def test_converter(transformation, frac_coords):
converter = DerivativeMultiLatticeHash(transformation, frac_coords)
index = converter.index
num_sites = converter.num_sites
all_factors = converter.get_all_factors()
assert len({tuple(f) for f in all_factors}) == index
all_lattice_points = converter.get_lattice_points()
assert len({tuple(f) for f in all_lattice_points}) == index
all_periodic_sites = converter.get_canonical_sites_list()
assert len(set(all_periodic_sites)) == num_sites
all_dsites = converter.get_distinct_derivative_sites_list()
for dsite in all_dsites:
csite, derivative_jimage = converter.hash_derivative_site(dsite, return_image=True)
fcoords1 = converter.get_frac_coords(dsite)
fcoords2 = (
converter.displacement_set[dsite.site_index]
+ np.dot(converter.left_inv, csite.factor)
+ np.dot(converter.hnf, derivative_jimage)
)
assert np.allclose(fcoords1, fcoords2)
for csite in all_periodic_sites:
ind = converter.ravel_canonical_site(csite)
csite2 = converter.unravel_to_canonical_site(ind)
assert csite2 == csite
def test_converter():
list_transformations = [
np.diag((2, 2, 2)),
np.array([[-1, 1, 1], [1, -1, 1], [1, 1, -1]]),
np.array([[-1, 1, 1], [1, -1, 1], [-1, -1, 1]]), # negative determinat
]
list_frac_coords = [
np.array([[0, 0, 0]]),
np.array([[0, 0, 0], [0.5, 0.5, 0.5]])
]
for transformation in list_transformations:
for frac_coords in list_frac_coords:
converter = DerivativeMultiLatticeHash(transformation, frac_coords)
index = converter.index
num_sites = converter.num_sites
all_factors = converter.get_all_factors()
assert len(set([tuple((f)) for f in all_factors])) == index
all_lattice_points = converter.get_lattice_points()
assert len(set([tuple(f) for f in all_lattice_points])) == index
all_periodic_sites = converter.get_canonical_sites_list()
assert len(set(all_periodic_sites)) == num_sites
all_dsites = converter.get_distinct_derivative_sites_list()
for dsite in all_dsites:
csite, derivative_jimage = converter.hash_derivative_site(
dsite, return_image=True)
fcoords1 = converter.get_frac_coords(dsite)
fcoords2 = (converter.displacement_set[dsite.site_index] +
np.dot(converter.left_inv, csite.factor) +
np.dot(converter.hnf, derivative_jimage))
assert np.allclose(fcoords1, fcoords2)
for csite in all_periodic_sites:
ind = converter.ravel_canonical_site(csite)
csite2 = converter.unravel_to_canonical_site(ind)
assert csite2 == csite
class DerivativeStructurePermutation:
"""
Permutation Representation of space group of superlattice
Parameters
----------
hnf: array, (dim, dim)
Hermite normal form(lower triangular)
displacement_set: array, (num_site_parent, dim)
fractinal coordinates in primitive cell of base structure
rotations: array, (# of symmetry operations, dim, dim)
rotations with primitive basis for base structure
translations: array, (# of symmetry operations, dim)
translations with primitive basis for base structure
Attributes
----------
dim : int
dimention of lattice
index: int
# of parent multilattice in super lattice
num_site: int
# of sites in unit cell of superlattice
"""
def __init__(
self,
hnf: np.ndarray,
displacement_set: np.ndarray,
rotations: np.ndarray,
translations: np.ndarray,
):
self.hnf = hnf
self.num_sites_base = len(displacement_set)
# TODO: check each site in displacement_set is in [0, 1)^dim
self.displacement_set = displacement_set
self.dhash = DerivativeMultiLatticeHash(self.hnf, self.displacement_set)
self.rotations, self.translations = self._get_superlattice_invariant_subgroup(
rotations, translations
)
self.list_dsites = self.dhash.get_distinct_derivative_sites_list()
self.list_csites = self.dhash.get_canonical_sites_list()
self._prm_t = self._get_translation_permutations()
self.prm_rigid = self._get_rigid_permutations()
@property
def dim(self):
return self.dhash.dim
@property
def index(self):
return self.dhash.index
@property
def num_sites(self):
return self.dhash.num_sites
@property
def prm_t(self):
return self._prm_t
def _get_superlattice_invariant_subgroup(
self, rotations: np.ndarray, translations: np.ndarray
):
valid_rotations = []
valid_translations = []
for R, tau in zip(rotations, translations):
if not is_same_lattice(np.dot(R, self.hnf), self.hnf):
continue
valid_rotations.append(R)
valid_translations.append(tau)
assert len(rotations) % len(valid_rotations) == 0
return np.array(valid_rotations), np.array(valid_translations)
def _get_translation_permutations(self):
list_permutations = []
for add_factor in self.dhash.get_all_factors():
new_list_csites = []
for csite in self.list_csites:
new_factor = self.dhash.modulus_factor(
np.array(csite.factor) + np.array(add_factor)
)
new_csite = CanonicalSite(csite.site_index, new_factor)
new_list_csites.append(new_csite)
# permutation represenation
perm = [self.dhash.ravel_canonical_site(csite) for csite in new_list_csites]
assert is_permutation(perm)
list_permutations.append(perm)
# assume list_permutations[0] is identity
assert is_identity_permutation(list_permutations[0])
return list_permutations
def _get_rigid_permutations(self):
identity = list(range(self.num_sites))
list_permutations = [
identity,
]
for R, tau in zip(self.rotations, self.translations):
new_list_csites = []
for dsite in self.list_dsites:
frac_coord = self.displacement_set[dsite.site_index] + np.array(dsite.jimage)
acted_frac_coord = np.dot(R, frac_coord) + tau
new_csite = self.dhash.hash_frac_coords(acted_frac_coord)
assert new_csite is not None
new_list_csites.append(new_csite)
perm = [self.dhash.ravel_canonical_site(csite) for csite in new_list_csites]
assert is_permutation(perm)
if perm not in list_permutations:
list_permutations.append(perm)
# this set of permutations is not group!
return list_permutations
def get_symmetry_operation_permutations(self):
"""
return permutation representation of the symmetry group of the supercell
"""
list_permutations = []
for p1 in self.prm_t:
for p2 in self.prm_rigid:
perm = product_permutations(p1, p2)
assert perm not in list_permutations
list_permutations.append(perm)
# assume list_permutations[0] is identity
assert is_identity_permutation(list_permutations[0])
return list_permutations