def test_thcl4(self):
filename = "../poscars/POSCAR_ThCl4"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms) # 88
rotations = symmetry.get_pointgroup_operations()
self.check_irreps(rotations, '4/m')
def test_b_h(self):
filename = "tests/poscars/POSCAR_WC"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms)
rotations = symmetry.get_pointgroup_operations()
self.check_irreps(rotations, '-6m2')
def test_97(self):
filename = "../poscars/POSCAR_NaGdCu2F8"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms)
rotations = symmetry.get_pointgroup_operations()
self.check_irreps(rotations, '422')
def test_cl12pd6(self):
filename = "../poscars/POSCAR_Cl12Pd6"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms) # 148
rotations = symmetry.get_pointgroup_operations()
self.check_irreps(rotations, '-3')
def __init__(self, atoms):
"""
Decomposer of vectors according to rotations
Parameters
----------
atoms : Phonopy Atoms object.
"""
self._atoms = atoms
self._symmetry = UnfolderSymmetry(atoms)
def test_a3(self):
filename = "tests/poscars/POSCAR_A3"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms)
rotations = symmetry.get_pointgroup_operations()
self.check_irreps(rotations, '6/mmm')
p = [0.0, 0.0, 0.5] # A (6/mmm)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '6/mmm')
p = [1.0 / 3.0, 1.0 / 3.0, 0.0] # K (-6m2)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '-6m2')
p = [0.5, 0.0, 0.0] # M (mmm)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, 'mmm')
p = [0.5, 0.0, 0.5] # L (mmm)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, 'mmm')
p = [0.0, 0.0, 0.25] # DT (6mm)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '6mm')
p = [1.0 / 3.0, 1.0 / 3.0, 0.25] # P (3m)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '3m')
def test_sc(self):
filename = "../poscars/POSCAR_Sc"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms) # 178
rotations = symmetry.get_pointgroup_operations()
self.check_irreps(rotations, '622')
p = [1.0 / 3.0, 1.0 / 3.0, 0.0] # K (32)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '32')
def test_a13(self):
filename = "../poscars/POSCAR_A13"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms) # 213
rotations = symmetry.get_pointgroup_operations()
self.check_irreps(rotations, '432')
p = [0.0, 0.5, 0.5] # X (422)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '422')
def test_b3(self):
filename = "../poscars/POSCAR_B3_conv"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms) # 216
rotations = symmetry.get_pointgroup_operations()
self.check_irreps(rotations, '-43m')
p = [0.0, 0.5, 0.5] # X (-42m)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '-42m')
def test_a3(self):
filename = "../poscars/POSCAR_A3"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms)
rotations = symmetry.get_pointgroup_operations()
self.check_irreps(rotations, '6/mmm')
p = [0.0, 0.0, 0.5] # A (6/mmm)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '6/mmm')
p = [1.0 / 3.0, 1.0 / 3.0, 0.0] # K (-6m2)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '-6m2')
p = [0.5, 0.0, 0.0] # M (mmm)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, 'mmm')
p = [0.5, 0.0, 0.5] # L (mmm)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, 'mmm')
p = [0.0, 0.0, 0.25] # DT (6mm)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '6mm')
def test_fcc_prim(self):
filename = "../poscars/POSCAR_fcc_prim"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms)
rotations = symmetry.get_pointgroup_operations()
check_irreps(rotations)
rotations = symmetry.get_group_of_wave_vector([0.00, 0.25, -0.25])[0]
check_irreps(rotations)
rotations = symmetry.get_group_of_wave_vector([0.50, 0.25, 0.25])[0]
check_irreps(rotations)
rotations = symmetry.get_group_of_wave_vector([0.25, 0.50, 0.25])[0]
check_irreps(rotations)
rotations = symmetry.get_group_of_wave_vector([0.25, 0.25, 0.50])[0]
check_irreps(rotations)
def test_fcc_conv(self):
filename = "../poscars/POSCAR_fcc"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms)
rotations = symmetry.get_pointgroup_operations()
self.check_irreps(rotations, 'm-3m')
rotations = symmetry.get_group_of_wave_vector([0.00, 0.25, 0.25])[0]
self.check_irreps(rotations, 'mm2')
rotations = symmetry.get_group_of_wave_vector([0.25, 0.00, 0.25])[0]
self.check_irreps(rotations, 'mm2')
rotations = symmetry.get_group_of_wave_vector([0.25, 0.25, 0.00])[0]
self.check_irreps(rotations, 'mm2')
def test_fcc_conv(self):
# np.set_printoptions(threshold=2304, linewidth=145) # 48 * 48
filename = "../poscars/POSCAR_fcc"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms)
rotations = symmetry.get_pointgroup_operations()
check_irreps(rotations)
rotations = symmetry.get_group_of_wave_vector([0.00, 0.25, 0.25])[0]
check_irreps(rotations)
rotations = symmetry.get_group_of_wave_vector([0.25, 0.00, 0.25])[0]
check_irreps(rotations)
rotations = symmetry.get_group_of_wave_vector([0.25, 0.25, 0.00])[0]
check_irreps(rotations)
def test_mgnh(self):
filename = "../poscars/POSCAR_MgNH"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms) # 216
rotations = symmetry.get_pointgroup_operations()
self.check_irreps(rotations, '6/m')
p = [1.0 / 3.0, 1.0 / 3.0, 0.0] # K (-6)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '-6')
p = [0.0, 0.0, 0.25] # DT (6)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '6')
p = [1.0 / 3.0, 1.0 / 3.0, 0.25] # P (3)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '3')
class RotationalProjector(object):
def __init__(self, atoms):
"""
Decomposer of vectors according to rotations
Parameters
----------
atoms : Phonopy Atoms object.
"""
self._atoms = atoms
self._symmetry = UnfolderSymmetry(atoms)
def create_standard_rotations(self, kpoint):
"""
Create standard rotations for IR labels
Parameters
----------
kpoint : 1d array
Reciprocal space point in fractional coordinates for PC.
This is the representative of the star.
IR labels are determined using this.
TODO
----
To be modified for nonsymmorphic space groups.
"""
symmetry = self._symmetry
rotations, translations = symmetry.get_group_of_wave_vector(kpoint)
self._create_irreps(rotations)
self._standard_rotations = rotations
# self.print_symmetry_operations(rotations, translations)
@staticmethod
def calculate_factor_system(rotations, translations, kpoint):
"""Calculate factor system
Here the factor system is defined as
.. math::
e^{-i (\mathbf{R}_i^T \mathbf{k} - \mathbf{k}) \cdot \mathbf{w}_j,
"""
nsyms = len(rotations)
factor_system = np.zeros((nsyms, nsyms), dtype=complex)
for i, rotation in enumerate(rotations):
for j, translation in enumerate(translations):
kdiff = np.dot(rotation.T, kpoint) - kpoint
factor_system[i, j] = np.exp(-2.0j * np.pi *
np.dot(kdiff, translation))
return factor_system
@staticmethod
def print_factor_system(factor_system):
nsyms = factor_system.shape[0]
print('Factor system:')
for i in range(nsyms):
for j in range(nsyms):
v = factor_system[i, j]
print('({:10.6f}{:+10.6f}i) '.format(v.real, v.imag), end='')
print()
@staticmethod
def is_trivial_factor_system(factor_system, prec=1e-6):
if np.any(np.abs(factor_system - 1.0) > prec):
return False
return True
@staticmethod
def print_symmetry_operations(rotations, translations):
print('Symmetry operations:')
for r, t in zip(rotations, translations):
for i in range(3):
for j in range(3):
print('{:10.6f}'.format(r[i, j]), end='')
print(' {:10.6f}'.format(t[i]))
print()
def _assign_characters_to_rotations(self, rotations, arm_transformation):
irreps = self._irreps
rotation_labels = self._assign_class_labels_to_rotations(
rotations, arm_transformation)
characters = irreps.assign_characters_to_rotations(rotation_labels)
return characters
def _assign_class_labels_to_rotations(self, rotations, arm_transformation):
standard_rotation_labels = self._standard_rotation_labels
modulated_standard_rotations = (
self._modulate_standard_rotations(arm_transformation))
rotation_labels = []
for r in rotations:
for i, sr in enumerate(modulated_standard_rotations):
if np.all(r == sr):
rotation_labels.append(standard_rotation_labels[i])
break
if len(rotation_labels) != len(standard_rotation_labels):
raise ValueError("Rotation labels cannot be correctly assigned.")
return rotation_labels
def _modulate_standard_rotations(self, arm_transformation):
standard_rotations = self._standard_rotations
modulated_standard_rotations = np.zeros_like(standard_rotations)
for i, r in enumerate(standard_rotations):
modulated_standard_rotations[i] = (np.dot(
np.dot(np.linalg.inv(arm_transformation), r),
arm_transformation))
return np.array(modulated_standard_rotations, dtype=int)
def _create_mappings(self, rotations, translations):
structure_analyzer = StructureAnalyzer(self._atoms)
mappings = []
for r, t in zip(rotations, translations):
mapping = structure_analyzer.extract_mapping_for_symopr(r, t)
mappings.append(mapping)
self._mappings = np.array(mappings)
self._mappings_modifier = MappingsModifier(mappings)
def _invert_mappings(self):
return self._mappings_modifier.invert_mappings()
def _create_irreps(self, rotations):
irreps = Irreps(rotations)
character_table_data = irreps.get_character_table_data()
self._ir_labels = character_table_data["ir_labels"]
character_table = np.array(character_table_data["character_table"])
self._ir_dimensions = character_table[:, 0]
self._standard_rotation_labels = irreps.get_rotation_labels()
self._irreps = irreps
def _create_rotations_cart(self, rotations):
rotations_cart = []
cell = self._atoms.get_cell()
for r in rotations:
rotation_cart = np.dot(np.dot(cell.T, r), np.linalg.inv(cell.T))
rotations_cart.append(rotation_cart)
return np.array(rotations_cart)
def project_vectors(self, vectors, kpoint, arm_transformation):
"""
Parameters
----------
vectors : Vectors without phase factors.
kpoint : K point in fractional coordinates for SC.
arm_transformation : 3 x 3 array
Matrix to get "kpoint" from the representative of the star.
TODO
----
To be modified for nonsymmorphic space groups.
"""
rotations, translations = self._symmetry.get_group_of_wave_vector(
kpoint)
factor_system = self.calculate_factor_system(rotations, translations,
kpoint)
if not self.is_trivial_factor_system(factor_system):
errmsg = (
"The current factor system is not trivial.\n"
"So far the code cannot treat nontrivial factor system correctly\n"
"(even if it is p-equivalent to the trivial system).")
raise ValueError(errmsg)
self._create_mappings(rotations, translations)
characters = self._assign_characters_to_rotations(
rotations, arm_transformation)
rotations_cart = self._create_rotations_cart(rotations)
ir_dimensions = self._ir_dimensions
natoms = self._atoms.get_number_of_atoms()
ndim = kpoint.shape[0] # The number of dimensions of space
order = rotations.shape[0]
expanded_mappings_inv = self._mappings_modifier.expand_mappings(
ndim, is_inverse=True)
# scaled_positions = self._atoms.get_scaled_positions()
# phases = np.exp(2.0j * np.pi * np.dot(scaled_positions, kpoint))
# phases = np.repeat(phases, ndim)
shape = (len(ir_dimensions), ) + vectors.shape
projected_vectors = np.zeros(shape, dtype=vectors.dtype)
for i, (r, expanded_mapping_inv) in enumerate(
zip(rotations_cart, expanded_mappings_inv)):
tmp = vectors[..., expanded_mapping_inv, :]
tmp2 = np.zeros_like(vectors)
for iatom in range(natoms):
tmp2[..., (3 * iatom):(3 * (iatom + 1)), :] = np.einsum(
'ij,...jk->...ik', r,
tmp[..., (3 * iatom):(3 * (iatom + 1)), :])
projected_vectors += (tmp2[None].T * np.conj(characters[i, :])).T
# projected_vectors *= phases[None, :, None]
projected_vectors = (projected_vectors.T * ir_dimensions[:]).T
projected_vectors /= order
return projected_vectors
def get_ir_labels(self):
return self._ir_labels
def get_num_irs(self):
return len(self._ir_labels)
def get_pointgroup_symbol(self):
return self._irreps.get_pointgroup_symbol()
def test_fcc_prim(self):
filename = "../poscars/POSCAR_fcc_prim"
atoms = read_vasp(filename)
symmetry = UnfolderSymmetry(atoms)
rotations = symmetry.get_pointgroup_operations()
self.check_irreps(rotations, 'm-3m')
rotations = symmetry.get_group_of_wave_vector([0.00, 0.25, -0.25])[0]
self.check_irreps(rotations, 'mm2')
p = [0.50, 0.25, 0.75] # W (-42m)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '-42m')
rotations = symmetry.get_group_of_wave_vector([0.50, 0.25, 0.25])[0]
self.check_irreps(rotations, 'mm2')
rotations = symmetry.get_group_of_wave_vector([0.25, 0.50, 0.25])[0]
self.check_irreps(rotations, 'mm2')
rotations = symmetry.get_group_of_wave_vector([0.25, 0.25, 0.50])[0]
self.check_irreps(rotations, 'mm2')
p = [0.5, 0.3, 0.7] # Q (2)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '2')
p = [0.4, 0.4, 0.1] # C (m)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, 'm')
p = [0.4, 0.2, 0.1] # GP (1)
rotations = symmetry.get_group_of_wave_vector(p)[0]
self.check_irreps(rotations, '1')
class TestUnfolderSymmetry(unittest.TestCase):
def setUp(self):
atoms = read_vasp("POSCAR_sc")
self._symmetry = UnfolderSymmetry(atoms)
def test_000(self):
kpoint = np.array([0.0, 0.0, 0.0])
(rotations_kpoint,
translations_kpoint) = self._symmetry.create_little_group(kpoint)
self.assertEqual(len(rotations_kpoint), 48)
def test_100(self):
kpoint = np.array([0.5, 0.0, 0.0]) # X: D_4h
(rotations_kpoint,
translations_kpoint) = self._symmetry.create_little_group(kpoint)
self.assertNotEqual(len(rotations_kpoint), 48)
self.assertEqual(len(rotations_kpoint), 16)
def test_110(self):
kpoint = np.array([0.5, 0.5, 0.0]) # M: D_4h
(rotations_kpoint,
translations_kpoint) = self._symmetry.create_little_group(kpoint)
self.assertNotEqual(len(rotations_kpoint), 48)
self.assertEqual(len(rotations_kpoint), 16)
def test_111(self):
kpoint = np.array([0.5, 0.5, 0.5]) # R: O_h
(rotations_kpoint,
translations_kpoint) = self._symmetry.create_little_group(kpoint)
self.assertEqual(len(rotations_kpoint), 48)
def test_star_000(self):
symmetry = self._symmetry
prec = 1e-9
kpoint = np.array([0.0, 0.0, 0.0])
star, transformation_matrices = symmetry.create_star(kpoint)
star_exp = [
[0.0, 0.0, 0.0],
]
self.assertTrue(np.all(np.abs(star - star_exp) < prec))
def test_star_100(self):
symmetry = self._symmetry
prec = 1e-9
kpoint = np.array([0.5, 0.0, 0.0])
star, transformation_matrices = symmetry.create_star(kpoint)
self.assertEqual(len(star), 6)
def test_star_110(self):
symmetry = self._symmetry
prec = 1e-9
kpoint = np.array([0.5, 0.5, 0.0])
star, transformation_matrices = symmetry.create_star(kpoint)
self.assertEqual(len(star), 12)
def test_star_111(self):
symmetry = self._symmetry
prec = 1e-9
kpoint = np.array([0.5, 0.5, 0.5])
star, transformation_matrices = symmetry.create_star(kpoint)
self.assertEqual(len(star), 8)
def setUp(self):
atoms = read_vasp("POSCAR_sc")
self._symmetry = UnfolderSymmetry(atoms)
def setUp(self):
atoms = read_vasp(os.path.join(POSCAR_DIR, "POSCAR_A_h"))
self._symmetry = UnfolderSymmetry(atoms)
