def test_kpm_reuse():
"""KPM should return the same result when a single object is used for multiple calculations"""
model = pb.Model(graphene.monolayer(), graphene.hexagon_ac(10))
kpm = pb.kpm(model, silent=True)
energy = np.linspace(-5, 5, 50)
broadening = 0.1
for position in [0, 0], [6, 0]:
actual = kpm.calc_ldos(energy, broadening, position)
expected = pb.kpm(model).calc_ldos(energy, broadening, position)
assert pytest.fuzzy_equal(actual, expected, rtol=1e-3, atol=1e-6)
def factory(v1, v2, energy=np.linspace(0, 0.1, 10)):
model = pb.Model(graphene.monolayer(),
graphene.hexagon_ac(side_width=15),
pb.constant_potential(v1), pb.constant_potential(v2))
kpm = pb.kpm(model, kernel=pb.lorentz_kernel())
return kpm.deferred_ldos(energy, broadening=0.15, position=[0, 0])
def test_dos(params, baseline, plot_if_fails):
configurations = [
{
'matrix_format': "ELL",
'optimal_size': False,
'interleaved': False
},
{
'matrix_format': "ELL",
'optimal_size': True,
'interleaved': True
},
]
model = pb.Model(*params)
kernel = pb.lorentz_kernel()
strategies = [
pb.kpm(model, kernel=kernel, silent=True, **c) for c in configurations
]
energy = np.linspace(0, 2, 25)
results = [kpm.calc_dos(energy, broadening=0.15) for kpm in strategies]
expected = results[0].with_data(
baseline(results[0].data.astype(np.float32)))
for i in range(len(results)):
plot_if_fails(results[i], expected, 'plot', label=i)
for result in results:
assert pytest.fuzzy_equal(result, expected, rtol=1e-3, atol=1e-6)
def test_ldos_sublattice():
"""LDOS for A and B sublattices should be antisymmetric for graphene with a mass term"""
model = pb.Model(graphene.monolayer(), graphene.hexagon_ac(10),
graphene.mass_term(1))
kpm = pb.kpm(model, silent=True)
a, b = (kpm.calc_ldos(np.linspace(-5, 5, 50), 0.1, [0, 0], sub)
for sub in ('A', 'B'))
assert pytest.fuzzy_equal(a.data, b.data[::-1], rtol=1e-3, atol=1e-6)
def test_moments(model, plot_if_fails):
energy = np.linspace(0, 2, 25)
broadening = 0.15
position = dict(position=[0, 0], sublattice="A")
kpm = pb.kpm(model, silent=True)
expected_ldos = kpm.calc_ldos(energy, broadening, **position)
def manual_ldos():
idx = model.system.find_nearest(**position)
alpha = np.zeros(model.hamiltonian.shape[0])
alpha[idx] = 1
a, b = kpm.scaling_factors
num_moments = kpm.kernel.required_num_moments(broadening / a)
moments = kpm.moments(num_moments, alpha)
ns = np.arange(num_moments)
scaled_energy = (energy - b) / a
k = 2 / (a * np.pi * np.sqrt(1 - scaled_energy**2))
chebyshev = np.cos(ns * np.arccos(scaled_energy[:, np.newaxis]))
return k * np.sum(moments.real * chebyshev, axis=1)
ldos = expected_ldos.with_data(manual_ldos())
plot_if_fails(ldos, expected_ldos, "plot")
assert pytest.fuzzy_equal(ldos, expected_ldos, rtol=1e-4, atol=1e-6)
with pytest.raises(RuntimeError) as excinfo:
kpm.moments(10, [1, 2, 3])
assert "Size mismatch" in str(excinfo.value)
with pytest.raises(RuntimeError) as excinfo:
kpm = pb.kpm(pb.Model(graphene.monolayer()))
kpm.moments(10, [1j, 2j])
assert "Hamiltonian is real, but the given argument 'alpha' is complex" in str(
excinfo.value)
def test_kpm_multiple_indices(model):
"""KPM can take a vector of column indices and return the Green's function for all of them"""
kpm = pb.kpm(model, silent=True)
num_sites = model.system.num_sites
i, j = num_sites // 2, num_sites // 4
energy = np.linspace(-0.3, 0.3, 10)
broadening = 0.8
cols = [j, j + 1, j + 2]
gs = kpm.calc_greens(i, cols, energy, broadening)
assert len(gs) == len(cols)
g = kpm.calc_greens(j, i, energy, broadening)
assert pytest.fuzzy_equal(gs[0], g)
def test_conductivity(params, baseline, plot_if_fails):
configurations = [
{
'matrix_format': "ELL",
'optimal_size': False,
'interleaved': False
},
{
'matrix_format': "ELL",
'optimal_size': True,
'interleaved': True
},
]
model = pb.Model(*params)
kernel = pb.lorentz_kernel()
strategies = [
pb.kpm(model, energy_range=[-9, 9], kernel=kernel, silent=True, **c)
for c in configurations
]
energy = np.linspace(-2, 2, 25)
results = [
kpm.calc_conductivity(energy,
broadening=0.5,
temperature=0,
num_points=200) for kpm in strategies
]
expected = results[0].with_data(
baseline(results[0].data.astype(np.float32)))
for i in range(len(results)):
plot_if_fails(results[i], expected, "plot", label=i)
for result in results:
assert pytest.fuzzy_equal(result, expected, rtol=1e-2, atol=1e-5)
complete_lattice = pb.load('lattice_' + name[:-4])
num_x = 1
num_y = 1
print('Done loading ', flush=True)
print('Making the model', flush=True)
# check for the bonds
model = pb.Model(
complete_lattice, pb.force_double_precision(),
pb.translational_symmetry(a1=num_x * np.linalg.norm(l1),
a2=num_y * np.linalg.norm(l2)))
model.eval()
print(model.report(), flush=True)
kpm = pb.kpm(model,
kernel=pb.jackson_kernel(),
matrix_format="CSR",
optimal_size=False,
interleaved=False)
print(kpm.scaling_factors)
nx = 5
ny = 4
e_min = -11.7
e_max = +9.3
num_a1 = 640
num_a2 = 512
num_moments = 12000
# make config object which caries info about
U = 5 * S3 # Onsite term
# Building the lattice model
lat = pb.Lattice(a1=[1, 0, 0], a2=[0, 1, 0], a3=[0, 0, 1])
lat.add_sublattices(('A', [0, 0, 0], U))
lat.add_hoppings(([1, 0, 0], 'A', 'A', Tx), ([0, 1, 0], 'A', 'A', Ty),
([0, 0, 1], 'A', 'A', Tz))
# generating the model object by combinig the lattice and the Peierls field
model = pb.Model(lat, pb.primitive(a1=dim, a2=dim, a3=dim),
constant_magnetic_field(B=B, theta=theta))
return model
# Calculate DOS
# We use jackson kernel here that is good for DOS
kpm = pb.kpm(mymodel(args.dim, theta, args.B),
silent=True,
energy_range=[-13, 13],
kernel=pb.jackson_kernel())
# we approximate the bulk dos with the local DOS at the center of the lattice
# the calculation is performed at this step
dos = kpm.calc_ldos(energy=linspace(-args.Eran, args.Eran, 3000),
position=[0, 0, 0],
broadening=args.broad)
# build up the name of the output file
if args.out == False:
out = '-'.join([
'dos', 'dim',
str(args.dim), 'theta',
str(args.theta0), 'B',
str(args.B)
])
