def _has_mesh_symmetry(self):
if self._rotations is None:
return False
m = self._mesh
mesh_equiv = [m[1] == m[2], m[2] == m[0], m[0] == m[1]]
lattice_equiv = get_lattice_vector_equivalence(
[r.T for r in self._rotations])
return np.extract(lattice_equiv, mesh_equiv).all()
def _has_mesh_symmetry(self):
if self._rotations is None:
return False
m = self._mesh
mesh_equiv = [m[1] == m[2], m[2] == m[0], m[0] == m[1]]
lattice_equiv = get_lattice_vector_equivalence(
[r.T for r in self._rotations])
return np.extract(lattice_equiv, mesh_equiv).all()
def length2mesh(length, lattice, rotations=None):
"""Convert length to mesh for q-point sampling
This conversion for each reciprocal axis follows VASP convention by
N = max(1, int(l * |a|^* + 0.5))
'int' means rounding down, not rounding to nearest integer.
Parameters
----------
length : float
Length having the unit of direct space length.
lattice : array_like
Basis vectors of primitive cell in row vectors.
dtype='double', shape=(3, 3)
rotations: array_like, optional
Rotation matrices in real space. When given, mesh numbers that are
symmetrically reasonable are returned. Default is None.
dtype='intc', shape=(rotations, 3, 3)
Returns
-------
array_like
dtype=int, shape=(3,)
"""
rec_lattice = np.linalg.inv(lattice)
rec_lat_lengths = np.sqrt(np.diagonal(np.dot(rec_lattice.T, rec_lattice)))
mesh_numbers = np.rint(rec_lat_lengths * length).astype(int)
if rotations is not None:
reclat_equiv = get_lattice_vector_equivalence(
[r.T for r in np.array(rotations)])
m = mesh_numbers
mesh_equiv = [m[1] == m[2], m[2] == m[0], m[0] == m[1]]
for i, pair in enumerate(([1, 2], [2, 0], [0, 1])):
if reclat_equiv[i] and not mesh_equiv:
m[pair] = max(m[pair])
return np.maximum(mesh_numbers, [1, 1, 1])
def length2mesh(length, lattice, rotations=None):
"""Convert length to mesh for q-point sampling
This conversion for each reciprocal axis follows VASP convention by
N = max(1, int(l * |a|^* + 0.5))
'int' means rounding down, not rounding to nearest integer.
Parameters
----------
length : float
Length having the unit of direct space length.
lattice : array_like
Basis vectors of primitive cell in row vectors.
dtype='double', shape=(3, 3)
rotations: array_like, optional
Rotation matrices in real space. When given, mesh numbers that are
symmetrically reasonable are returned. Default is None.
dtype='intc', shape=(rotations, 3, 3)
Returns
-------
array_like
dtype=int, shape=(3,)
"""
rec_lattice = np.linalg.inv(lattice)
rec_lat_lengths = np.sqrt(np.diagonal(np.dot(rec_lattice.T, rec_lattice)))
mesh_numbers = np.rint(rec_lat_lengths * length).astype(int)
if rotations is not None:
reclat_equiv = get_lattice_vector_equivalence(
[r.T for r in np.array(rotations)])
m = mesh_numbers
mesh_equiv = [m[1] == m[2], m[2] == m[0], m[0] == m[1]]
for i, pair in enumerate(([1, 2], [2, 0], [0, 1])):
if reclat_equiv[i] and not mesh_equiv:
m[pair] = max(m[pair])
return np.maximum(mesh_numbers, [1, 1, 1])
mapping_table, grid_address = get_ir_reciprocal_mesh(
mesh,
cell,
is_shift=is_shift)
ir_grid_points = np.unique(mapping_table)
primitive_vectors = np.linalg.inv(cell.get_cell())
bz_grid_address, bz_map = relocate_BZ_grid_address(
grid_address,
mesh,
np.linalg.inv(cell.get_cell()),
is_shift=is_shift)
bz_points = np.extract(bz_map > -1, bz_map)
qpoints = (grid_address + is_shift / 2.0) / mesh
qpoints -= (qpoints > 0.5001) * 1
bz = BrillouinZone(primitive_vectors)
bz.run(qpoints)
sv = bz.get_shortest_qpoints()
print("%d %d" % (len(bz_points), np.sum(len(x) for x in sv)))
for q, vs in zip(qpoints, sv):
if np.allclose(q, vs[0]):
print(q)
else:
print("%s * %s" % (q, np.linalg.norm(np.dot(primitive_vectors, q))))
for v in vs:
print("%s %s" % (v, np.linalg.norm(np.dot(primitive_vectors, v))))
rotations = symmetry.get_reciprocal_operations()
print(get_lattice_vector_equivalence(rotations))
mapping_table, grid_address = get_ir_reciprocal_mesh(
mesh,
cell,
is_shift=is_shift)
ir_grid_points = np.unique(mapping_table)
primitive_vectors = np.linalg.inv(cell.get_cell())
bz_grid_address, bz_map = relocate_BZ_grid_address(
grid_address,
mesh,
np.linalg.inv(cell.get_cell()),
is_shift=is_shift)
bz_points = np.extract(bz_map > -1, bz_map)
qpoints = (grid_address + is_shift / 2.0) / mesh
qpoints -= (qpoints > 0.5001) * 1
bz = BrillouinZone(primitive_vectors)
bz.run(qpoints)
sv = bz.get_shortest_qpoints()
print("%d %d" % (len(bz_points), np.sum(len(x) for x in sv)))
for q, vs in zip(qpoints, sv):
if np.allclose(q, vs[0]):
print(q)
else:
print("%s * %s" % (q, np.linalg.norm(np.dot(primitive_vectors, q))))
for v in vs:
print("%s %s" % (v, np.linalg.norm(np.dot(primitive_vectors, v))))
rotations = symmetry.get_reciprocal_operations()
print(get_lattice_vector_equivalence(rotations))