atoms_target)
atoms_ref_rotated = rotate_atoms(atoms_ref, R)
atoms_ref_rotated.translate(T)
atoms_ref_rotated.wrap()
atoms_ref_rotated == atoms_target
Parameters
----------
reference : ase.Atoms
The reference structure to be mapped
target : ase.Atoms
The target structure
Returns
-------
R : numpy.ndarray
rotation matrix in Cartesian coordinates (`3x3` array)
T : numpy.ndarray
translation vector in Cartesian coordinates
"""
logger.debug('Reference atoms:')
_debug_log_atoms(reference)
reference_primitive_cell = get_primitive_cell(reference, symprec=symprec)
logger.debug('Reference primitive cell')
_debug_log_atoms(reference_primitive_cell)
logger.debug('Target atoms:')
_debug_log_atoms(target)
target_primitive_cell = get_primitive_cell(target, symprec=symprec)
logger.debug('Target primitive cell')
_debug_log_atoms(target_primitive_cell)
logger.debug('Sane check that primitive cells can match...')
_assert_structures_match(reference_primitive_cell, target_primitive_cell)
logger.debug('Finding rotations...')
rotations = _find_rotations(reference_primitive_cell.cell,
target_primitive_cell.cell)
logger.debug('Finding transformations...')
for R in rotations:
rotated_reference_primitive_cell = \
rotate_atoms(reference_primitive_cell, R)
T = _find_translation(rotated_reference_primitive_cell,
target_primitive_cell)
if T is not None:
break
else:
raise Exception(('Found no translation!\n'
'Reference primitive cell basis:\n'
'{}\n'
'Target primitive cell basis:\n'
'{}')
.format(reference_primitive_cell.basis,
target_primitive_cell.basis))
logger.debug(('Found rotation\n'
'{}\n'
'and translation\n'
'{}')
.format(R, T))
return R, T
[docs]def is_rotation(R, cell_metric=None):
"""Checks if rotation matrix is orthonormal
A cell metric can be passed of the rotation matrix is in scaled coordinates
Parameters
----------
R : numpy.ndarray
rotation matrix (`3x3` array)
cell_metric : numpy.ndarray
cell metric if the rotation is in scaled coordinates
"""
if not cell_metric:
cell_metric = np.eye(3)
V = cell_metric
V_inv = np.linalg.inv(V)
lhs = np.linalg.multi_dot([V_inv, R.T, V, V.T, R, V_inv.T])
return np.allclose(lhs, np.eye(3), atol=1e-4) # TODO: tol
def _find_rotations(reference_cell_metric, target_cell_metric):
""" Generates all proper and improper rotations aligning two cell
metrics. """
rotations = []
V1 = reference_cell_metric
for perm in itertools.permutations([0, 1, 2]):
# Make sure the improper rotations are included
for inv in itertools.product([1, -1], repeat=3):
V2 = np.diag(inv) @ target_cell_metric[perm, :]
R = np.linalg.solve(V1, V2).T
# Make sure the rotation is orthonormal
if is_rotation(R):
for R_tmp in rotations:
if np.allclose(R, R_tmp): # TODO: tol
break
else:
rotations.append(R)
assert rotations, ('Found no rotations! Reference cell metric:\n'
'{}\n'
'Target cell metric:\n'
'{}').format(reference_cell_metric, target_cell_metric)
logger.debug('Found {} rotations'.format(len(rotations)))
return rotations
def _assert_structures_match(ref, prim):
""" Asserts the structures are compatible with respect to number of atoms,
atomic numbers and volume.
TODO: tol
"""
if len(ref) != len(prim):
raise ValueError(
'Number of atoms in reference primitive cell {} does not match '
'target primitive {}'.format(len(ref), len(prim)))
if sorted(ref.numbers) != sorted(prim.numbers):
raise ValueError('Atomic numbers do not match\nReference: {}\nTarget:'
' {}\n'.format(ref.numbers, prim.numbers))
if not np.isclose(ref.get_volume(), prim.get_volume()):
raise ValueError(
'Volume for reference primitive cell {} does not match target '
'primitive cell {}\n'.format(ref.get_volume(), prim.get_volume()))
[docs]def get_primitive_cell(atoms, to_primitive=True, no_idealize=True,
symprec=1e-5):
""" Gets primitive cell from spglib.
Parameters
----------
atoms : ase.Atoms
atomic structure
to_primitive : bool
passed to spglib
no_idealize : bool
passed to spglib
"""
if not all(atoms.pbc):
raise ValueError('atoms must have pbc.')
atoms_as_tuple = ase_atoms_to_spglib_tuple(atoms)
spg_primitive_cell = spg.standardize_cell(atoms_as_tuple, to_primitive=True,
no_idealize=True,
symprec=symprec)
primitive_cell = atoms_module.Atoms(cell=spg_primitive_cell[0],
scaled_positions=spg_primitive_cell[1],
numbers=spg_primitive_cell[2],
pbc=True)
return primitive_cell
def _debug_log_atoms(atoms):
logger.debug('cell:\n{}'.format(atoms.cell))
logger.debug('spos:\n{}'.format(atoms.get_scaled_positions()))
logger.debug('pos:\n{}'.format(atoms.positions))
logger.debug('numbers:\n{}'.format(atoms.numbers))
[docs]def rotate_atoms(atoms, rotation):
"""Rotates the cell and positions of Atoms and returns a copy
Parameters
----------
atoms : ase.Atoms
atomic structure
rotation : numpy.ndarray
rotation matrix (`3x3` array)
"""
cell = np.dot(rotation, atoms.cell.T).T
positions = np.dot(rotation, atoms.positions.T).T
return atoms_module.Atoms(cell=cell, positions=positions,
numbers=atoms.numbers, pbc=atoms.pbc)
def _find_translation(reference, target):
"""Returns the translation between two compatible atomic structures.
The two structures must describe the same structure when infinitely
repeated but differ by a translation.
Parameters
----------
reference : ase.Atoms
target : ase.Atoms
Returns
-------
numpy.ndarray or None
translation vector or `None` if structures are incompatible
"""
atoms = atoms_module.Atoms(cell=target.cell,
positions=reference.positions,
numbers=reference.numbers,
pbc=True)
atoms.wrap()
atoms_atom_0 = atoms[0]
for atom in target:
if atoms_atom_0.symbol != atom.symbol:
continue
T = atom.position - atoms_atom_0.position
atoms_copy = atoms.copy()
atoms_copy.positions += T
if are_nonpaired_configurations_equal(atoms_copy, target):
return T
return None
[docs]def are_nonpaired_configurations_equal(atoms1, atoms2):
""" Checks whether two configurations are identical. To be considered
equal the structures must have the same cell metric, elemental
occupation, scaled positions (modulo one), and periodic boundary
conditions.
Unlike the ``__eq__`` operator of :class:`ase.Atoms` the order of the
atoms does not matter.
Parameters
----------
atoms1 : ase.Atoms
atoms2 : ase.Atoms
Returns
-------
bool
True if atoms are equal, False otherwise
TODO: tol
"""
n_atoms = len(atoms1)
if not (np.allclose(atoms1.cell, atoms2.cell, atol=1e-4) and
n_atoms == len(atoms2) and
sorted(atoms1.numbers) == sorted(atoms2.numbers) and
all(atoms1.pbc == atoms2.pbc)):
return False
new_cell = (atoms1.cell + atoms2.cell) / 2
pos = [a.position for a in atoms1] + [a.position for a in atoms2]
num = [a.number for a in atoms1] + [a.number for a in atoms2]
s3 = atoms_module.Atoms(cell=new_cell, positions=pos, numbers=num,
pbc=True)
for i in range(n_atoms):
for j in range(n_atoms, len(s3)):
d = s3.get_distance(i, j, mic=True)
if abs(d) < 1e-4: # TODO: tol
if s3[i].number != s3[j].number:
return False
break
else:
return False
return True