def test_simple_ordered_stars():
basis = np.array([
[1, 0, 0],
[2, 2, 0],
[0, 0, 1]
])
stars = get_ordered_stars(basis, 0.5)
ref_stars = np.array([
[0, 0, 0]
])
assert np.abs(ref_stars - stars).sum() < 1e-6
stars = get_ordered_stars(basis, 1.0)
ref_stars = np.array([
[ 0, 0, 0],
[-1, 0, 0],
[ 0, 0, -1],
[ 0, 0, 1],
[ 1, 0, 0]
])
assert np.abs(ref_stars - stars).sum() < 1e-6
stars = get_ordered_stars(basis, 2.0)
ref_stars = np.array([
[ 0, 0, 0],
[-1, 0, 0],
[ 0, 0, -1],
[ 0, 0, 1],
[ 1, 0, 0],
[-1, 0, -1],
[-1, 0, 1],
[ 1, 0, -1],
[ 1, 0, 1],
[-2, 0, 0],
[-2, 1, 0],
[ 0, 0, -2],
[ 0, 0, 2],
[ 2, -1, 0],
[ 2, 0, 0]
])
assert np.abs(ref_stars - stars).sum() < 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