from typing import Mapping, Sequence, Union
import numpy as np
import ase
from ase.utils import pbc2pbc
from ase.utils.arraywrapper import arraylike
__all__ = ['Cell']
[docs]@arraylike
class Cell:
"""Parallel epipedal unit cell of up to three dimensions.
This object resembles a 3x3 array whose [i, j]-th element is the jth
Cartesian coordinate of the ith unit vector.
Cells of less than three dimensions are represented by placeholder
unit vectors that are zero."""
ase_objtype = 'cell' # For JSON'ing
def __init__(self, array):
"""Create cell.
Parameters:
array: 3x3 arraylike object
The three cell vectors: cell[0], cell[1], and cell[2].
"""
array = np.asarray(array, dtype=float)
assert array.shape == (3, 3)
self.array = array
[docs] def cellpar(self, radians=False):
"""Get unit cell parameters. Sequence of 6 numbers.
First three are unit cell vector lengths and second three
are angles between them::
[len(a), len(b), len(c), angle(b,c), angle(a,c), angle(a,b)]
in degrees.
See also :func:`ase.geometry.cell.cell_to_cellpar`."""
from ase.geometry.cell import cell_to_cellpar
return cell_to_cellpar(self.array, radians)
def todict(self):
return dict(array=self.array)
[docs] @classmethod
def ascell(cls, cell):
"""Return argument as a Cell object. See :meth:`ase.cell.Cell.new`.
A new Cell object is created if necessary."""
if isinstance(cell, cls):
return cell
return cls.new(cell)
[docs] @classmethod
def new(cls, cell=None):
"""Create new cell from any parameters.
If cell is three numbers, assume three lengths with right angles.
If cell is six numbers, assume three lengths, then three angles.
If cell is 3x3, assume three cell vectors."""
if cell is None:
cell = np.zeros((3, 3))
cell = np.array(cell, float)
if cell.shape == (3,):
cell = np.diag(cell)
elif cell.shape == (6,):
from ase.geometry.cell import cellpar_to_cell
cell = cellpar_to_cell(cell)
elif cell.shape != (3, 3):
raise ValueError('Cell must be length 3 sequence, length 6 '
'sequence or 3x3 matrix!')
cellobj = cls(cell)
return cellobj
[docs] @classmethod
def fromcellpar(cls, cellpar, ab_normal=(0, 0, 1), a_direction=None):
"""Return new Cell from cell lengths and angles.
See also :func:`~ase.geometry.cell.cellpar_to_cell()`."""
from ase.geometry.cell import cellpar_to_cell
cell = cellpar_to_cell(cellpar, ab_normal, a_direction)
return cls(cell)
[docs] def get_bravais_lattice(self, eps=2e-4, *, pbc=True):
"""Return :class:`~ase.lattice.BravaisLattice` for this cell:
>>> from ase.cell import Cell
>>> cell = Cell.fromcellpar([4, 4, 4, 60, 60, 60])
>>> print(cell.get_bravais_lattice())
FCC(a=5.65685)
.. note:: The Bravais lattice object follows the AFlow
conventions. ``cell.get_bravais_lattice().tocell()`` may
differ from the original cell by a permutation or other
operation which maps it to the AFlow convention. For
example, the orthorhombic lattice enforces a < b < c.
To build a bandpath for a particular cell, use
:meth:`ase.cell.Cell.bandpath` instead of this method.
This maps the kpoints back to the original input cell.
"""
from ase.lattice import identify_lattice
pbc = self.mask() & pbc2pbc(pbc)
lat, op = identify_lattice(self, eps=eps, pbc=pbc)
return lat
[docs] def bandpath(
self,
path: str = None,
npoints: int = None,
*,
density: float = None,
special_points: Mapping[str, Sequence[float]] = None,
eps: float = 2e-4,
pbc: Union[bool, Sequence[bool]] = True
) -> "ase.dft.kpoints.BandPath":
"""Build a :class:`~ase.dft.kpoints.BandPath` for this cell.
If special points are None, determine the Bravais lattice of
this cell and return a suitable Brillouin zone path with
standard special points.
If special special points are given, interpolate the path
directly from the available data.
Parameters:
path: string
String of special point names defining the path, e.g. 'GXL'.
npoints: int
Number of points in total. Note that at least one point
is added for each special point in the path.
density: float
density of kpoints along the path in Å⁻¹.
special_points: dict
Dictionary mapping special points to scaled kpoint coordinates.
For example ``{'G': [0, 0, 0], 'X': [1, 0, 0]}``.
eps: float
Tolerance for determining Bravais lattice.
pbc: three bools
Whether cell is periodic in each direction. Normally not
necessary. If cell has three nonzero cell vectors, use
e.g. pbc=[1, 1, 0] to request a 2D bandpath nevertheless.
Example
-------
>>> from ase.cell import Cell
>>> cell = Cell.fromcellpar([4, 4, 4, 60, 60, 60])
>>> cell.bandpath('GXW', npoints=20)
BandPath(path='GXW', cell=[3x3], special_points={GKLUWX}, kpts=[20x3])
"""
# TODO: Combine with the rotation transformation from bandpath()
cell = self.uncomplete(pbc)
if special_points is None:
from ase.lattice import identify_lattice
lat, op = identify_lattice(cell, eps=eps)
bandpath = lat.bandpath(path, npoints=npoints, density=density)
return bandpath.transform(op)
else:
from ase.dft.kpoints import BandPath, resolve_custom_points
path, special_points = resolve_custom_points(
path, special_points, eps=eps)
bandpath = BandPath(cell, path=path, special_points=special_points)
return bandpath.interpolate(npoints=npoints, density=density)
[docs] def uncomplete(self, pbc):
"""Return new cell, zeroing cell vectors where not periodic."""
_pbc = np.empty(3, bool)
_pbc[:] = pbc
cell = self.copy()
cell[~_pbc] = 0
return cell
[docs] def complete(self):
"""Convert missing cell vectors into orthogonal unit vectors."""
from ase.geometry.cell import complete_cell
return Cell(complete_cell(self.array))
[docs] def copy(self):
"""Return a copy of this cell."""
return Cell(self.array.copy())
[docs] def mask(self):
"""Boolean mask of which cell vectors are nonzero."""
return self.any(1)
@property
def rank(self) -> int:
""""Return the dimension of the cell.
Equal to the number of nonzero lattice vectors."""
# The name ndim clashes with ndarray.ndim
return sum(self.mask())
@property
def orthorhombic(self) -> bool:
"""Return whether this cell is represented by a diagonal matrix."""
from ase.geometry.cell import is_orthorhombic
return is_orthorhombic(self)
[docs] def lengths(self):
"""Return the length of each lattice vector as an array."""
return np.linalg.norm(self, axis=1)
[docs] def angles(self):
"""Return an array with the three angles alpha, beta, and gamma."""
return self.cellpar()[3:].copy()
def __array__(self, dtype=None, copy=False):
return np.array(self.array, dtype=dtype, copy=copy)
def __bool__(self):
return bool(self.any()) # need to convert from np.bool_
@property
def volume(self) -> float:
"""Get the volume of this cell.
If there are less than 3 lattice vectors, return 0."""
# Fail or 0 for <3D cells?
# Definitely 0 since this is currently a property.
# I think normally it is more convenient just to get zero
return np.abs(np.linalg.det(self))
@property
def handedness(self) -> int:
"""Sign of the determinant of the matrix of cell vectors.
1 for right-handed cells, -1 for left, and 0 for cells that
do not span three dimensions."""
return int(np.sign(np.linalg.det(self)))
[docs] def scaled_positions(self, positions) -> np.ndarray:
"""Calculate scaled positions from Cartesian positions.
The scaled positions are the positions given in the basis
of the cell vectors. For the purpose of defining the basis, cell
vectors that are zero will be replaced by unit vectors as per
:meth:`~ase.cell.Cell.complete`."""
return np.linalg.solve(self.complete().T, np.transpose(positions)).T
[docs] def cartesian_positions(self, scaled_positions) -> np.ndarray:
"""Calculate Cartesian positions from scaled positions."""
return scaled_positions @ self.complete()
[docs] def reciprocal(self) -> 'Cell':
"""Get reciprocal lattice as a Cell object.
The reciprocal cell is defined such that
cell.reciprocal() @ cell.T == np.diag(cell.mask())
within machine precision.
Does not include factor of 2 pi."""
icell = Cell(np.linalg.pinv(self).transpose())
icell[~self.mask()] = 0.0 # type: ignore[index]
return icell
[docs] def normal(self, i):
"""Normal vector of the two vectors with index different from i.
This is the cross product of those vectors in cyclic order from i."""
return np.cross(self[i - 2], self[i - 1])
[docs] def normals(self):
"""Normal vectors of each axis as a 3x3 matrix."""
return np.array([self.normal(i) for i in range(3)])
[docs] def area(self, i):
"""Area spanned by the two vectors with index different from i."""
return np.linalg.norm(self.normal(i))
[docs] def areas(self):
"""Areas spanned by cell vector pairs (1, 2), (2, 0), and (0, 2)."""
return np.linalg.norm(self.normals(), axis=1)
def __repr__(self):
if self.orthorhombic:
numbers = self.lengths().tolist()
else:
numbers = self.tolist()
return f'Cell({numbers})'
[docs] def niggli_reduce(self, eps=1e-5):
"""Niggli reduce this cell, returning a new cell and mapping.
See also :func:`ase.build.tools.niggli_reduce_cell`."""
from ase.build.tools import niggli_reduce_cell
cell, op = niggli_reduce_cell(self, epsfactor=eps)
result = Cell(cell)
return result, op
[docs] def minkowski_reduce(self):
"""Minkowski-reduce this cell, returning new cell and mapping.
See also :func:`ase.geometry.minkowski_reduction.minkowski_reduce`."""
from ase.geometry.minkowski_reduction import minkowski_reduce
cell, op = minkowski_reduce(self, self.mask())
result = Cell(cell)
return result, op
[docs] def permute_axes(self, permutation):
"""Permute axes of cell."""
assert (np.sort(permutation) == np.arange(3)).all()
permuted = Cell(self[permutation][:, permutation])
return permuted
# XXX We want a reduction function that brings the cell into
# standard form as defined by Setyawan and Curtarolo.