Source code for hiphive.core.structure_alignment

import itertools
import numpy as np
import spglib as spg
from . import atoms as atoms_module
from ..io.logging import logger

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.') spg_primitive_cell = spg.standardize_cell(atoms, 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