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
def test_read_pseudo():
filename = 'test_pseudo.dat'
with open('test_pseudo.dat', 'w') as fin:
fin.write('#\n')
fin.write('3 4 5 0.2 0.1\n')
fin.write(' 4 1 87 0.99 -0.27\n')
reference_G_vectors = np.array([
[3, 4, 5],
[4, 1, 87]
]).astype('int')
reference_coefficients = np.array([
0.2+0.1j, 0.99-0.27j]).astype('complex')
G_vectors, coefficients = read_pseudo(filename)
assert np.abs(reference_G_vectors - G_vectors).sum() < 1e-6
assert np.abs(reference_coefficients - coefficients).sum() < 1e-6
os.remove(filename)
return