from __future__ import annotations import numpy as np from spglib import ( SpglibMagneticDataset, get_magnetic_spacegroup_type_from_symmetry, get_magnetic_symmetry, get_magnetic_symmetry_dataset, get_symmetry_dataset, ) def _check_magnetic_spacegroup_type( dataset: SpglibMagneticDataset, lattice: np.ndarray, uni_number: int ): msg_type = get_magnetic_spacegroup_type_from_symmetry( rotations=dataset.rotations, translations=dataset.translations, time_reversals=dataset.time_reversals, lattice=lattice, ) assert msg_type.uni_number == uni_number def test_type1(): # 0.107_Ho2Ge2O7.mcif # Type-I: 92.111 P 4abw 2nw lattice = np.diag([6.8083, 6.8083, 12.3795]) positions = np.array( [ [0.87664, 0.35295, 0.13499], [0.14705, 0.37664, 0.38499], [0.85295, 0.62336, 0.88499], [0.37664, 0.14705, 0.61501], [0.62336, 0.85295, 0.11501], [0.12336, 0.64705, 0.63499], [0.35295, 0.87664, 0.86501], [0.64705, 0.12336, 0.36501], ], ) numbers = [0, 0, 0, 0, 0, 0, 0, 0] magmoms = np.array( [ [1.67, -8.9, 0.0], [8.9, 1.67, 0.0], [-8.9, -1.67, 0.0], [1.67, 8.9, 0.0], [-1.67, -8.9, 0.0], [-1.67, 8.9, 0.0], [-8.9, 1.67, 0.0], [8.9, -1.67, 0.0], ], ) dataset = get_magnetic_symmetry_dataset((lattice, positions, numbers, magmoms)) uni_number = 771 # BNS=92.111 assert dataset.hall_number == 369 assert dataset.msg_type == 1 assert dataset.uni_number == uni_number # all dataset['time_reversals'] should be False assert not np.any(dataset.time_reversals) _check_magnetic_spacegroup_type(dataset, lattice, uni_number) def test_type3(): # MAGNDATA 0.101_Mn2GeO4.mcif # Type-III # BNS: Pn'm'a" (62.446) # MHall: -P 2ac 2n' lattice = np.array( [ [1.06949000e01, 0.00000000e00, 0.00000000e00], [3.84998337e-16, 6.28750000e00, 0.00000000e00], [3.09590711e-16, 3.09590711e-16, 5.05600000e00], ], ) positions = np.array( [ [0.0, 0.0, 0.0], [0.5, 0.0, 0.5], [0.5, 0.5, 0.5], [0.0, 0.5, 0.0], [0.2794, 0.25, 0.9906], [0.2206, 0.75, 0.4906], [0.7206, 0.75, 0.0094], [0.7794, 0.25, 0.5094], ], ) numbers = [0, 0, 0, 0, 0, 0, 0, 0] magmoms = np.array( [ [3.0, 0.4, 0.0], [-3.0, -0.4, 0.0], [-3.0, 0.4, 0.0], [3.0, -0.4, 0.0], [4.5, 0.0, 0.0], [-4.5, 0.0, 0.0], [4.5, 0.0, 0.0], [-4.5, 0.0, 0.0], ], ) dataset = get_magnetic_symmetry_dataset((lattice, positions, numbers, magmoms)) uni_number = 544 assert dataset.hall_number == 292 assert dataset.msg_type == 3 assert dataset.uni_number == uni_number _check_magnetic_spacegroup_type(dataset, lattice, uni_number) def test_monoclinic(): # MAGNDATA 0.103_Mn2GeO4.mcif # Type-I # unique axis-c a = 10.69260000 b = 6.28510000 c = 5.05570000 lattice = np.diag([a, b, c]) positions = np.array( [ [0.00000000, 0.00000000, 0.00000000], [0.50000000, 0.00000000, 0.50000000], [0.00000000, 0.50000000, 0.00000000], [0.50000000, 0.50000000, 0.50000000], [0.27940000, 0.25000000, 0.99030000], [0.22060000, 0.75000000, 0.49030000], [0.72060000, 0.75000000, 0.00970000], [0.77940000, 0.25000000, 0.50970000], ], ) numbers = np.array([0, 0, 0, 0, 0, 0, 0, 0]) magmoms = np.array( [ [1.90000000, 2.80000000, 0.30000000], [-1.90000000, -2.80000000, 0.30000000], [1.70000000, 2.40000000, -0.30000000], [-1.70000000, -2.40000000, -0.30000000], [2.90000000, 3.40000000, 0.00000000], [-2.90000000, -3.40000000, 0.00000000], [2.90000000, 3.40000000, 0.00000000], [-2.90000000, -3.40000000, 0.00000000], ], ) dataset = get_magnetic_symmetry_dataset((lattice, positions, numbers, magmoms)) uni_number = 82 # BNS: 14.75 assert dataset.msg_type == 1 assert dataset.uni_number == uni_number assert np.allclose( dataset.transformation_matrix, np.array([[0, 1, 0], [0, 0, 1], [1, 0, 0]]), ) assert np.allclose(dataset.std_rotation_matrix, np.eye(3)) std_lattice_expect = np.array([[0, b, 0], [0, 0, c], [a, 0, 0]]) # unique-axis assert np.allclose(dataset.std_lattice, std_lattice_expect) std_positions_expect = np.array( [ [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.50000000, 0.50000000], [0.50000000, 0.00000000, 0.00000000], [0.50000000, 0.50000000, 0.50000000], [0.25000000, 0.99030000, 0.27940000], [0.75000000, 0.49030000, 0.22060000], [0.75000000, 0.00970000, 0.72060000], [0.25000000, 0.50970000, 0.77940000], ], ) assert np.allclose(dataset.std_positions, std_positions_expect) assert np.allclose(dataset.std_tensors, magmoms) _check_magnetic_spacegroup_type(dataset, lattice, uni_number) def test_centered_monoclinic(): # MAGNDATA: 0.208_TlFe1.6Se2.mcif lattice = np.array( [ [8.62700000, 0.00000000, 0.00000000], [0.00000000, 8.62700000, 0.00000000], [0.00000000, 0.00000000, 13.82200000], ], ) positions = np.array( [ [0.09250000, 0.19644000, 0.24573000], [0.59250000, 0.69644000, 0.74573000], [0.09250000, 0.19644000, 0.75427000], [0.59250000, 0.69644000, 0.25427000], [0.90750000, 0.80356000, 0.24573000], [0.40750000, 0.30356000, 0.74573000], [0.90750000, 0.80356000, 0.75427000], [0.40750000, 0.30356000, 0.25427000], [0.80356000, 0.09250000, 0.24573000], [0.30356000, 0.59250000, 0.74573000], [0.80356000, 0.09250000, 0.75427000], [0.30356000, 0.59250000, 0.25427000], [0.19644000, 0.90750000, 0.24573000], [0.69644000, 0.40750000, 0.74573000], [0.19644000, 0.90750000, 0.75427000], [0.69644000, 0.40750000, 0.25427000], ], ) numbers = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) magmoms = np.array( [ [2.67400000, -1.33700000, 0.00000000], [2.67400000, -1.33700000, 0.00000000], [-2.67400000, 1.33700000, 0.00000000], [-2.67400000, 1.33700000, 0.00000000], [2.67400000, -1.33700000, 0.00000000], [2.67400000, -1.33700000, 0.00000000], [-2.67400000, 1.33700000, 0.00000000], [-2.67400000, 1.33700000, 0.00000000], [2.67400000, -1.33700000, 0.00000000], [2.67400000, -1.33700000, 0.00000000], [-2.67400000, 1.33700000, 0.00000000], [-2.67400000, 1.33700000, 0.00000000], [2.67400000, -1.33700000, 0.00000000], [2.67400000, -1.33700000, 0.00000000], [-2.67400000, 1.33700000, 0.00000000], [-2.67400000, 1.33700000, 0.00000000], ], ) dataset = get_magnetic_symmetry_dataset((lattice, positions, numbers, magmoms)) uni_number = 67 assert dataset.uni_number == uni_number _check_magnetic_spacegroup_type(dataset, lattice, uni_number) def test_trigonal(): # MAGNDATA: 0.108_Mn3Ir.mcif # hall_number=459 (166:R) # Type-III, BNS: 166.101 lattice = np.array( [ [3.77000000, 0.00000000, 0.00000000], [0.00000000, 3.77000000, 0.00000000], [0.00000000, 0.00000000, 3.77000000], ], ) positions = np.array( [ [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.50000000, 0.50000000], [0.50000000, 0.00000000, 0.50000000], [0.50000000, 0.50000000, 0.00000000], ], ) numbers = np.array([0, 1, 1, 1]) magmoms = np.array( [ [0.00000000, 0.00000000, 0.00000000], [2.00000000, -1.00000000, -1.00000000], [-1.00000000, 2.00000000, -1.00000000], [-1.00000000, -1.00000000, 2.00000000], ], ) dataset = get_magnetic_symmetry_dataset((lattice, positions, numbers, magmoms)) uni_number = 1331 assert dataset.uni_number == uni_number assert dataset.hall_number == 458 # choose hexagonal axes in default assert dataset.msg_type == 3 assert len(dataset.time_reversals) == 12 # Use hexagonal axes for standardized cell assert np.around(1 / np.linalg.det(dataset.transformation_matrix)) == 3 assert dataset.std_positions.shape[0] == positions.shape[0] * 3 assert dataset.std_types.shape[0] == numbers.shape[0] * 3 assert dataset.std_tensors.shape[0] == magmoms.shape[0] * 3 # Test hR with the standardized cell std_cell = ( dataset.std_lattice, dataset.std_positions, dataset.std_types, dataset.std_tensors, ) dataset2 = get_magnetic_symmetry_dataset(std_cell) assert dataset2.uni_number == 1331 assert dataset2.hall_number == 458 assert dataset2.n_operations == 12 * 3 assert np.isclose( np.linalg.det(dataset2.primitive_lattice), np.linalg.det(lattice), ) _check_magnetic_spacegroup_type(dataset, lattice, uni_number) def test_conventional(): # MAGNDATA: 0.110_Cr2O3.mcif # BNS: 15.87, MHall: C 2yc' -1' lattice = np.array( [ [4.95700000, 0.00000000, 0.00000000], [-2.47850000, 4.29288793, 0.00000000], [0.00000000, 0.00000000, 13.59230000], ], ) positions = np.array( [ [0.00000000, 0.00000000, 0.34751000], [0.33333333, 0.66666667, 0.01417667], [0.66666667, 0.33333333, 0.68084333], [0.33333333, 0.66666667, 0.51417667], [0.66666667, 0.33333333, 0.18084333], [0.00000000, 0.00000000, 0.84751000], [0.33333333, 0.66666667, 0.81915667], [0.00000000, 0.00000000, 0.15249000], [0.66666667, 0.33333333, 0.48582333], [0.00000000, 0.00000000, 0.65249000], [0.66666667, 0.33333333, 0.98582333], [0.33333333, 0.66666667, 0.31915667], [0.30570000, 0.00000000, 0.25000000], [0.63903333, 0.66666667, 0.91666667], [0.97236667, 0.33333333, 0.58333333], [0.02763333, 0.66666667, 0.41666667], [0.36096667, 0.33333333, 0.08333333], [0.69430000, 0.00000000, 0.75000000], ], ) numbers = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]) magmoms = np.array( [ [-1.00000000, 0.00000000, 0.00000000], [-1.00000000, 0.00000000, 0.00000000], [-1.00000000, 0.00000000, 0.00000000], [-1.00000000, 0.00000000, 0.00000000], [-1.00000000, 0.00000000, 0.00000000], [-1.00000000, 0.00000000, 0.00000000], [1.00000000, 0.00000000, 0.00000000], [1.00000000, 0.00000000, 0.00000000], [1.00000000, 0.00000000, 0.00000000], [1.00000000, 0.00000000, 0.00000000], [1.00000000, 0.00000000, 0.00000000], [1.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], ], ) dataset = get_magnetic_symmetry_dataset((lattice, positions, numbers, magmoms)) uni_number = 94 assert dataset.uni_number == uni_number assert dataset.hall_number == 90 assert dataset.rotations.shape[0] == 12 # Original hP setting with 18 atoms are converted to mS # with 12 (= 18 / 3 * 2) atoms assert dataset.n_std_atoms == 12 _check_magnetic_spacegroup_type(dataset, lattice, uni_number) def test_type4(): # MAGNDATA: 0.651_Er3Cu4Sn4.mcif # _space_group_magn.number_BNS 12.63 lattice = np.array( [ [16.08310000, 0.00000000, 0.00000000], [0.00000000, 4.38870000, 0.00000000], [-5.97205829, 0.00000000, 12.38135828], ], ) positions = np.array( [ [0.00000000, 0.00000000, 0.25000000], [0.50000000, 0.50000000, 0.25000000], [0.00000000, 0.00000000, 0.75000000], [0.50000000, 0.50000000, 0.75000000], [0.12900000, 0.00000000, 0.05850000], [0.62900000, 0.50000000, 0.05850000], [0.12900000, 0.00000000, 0.55850000], [0.62900000, 0.50000000, 0.55850000], [0.87100000, 0.00000000, 0.44150000], [0.37100000, 0.50000000, 0.44150000], [0.87100000, 0.00000000, 0.94150000], [0.37100000, 0.50000000, 0.94150000], ], ) numbers = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) magmoms = np.array( [ [0.00000000, 8.86000000, 0.00000000], [0.00000000, 8.86000000, 0.00000000], [-0.00000000, -8.86000000, 0.00000000], [-0.00000000, -8.86000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], ], ) dataset = get_magnetic_symmetry_dataset((lattice, positions, numbers, magmoms)) uni_number = 70 assert dataset.uni_number == uni_number assert dataset.hall_number == 63 assert dataset.msg_type == 4 _check_magnetic_spacegroup_type(dataset, lattice, uni_number) def test_nonstandard_setting(): # MAGNDATA: 0.131_Mn\(N\(CN2\)\)2.mcif # BNS: 58.398 lattice = np.array( [ [6.10960000, 0.00000000, 0.00000000], [0.00000000, 7.25550000, 0.00000000], [0.00000000, 0.00000000, 7.57080000], ], ) positions = np.array( [ [0.00000000, 0.00000000, 0.00000000], [0.50000000, 0.50000000, 0.50000000], [0.27320000, 0.85790000, 0.35200000], [0.22680000, 0.35790000, 0.14800000], [0.72680000, 0.14210000, 0.64800000], [0.77320000, 0.64210000, 0.85200000], [0.77320000, 0.64210000, 0.14800000], [0.72680000, 0.14210000, 0.35200000], [0.22680000, 0.35790000, 0.85200000], [0.27320000, 0.85790000, 0.64800000], ], ) numbers = np.array([0, 0, 1, 1, 1, 1, 1, 1, 1, 1]) magmoms = np.array( [ [5.01000000, 0.00000000, 0.00000000], [-5.01000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], ], ) dataset = get_magnetic_symmetry_dataset((lattice, positions, numbers, magmoms)) uni_number = 496 assert dataset.uni_number == uni_number assert dataset.msg_type == 3 _check_magnetic_spacegroup_type(dataset, lattice, uni_number) def test_nonstandard_setting2(): # MAGNDATA: 0.129_Cu3Mo2O9.mcif # _space_group_magn.number_BNS 19.27 lattice = np.array( [ [7.64760000, 0.00000000, 0.00000000], [0.00000000, 6.88550000, 0.00000000], [0.00000000, 0.00000000, 14.60580000], ], ) positions = np.array( [ [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.50000000, 0.00000000], [0.50000000, 0.50000000, 0.50000000], [0.50000000, 0.00000000, 0.50000000], [0.33860000, 0.25000000, 0.64260000], [0.66140000, 0.75000000, 0.35740000], [0.83860000, 0.25000000, 0.85740000], [0.16140000, 0.75000000, 0.14260000], [0.20550000, 0.25000000, 0.43720000], [0.79450000, 0.75000000, 0.56280000], [0.70550000, 0.25000000, 0.06280000], [0.29450000, 0.75000000, 0.93720000], ], ) numbers = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) magmoms = np.array( [ [0.70000000, 0.00000000, 0.70000000], [-0.70000000, -0.00000000, -0.70000000], [-0.70000000, 0.00000000, 0.70000000], [0.70000000, -0.00000000, -0.70000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.00000000, 0.00000000, 0.00000000], [0.70000000, 0.00000000, 0.70000000], [-0.70000000, -0.00000000, -0.70000000], [-0.70000000, 0.00000000, 0.70000000], [0.70000000, -0.00000000, -0.70000000], ], ) dataset = get_magnetic_symmetry_dataset((lattice, positions, numbers, magmoms)) uni_number = 125 assert dataset.uni_number == uni_number _check_magnetic_spacegroup_type(dataset, lattice, uni_number) def test_nonstandard_setting3(): lattice = np.array( [ [19.27760000, 0.00000000, 0.00000000], [0.00000000, 9.24090000, 0.00000000], [0.00000000, 0.00000000, 5.46760000], ], ) positions = np.array( [ [0.12280000, 0.34560000, 0.35920000], [0.37720000, 0.65440000, 0.85920000], [0.37720000, 0.84560000, 0.35920000], [0.12280000, 0.15440000, 0.85920000], [0.62280000, 0.15440000, 0.64080000], [0.87720000, 0.84560000, 0.14080000], [0.87720000, 0.65440000, 0.64080000], [0.62280000, 0.34560000, 0.14080000], [0.37770000, 0.48180000, 0.34870000], [0.12230000, 0.51820000, 0.84870000], [0.12230000, 0.98180000, 0.34870000], [0.37770000, 0.01820000, 0.84870000], [0.87770000, 0.01820000, 0.65130000], [0.62230000, 0.98180000, 0.15130000], [0.62230000, 0.51820000, 0.65130000], [0.87770000, 0.48180000, 0.15130000], ], ) numbers = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) magmoms = np.array( [ [4.05000000, 0.00000000, 0.10000000], [-4.05000000, 0.00000000, 0.10000000], [4.05000000, -0.00000000, -0.10000000], [-4.05000000, -0.00000000, -0.10000000], [-4.05000000, 0.00000000, 0.10000000], [4.05000000, 0.00000000, 0.10000000], [-4.05000000, -0.00000000, -0.10000000], [4.05000000, -0.00000000, -0.10000000], [4.05000000, 0.00000000, 0.10000000], [-4.05000000, 0.00000000, 0.10000000], [4.05000000, -0.00000000, -0.10000000], [-4.05000000, -0.00000000, -0.10000000], [-4.05000000, 0.00000000, 0.10000000], [4.05000000, 0.00000000, 0.10000000], [-4.05000000, -0.00000000, -0.10000000], [4.05000000, -0.00000000, -0.10000000], ], ) dataset = get_magnetic_symmetry_dataset((lattice, positions, numbers, magmoms)) uni_number = 533 assert dataset.uni_number == uni_number _check_magnetic_spacegroup_type(dataset, lattice, uni_number) def test_nonstandard_type4(): # MAGNDATA: 1.14_Ho2BaNiO5.mcif # Non-standard centering lattice = np.array( [ [7.50910000, 0.00000000, 0.00000000], [0.00000000, 5.73190000, 0.00000000], [0.00000000, 0.00000000, 22.54300000], ], ) positions = np.array( [ [0.25000000, 0.00000000, 0.10125000], [0.50000000, 0.50000000, 0.85125000], [0.75000000, 0.00000000, 0.60125000], [0.00000000, 0.50000000, 0.35125000], [0.75000000, 0.00000000, 0.10125000], [0.00000000, 0.50000000, 0.85125000], [0.50000000, 0.50000000, 0.35125000], [0.25000000, 0.00000000, 0.60125000], [0.75000000, 0.00000000, 0.39875000], [0.50000000, 0.50000000, 0.64875000], [0.25000000, 0.00000000, 0.89875000], [0.00000000, 0.50000000, 0.14875000], [0.25000000, 0.00000000, 0.39875000], [0.00000000, 0.50000000, 0.64875000], [0.50000000, 0.50000000, 0.14875000], [0.75000000, 0.00000000, 0.89875000], [0.00000000, 0.00000000, 0.00000000], [0.25000000, 0.50000000, 0.75000000], [0.50000000, 0.00000000, 0.50000000], [0.75000000, 0.50000000, 0.25000000], [0.50000000, 0.00000000, 0.00000000], [0.75000000, 0.50000000, 0.75000000], [0.25000000, 0.50000000, 0.25000000], [0.00000000, 0.00000000, 0.50000000], ], ) numbers = np.array( [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], ) magmoms = np.array( [ [0.12000000, 0.00000000, 9.06000000], [0.12000000, 0.00000000, 9.06000000], [0.12000000, 0.00000000, 9.06000000], [0.12000000, 0.00000000, 9.06000000], [-0.12000000, -0.00000000, -9.06000000], [-0.12000000, -0.00000000, -9.06000000], [-0.12000000, -0.00000000, -9.06000000], [-0.12000000, -0.00000000, -9.06000000], [-0.12000000, -0.00000000, -9.06000000], [-0.12000000, -0.00000000, -9.06000000], [-0.12000000, -0.00000000, -9.06000000], [-0.12000000, -0.00000000, -9.06000000], [0.12000000, 0.00000000, 9.06000000], [0.12000000, 0.00000000, 9.06000000], [0.12000000, 0.00000000, 9.06000000], [0.12000000, 0.00000000, 9.06000000], [0.58000000, -0.00000000, -1.26000000], [0.58000000, -0.00000000, -1.26000000], [0.58000000, -0.00000000, -1.26000000], [0.58000000, -0.00000000, -1.26000000], [-0.58000000, 0.00000000, 1.26000000], [-0.58000000, 0.00000000, 1.26000000], [-0.58000000, 0.00000000, 1.26000000], [-0.58000000, 0.00000000, 1.26000000], ], ) dataset = get_magnetic_symmetry_dataset((lattice, positions, numbers, magmoms)) uni_number = 97 assert dataset.uni_number == uni_number _check_magnetic_spacegroup_type(dataset, lattice, uni_number) def test_std_rotation(): # Cmce rigid_rotation = np.array( [ [1 / np.sqrt(2), -1 / np.sqrt(2), 0], [1 / np.sqrt(2), 1 / np.sqrt(2), 0], [0, 0, 1], ], ) a = 7.17851431 b = 3.99943947 c = 8.57154746 lattice = np.diag([a, b, c]) @ rigid_rotation.T positions = [ [0.0, 0.84688439, 0.1203133], [0.0, 0.65311561, 0.6203133], [0.0, 0.34688439, 0.3796867], [0.0, 0.15311561, 0.8796867], [0.5, 0.34688439, 0.1203133], [0.5, 0.15311561, 0.6203133], [0.5, 0.84688439, 0.3796867], [0.5, 0.65311561, 0.8796867], ] numbers = [ 35, ] * len(positions) dataset_sg = get_symmetry_dataset((lattice, positions, numbers)) assert np.allclose(dataset_sg.std_lattice, np.diag([a, b, c])) assert np.allclose(dataset_sg.transformation_matrix, np.eye(3)) assert np.allclose(dataset_sg.std_rotation_matrix, rigid_rotation.T) magmoms = [1.0] * len(positions) dataset_msg = get_symmetry_dataset((lattice, positions, numbers, magmoms)) assert np.allclose(dataset_msg.std_lattice, np.diag([a, b, c])) assert np.allclose(dataset_msg.transformation_matrix, np.eye(3)) assert np.allclose(dataset_msg.std_rotation_matrix, rigid_rotation.T) def test_primitive_lattice(): # https://github.com/spglib/spglib/issues/370 lattice = np.array( [ [10.6949, 0, 0], [0, 6.2875, 0], [0, 0, 5.056], ], ) positions = np.array( [ [0.0, 0.0, 0.0], [0.5, 0.0, 0.5], [0.5, 0.5, 0.5], [0.0, 0.5, 0.0], ], ) numbers = [0, 0, 0, 0] magmoms = np.array( [ [3.0, 0.4, 0.0], [-3.0, -0.4, 0.0], [-3.0, 0.4, 0.0], [3.0, -0.4, 0.0], ], ) primitive_lattice1 = get_magnetic_symmetry_dataset( (lattice, positions, numbers, magmoms), ).primitive_lattice primitive_lattice2 = get_magnetic_symmetry( (lattice, positions, numbers, magmoms), )["primitive_lattice"] assert np.allclose(primitive_lattice1, primitive_lattice2) def test_better_choice_of_orientation(): """Check standardized cell is recovered by tmat and origin shift. This test also examines the nice orientation of the standardized cell. """ a = 5.6903014761756712 lattice = np.diag([a, a, a]) positions = np.array( [ [0.0, 0.0, 0.0], [0.0, 0.5, 0.5], [0.5, 0.0, 0.5], [0.5, 0.5, 0.0], [0.5, 0.5, 0.5], [0.5, 0.0, 0.0], [0.0, 0.5, 0.0], [0.0, 0.0, 0.5], ] ) shift = [0.1, 0.2, 0.3] positions += shift numbers = np.array([1, 1, 1, 1, 2, 2, 2, 2]) magmoms = np.array([1, 1, 1, 1, -1, -1, -1, -1]) dataset = get_magnetic_symmetry_dataset((lattice, positions, numbers, magmoms)) tmat = dataset.transformation_matrix origin_shift = dataset.origin_shift std_lattice = np.linalg.inv(tmat).T @ lattice std_positions = positions @ tmat.T + origin_shift std_positions -= np.rint(std_positions) std_positions += np.where(std_positions < -1e-8, 1, 0) # _show_structure( # dataset.std_lattice, # dataset.std_positions, # dataset.std_types, # dataset.std_tensors, # ) # _show_structure(std_lattice, std_positions, numbers, magmoms) np.testing.assert_allclose(std_lattice, dataset.std_lattice) indices = [] for pos in std_positions: diff = dataset.std_positions - pos diff -= np.rint(diff) dist = np.linalg.norm(diff, axis=1) indices.append(np.where(dist < 1e-8)[0][0]) np.testing.assert_array_equal(numbers, dataset.std_types[indices]) np.testing.assert_allclose(magmoms, dataset.std_tensors[indices]) # check orientation np.testing.assert_allclose(std_lattice, lattice) # def _show_structure( # lattice: NDArray, positions: NDArray, types: NDArray, magmoms: NDArray # ): # print("") # for axis, v in zip(("a", "b", "c"), lattice): # print(f"{axis}: {v[0]:12.8f} {v[1]:12.8f} {v[2]:12.8f}") # print() # for n, pos, mom in zip(types, positions, magmoms): # print(f"{n}: {pos[0]:12.8f} {pos[1]:12.8f} {pos[2]:12.8f} {mom:12.8f}")