def test_cartesian_Euclidean_dot_product():
basis = np.array([
[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]
]).astype('d')
mydot = get_Euclidean_dot_product(basis)
for i in range(100):
m1, m2, m3 = np.random.randint(0, 100, size=3)
n1, n2, n3 = np.random.randint(0, 100, size=3)
expected_dot = m1*n1+m2*n2+m3*n3
actual_dot = mydot([m1, m2, m3], [n1, n2, n3])
assert abs(expected_dot - actual_dot) < 1e-6
return
def test_reciprocal_Euclidean_dot_product_of_ZnS():
basis = 0.5 * np.array([
[0., 1., 1.],
[1., 0., 1.],
[1., 1., 0.]
]).astype('d')
reciprocal_basis = get_reciprocal_space_elementary_vectors(basis)
rs_dot = get_Euclidean_dot_product(reciprocal_basis)
for i in range(100):
m1, m2, m3 = np.random.randint(0, 100, size=3)
expected_norm_sq = (2*pi) ** 2 * (3.*(m1**2+m2**2+m3**2) -
2.*(m1*m2+m1*m3+m2*m3))
norm_sq = rs_dot([m1, m2, m3], [m1, m2, m3])
assert abs(expected_norm_sq - norm_sq) < 1e-6
return
def band_structure(
direct_space_basis,
pseudo_fname,
k_list_fname,
G_norm_cutoff,
n_bands,
):
# -- get all necessary objects needed to compute the band structure
pseudo_Gs, pseudo_coefficients = read_pseudo(pseudo_fname)
k_vectors = read_kpoints(k_list_fname)
reciprocal_space_basis = \
get_reciprocal_space_elementary_vectors(direct_space_basis)
rs_dot = get_Euclidean_dot_product(reciprocal_space_basis)
assert pseudo_Gs.shape[0] == pseudo_coefficients.size
assert k_vectors.shape[1] == 3
# -- Basis of G vectors used for the matrix diagonalization
G_basis = get_ordered_stars(reciprocal_space_basis, G_norm_cutoff)
# -- generate potential matrix, which is k-independent
potential_matrix = build_potential_matrix(
G_basis, pseudo_Gs, pseudo_coefficients
)
# -- loop over the k points to compute the band energies
band_energies = []
for idx, k_vec in enumerate(k_vectors):
kinetic_matrix = build_kinetic_matrix(k_vec, G_basis, rs_dot)
hamiltonian = kinetic_matrix + potential_matrix
eigvals = np.sort(eigvalsh(hamiltonian))[:n_bands]
band_energies += [eigvals]
# -- simple check to see if the eigenvalues are real
band_energies = np.array(band_energies)
assert np.abs(band_energies.imag).sum() < 1e-3
return band_energies
