def __init__(self,
interaction,
symmetry,
sigmas=[0.1],
asigma_step =1,
temperatures=None,
mesh_divisors=None,
coarse_mesh_shifts=None,
grid_points=None,
cutoff_lifetime=1e-4, # in second
diff_kappa = 1e-3, # W/m-K
nu=None, # is Normal or Umklapp
no_kappa_stars=False,
gv_delta_q=1e-4, # finite difference for group velocity
log_level=0,
write_tecplot=False,
kappa_write_step=None,
is_thm=False,
filename=None):
Conductivity.__init__(self,
interaction,
symmetry,
grid_points=grid_points,
temperatures=temperatures,
sigmas=sigmas,
mesh_divisors=mesh_divisors,
coarse_mesh_shifts=coarse_mesh_shifts,
no_kappa_stars=no_kappa_stars,
gv_delta_q=gv_delta_q,
log_level=log_level,
write_tecplot=write_tecplot)
self._ise = ImagSelfEnergy(self._pp, nu, is_thm=is_thm, cutoff_lifetime= cutoff_lifetime)
self._max_sigma_step=asigma_step
self._is_asigma = False if asigma_step==1 else True
self._sigma_iteration_step = 0
self._nu=nu
self._filename = filename
if asigma_step > 1:
if self._filename is not None:
self._filename ="-adapt" + self._filename
else:
self._filename = "-adapt"
self._cutoff_lifetime = cutoff_lifetime
self._diff_kappa = diff_kappa
self._is_converge = None
if self._no_kappa_stars:
self._kpoint_operations = np.eye(3,dtype="intc")
else:
self._kpoint_operations = get_pointgroup_operations(
self._pp.get_point_group_operations())
self._gamma_N = [None] * len(sigmas)
self._gamma_U = [None]*len(sigmas)
self._read_f = False
self._read_gv = False
self._cv = None
self._wstep=kappa_write_step
self._sum_num_kstar = 0
self._scale_bar = 0
if temperatures is not None:
self._allocate_values()
def _allocate_values(self):
num_band0 = len(self._pp.get_band_indices())
num_band = self._primitive.get_number_of_atoms() * 3
num_grid_points = len(self._grid_points)
self._kappa = np.zeros((len(self._sigmas), len(self._temperatures), 6),
dtype='double')
self._mode_kappa = np.zeros((len(self._sigmas), len(
self._temperatures), num_grid_points, num_band0, 6),
dtype='double')
if not self._read_gamma:
self._gamma = np.zeros((len(self._sigmas), len(
self._temperatures), num_grid_points, num_band0),
dtype='double')
self._gv = np.zeros((num_grid_points, num_band0, 3), dtype='double')
self._cv = np.zeros(
(len(self._temperatures), num_grid_points, num_band0),
dtype='double')
if self._isotope is not None:
self._gamma_iso = np.zeros(
(len(self._sigmas), num_grid_points, num_band0),
dtype='double')
if self._is_full_pp or self._use_ave_pp:
self._averaged_pp_interaction = np.zeros(
(num_grid_points, num_band0), dtype='double')
self._num_ignored_phonon_modes = np.zeros(
(len(self._sigmas), len(self._temperatures)), dtype='intc')
self._collision = ImagSelfEnergy(
self._pp, unit_conversion=self._gamma_unit_conversion)
def __init__(self,
interaction,
point_operations=None,
ir_grid_points=None,
rotated_grid_points=None,
temperature=None,
sigma=None,
is_reducible_collision_matrix=False,
lang='C'):
self._pp = None
self._sigma = None
self._frequency_points = None
self._temperature = None
self._grid_point = None
self._lang = None
self._imag_self_energy = None
self._collision_matrix = None
self._pp_strength = None
self._frequencies = None
self._triplets_at_q = None
self._triplets_map_at_q = None
self._weights_at_q = None
self._band_indices = None
self._unit_conversion = None
self._cutoff_frequency = None
self._g = None
self._mesh = None
self._is_collision_matrix = None
self._unit_conversion = None
ImagSelfEnergy.__init__(self,
interaction,
temperature=temperature,
sigma=sigma,
lang=lang)
self._is_reducible_collision_matrix = is_reducible_collision_matrix
self._is_collision_matrix = True
if not self._is_reducible_collision_matrix:
self._ir_grid_points = ir_grid_points
self._rot_grid_points = rotated_grid_points
self._point_operations = point_operations
self._primitive = self._pp.get_primitive()
rec_lat = np.linalg.inv(self._primitive.get_cell())
self._rotations_cartesian = np.array([
similarity_transformation(rec_lat, r)
for r in self._point_operations
],
dtype='double',
order='C')
def __init__(self,
interaction,
point_operations=None,
ir_grid_points=None,
rotated_grid_points=None,
temperature=None,
sigma=None,
is_reducible_collision_matrix=False,
lang='C'):
self._pp = None
self._sigma = None
self._frequency_points = None
self._temperature = None
self._grid_point = None
self._lang = None
self._imag_self_energy = None
self._collision_matrix = None
self._pp_strength = None
self._frequencies = None
self._triplets_at_q = None
self._triplets_map_at_q = None
self._weights_at_q = None
self._band_indices = None
self._unit_conversion = None
self._cutoff_frequency = None
self._g = None
self._mesh = None
self._is_collision_matrix = None
self._unit_conversion = None
ImagSelfEnergy.__init__(self,
interaction,
temperature=temperature,
sigma=sigma,
lang=lang)
self._is_reducible_collision_matrix = is_reducible_collision_matrix
self._is_collision_matrix = True
if not self._is_reducible_collision_matrix:
self._ir_grid_points = ir_grid_points
self._rot_grid_points = rotated_grid_points
self._point_operations = point_operations
self._primitive = self._pp.get_primitive()
rec_lat = np.linalg.inv(self._primitive.get_cell())
self._rotations_cartesian = np.array(
[similarity_transformation(rec_lat, r)
for r in self._point_operations], dtype='double', order='C')
def _allocate_values(self):
num_band = self._primitive.get_number_of_atoms() * 3
num_grid_points = len(self._grid_points)
self._kappa = np.zeros((len(self._sigmas),
len(self._temperatures),
6), dtype='double')
self._mode_kappa = np.zeros((len(self._sigmas),
len(self._temperatures),
num_grid_points,
num_band,
6), dtype='double')
if not self._read_gamma:
self._gamma = np.zeros((len(self._sigmas),
len(self._temperatures),
num_grid_points,
num_band), dtype='double')
self._gv = np.zeros((num_grid_points,
num_band,
3), dtype='double')
self._cv = np.zeros((len(self._temperatures),
num_grid_points,
num_band), dtype='double')
if self._isotope is not None:
self._gamma_iso = np.zeros((len(self._sigmas),
num_grid_points,
num_band), dtype='double')
self._averaged_pp_interaction = np.zeros((num_grid_points, num_band),
dtype='double')
self._num_ignored_phonon_modes = np.zeros((len(self._sigmas),
len(self._temperatures)),
dtype='intc')
self._collision = ImagSelfEnergy(
self._pp,
unit_conversion=self._gamma_unit_conversion)
def _allocate_values(self):
num_band = self._primitive.get_number_of_atoms() * 3
num_grid_points = len(self._grid_points)
self._kappa = np.zeros((len(self._sigmas),
len(self._temperatures),
6), dtype='double')
self._mode_kappa = np.zeros((len(self._sigmas),
len(self._temperatures),
num_grid_points,
num_band,
6), dtype='double')
if not self._read_gamma:
self._gamma = np.zeros((len(self._sigmas),
len(self._temperatures),
num_grid_points,
num_band), dtype='double')
self._gv = np.zeros((num_grid_points,
num_band,
3), dtype='double')
self._cv = np.zeros((num_grid_points,
len(self._temperatures),
num_band), dtype='double')
if self._isotope is not None:
self._gamma_iso = np.zeros((len(self._sigmas),
num_grid_points,
num_band), dtype='double')
self._mean_square_pp_strength = np.zeros((num_grid_points, num_band),
dtype='double')
self._collision = ImagSelfEnergy(self._pp)
def _allocate_values(self):
num_band = self._primitive.get_number_of_atoms() * 3
num_grid_points = len(self._grid_points)
self._kappa = np.zeros((len(self._sigmas), len(self._temperatures), 6),
dtype='double')
self._mode_kappa = np.zeros((len(self._sigmas), len(
self._temperatures), num_grid_points, num_band, 6),
dtype='double')
if not self._read_gamma:
self._gamma = np.zeros((len(self._sigmas), len(
self._temperatures), num_grid_points, num_band),
dtype='double')
self._gv = np.zeros((num_grid_points, num_band, 3), dtype='double')
self._cv = np.zeros(
(num_grid_points, len(self._temperatures), num_band),
dtype='double')
if self._isotope is not None:
self._gamma_iso = np.zeros(
(len(self._sigmas), num_grid_points, num_band), dtype='double')
self._mean_square_pp_strength = np.zeros((num_grid_points, num_band),
dtype='double')
self._collision = ImagSelfEnergy(self._pp)
def get_linewidth(self,
grid_points,
sigmas=[0.1],
temperatures=None,
read_amplitude=False,
nu=None,
scattering_class=None,
band_paths=None,
filename=None):
self._interaction.set_is_disperse(True)
ise = ImagSelfEnergy(self._interaction, nu=nu)
if temperatures is None:
temperatures = np.arange(0, 1000.0 + 10.0 / 2.0, 10.0)
self._temperatures = temperatures
self._read_amplitude = read_amplitude
if grid_points is not None:
self.get_linewidth_at_grid_points(ise, sigmas, temperatures,
grid_points, nu,
scattering_class, filename)
elif band_paths is not None:
self.get_linewidth_at_paths(ise, sigmas, temperatures, band_paths,
nu, scattering_class, filename)
class Conductivity_RTA(Conductivity):
def __init__(self,
interaction,
symmetry,
grid_points=None,
temperatures=np.arange(0, 1001, 10, dtype='double'),
sigmas=[],
is_isotope=False,
mass_variances=None,
boundary_mfp=None, # in micrometre
use_averaged_pp_interaction=False,
gamma_unit_conversion=None,
mesh_divisors=None,
coarse_mesh_shifts=None,
no_kappa_stars=False,
gv_delta_q=None, # finite difference for group veolocity
log_level=0):
self._pp = None
self._temperatures = None
self._sigmas = None
self._no_kappa_stars = None
self._gv_delta_q = None
self._log_level = None
self._primitive = None
self._dm = None
self._frequency_factor_to_THz = None
self._cutoff_frequency = None
self._boundary_mfp = None
self._symmetry = None
self._point_operations = None
self._rotations_cartesian = None
self._grid_points = None
self._grid_weights = None
self._grid_address = None
self._read_gamma = False
self._read_gamma_iso = False
self._frequencies = None
self._gv = None
self._gamma = None
self._gamma_iso = None
self._gamma_unit_conversion = gamma_unit_conversion
self._use_ave_pp = use_averaged_pp_interaction
self._averaged_pp_interaction = None
self._num_ignored_phonon_modes = None
self._num_sampling_grid_points = None
self._mesh = None
self._mesh_divisors = None
self._coarse_mesh = None
self._coarse_mesh_shifts = None
self._conversion_factor = None
self._is_isotope = None
self._isotope = None
self._mass_variances = None
self._grid_point_count = None
Conductivity.__init__(self,
interaction,
symmetry,
grid_points=grid_points,
temperatures=temperatures,
sigmas=sigmas,
is_isotope=is_isotope,
mass_variances=mass_variances,
mesh_divisors=mesh_divisors,
coarse_mesh_shifts=coarse_mesh_shifts,
boundary_mfp=boundary_mfp,
no_kappa_stars=no_kappa_stars,
gv_delta_q=gv_delta_q,
log_level=log_level)
self._cv = None
if self._temperatures is not None:
self._allocate_values()
def set_kappa_at_sigmas(self):
num_band = self._primitive.get_number_of_atoms() * 3
self._num_sampling_grid_points = 0
for i, grid_point in enumerate(self._grid_points):
cv = self._cv[:, i, :]
gp = self._grid_points[i]
frequencies = self._frequencies[gp]
# Outer product of group velocities (v x v) [num_k*, num_freqs, 3, 3]
gv_by_gv_tensor, order_kstar = self._get_gv_by_gv(i)
self._num_sampling_grid_points += order_kstar
# Sum all vxv at k*
gv_sum2 = np.zeros((6, num_band), dtype='double')
for j, vxv in enumerate(
([0, 0], [1, 1], [2, 2], [1, 2], [0, 2], [0, 1])):
gv_sum2[j] = gv_by_gv_tensor[:, vxv[0], vxv[1]]
# Kappa
for j in range(len(self._sigmas)):
for k in range(len(self._temperatures)):
g_sum = self._get_main_diagonal(i, j, k)
for l in range(num_band):
if frequencies[l] < self._cutoff_frequency:
self._num_ignored_phonon_modes[j, k] += 1
continue
self._mode_kappa[j, k, i, l] = (
gv_sum2[:, l] * cv[k, l] / (g_sum[l] * 2) *
self._conversion_factor)
self._mode_kappa /= self._num_sampling_grid_points
self._kappa = self._mode_kappa.sum(axis=2).sum(axis=2)
def get_mode_heat_capacities(self):
return self._cv
def get_number_of_ignored_phonon_modes(self):
return self._num_ignored_phonon_modes
def get_number_of_sampling_grid_points(self):
return self._num_sampling_grid_points
def get_averaged_pp_interaction(self):
return self._averaged_pp_interaction
def set_averaged_pp_interaction(self, ave_pp):
self._averaged_pp_interaction = ave_pp
def _run_at_grid_point(self):
i = self._grid_point_count
self._show_log_header(i)
grid_point = self._grid_points[i]
if self._read_gamma:
if self._use_ave_pp:
self._collision.set_grid_point(grid_point)
self._collision.set_averaged_pp_interaction(
self._averaged_pp_interaction[i])
self._set_gamma_at_sigmas(i)
else:
self._collision.set_grid_point(grid_point)
if self._log_level:
print "Number of triplets:",
print len(self._pp.get_triplets_at_q()[0])
print "Calculating interaction..."
self._collision.run_interaction()
self._averaged_pp_interaction[i] = (
self._pp.get_averaged_interaction())
self._set_gamma_at_sigmas(i)
if self._isotope is not None and not self._read_gamma_iso:
self._set_gamma_isotope_at_sigmas(i)
self._cv[:, i, :] = self._get_cv(self._frequencies[grid_point])
self._set_gv(i)
if self._log_level:
self._show_log(self._qpoints[i], i)
def _allocate_values(self):
num_band = self._primitive.get_number_of_atoms() * 3
num_grid_points = len(self._grid_points)
self._kappa = np.zeros((len(self._sigmas),
len(self._temperatures),
6), dtype='double')
self._mode_kappa = np.zeros((len(self._sigmas),
len(self._temperatures),
num_grid_points,
num_band,
6), dtype='double')
if not self._read_gamma:
self._gamma = np.zeros((len(self._sigmas),
len(self._temperatures),
num_grid_points,
num_band), dtype='double')
self._gv = np.zeros((num_grid_points,
num_band,
3), dtype='double')
self._cv = np.zeros((len(self._temperatures),
num_grid_points,
num_band), dtype='double')
if self._isotope is not None:
self._gamma_iso = np.zeros((len(self._sigmas),
num_grid_points,
num_band), dtype='double')
self._averaged_pp_interaction = np.zeros((num_grid_points, num_band),
dtype='double')
self._num_ignored_phonon_modes = np.zeros((len(self._sigmas),
len(self._temperatures)),
dtype='intc')
self._collision = ImagSelfEnergy(
self._pp,
unit_conversion=self._gamma_unit_conversion)
def _set_gamma_at_sigmas(self, i):
for j, sigma in enumerate(self._sigmas):
if self._log_level:
print "Calculating Gamma of ph-ph with",
if sigma is None:
print "tetrahedron method"
else:
print "sigma=%s" % sigma
self._collision.set_sigma(sigma)
if not sigma:
self._collision.set_integration_weights()
for k, t in enumerate(self._temperatures):
self._collision.set_temperature(t)
self._collision.run()
self._gamma[j, k, i] = self._collision.get_imag_self_energy()
def _get_gv_by_gv(self, i):
rotation_map = get_grid_points_by_rotations(
self._grid_address[self._grid_points[i]],
self._point_operations,
self._mesh)
gv_by_gv = np.zeros((len(self._gv[i]), 3, 3), dtype='double')
for r in self._rotations_cartesian:
gvs_rot = np.dot(self._gv[i], r.T)
gv_by_gv += [np.outer(r_gv, r_gv) for r_gv in gvs_rot]
gv_by_gv /= len(rotation_map) / len(np.unique(rotation_map))
order_kstar = len(np.unique(rotation_map))
if order_kstar != self._grid_weights[i]:
if self._log_level:
print "*" * 33 + "Warning" + "*" * 33
print (" Number of elements in k* is unequal "
"to number of equivalent grid-points.")
print "*" * 73
return gv_by_gv, order_kstar
def _get_cv(self, freqs):
cv = np.zeros((len(self._temperatures), len(freqs)), dtype='double')
# T/freq has to be large enough to avoid divergence.
# Otherwise just set 0.
for i, f in enumerate(freqs):
finite_t = (self._temperatures > f / 100)
if f > self._cutoff_frequency:
cv[:, i] = np.where(
finite_t, get_mode_cv(
np.where(finite_t, self._temperatures, 10000),
f * THzToEv), 0)
return cv
def _show_log(self, q, i):
gp = self._grid_points[i]
frequencies = self._frequencies[gp]
gv = self._gv[i]
ave_pp = self._averaged_pp_interaction[i]
print "Frequency group velocity (x, y, z) |gv| Pqj",
if self._gv_delta_q is None:
print
else:
print " (dq=%3.1e)" % self._gv_delta_q
if self._log_level > 1:
rotation_map = get_grid_points_by_rotations(
self._grid_address[gp],
self._point_operations,
self._mesh)
for i, j in enumerate(np.unique(rotation_map)):
for k, (rot, rot_c) in enumerate(zip(
self._point_operations, self._rotations_cartesian)):
if rotation_map[k] != j:
continue
print " k*%-2d (%5.2f %5.2f %5.2f)" % (
(i + 1,) + tuple(np.dot(rot, q)))
for f, v, pp in zip(frequencies,
np.dot(rot_c, gv.T).T,
ave_pp):
print "%8.3f (%8.3f %8.3f %8.3f) %8.3f %11.3e" % (
f, v[0], v[1], v[2], np.linalg.norm(v), pp)
print
else:
for f, v, pp in zip(frequencies, gv, ave_pp):
print "%8.3f (%8.3f %8.3f %8.3f) %8.3f %11.3e" % (
f, v[0], v[1], v[2], np.linalg.norm(v), pp)
def get_imag_self_energy(self,
grid_points,
frequency_step=1.0,
sigmas=[None],
temperatures=[0.0],
filename=None):
ise = ImagSelfEnergy(self._interaction, is_thm=self._is_thm)
for gp in grid_points:
ise.set_grid_point(gp)
ise.run_interaction()
for sigma in sigmas:
ise.set_sigma(sigma)
for t in temperatures:
ise.set_temperature(t)
max_freq = (
np.amax(self._interaction.get_phonons()[0]) * 2 +
sigma * 4)
fpoints = np.arange(0, max_freq + frequency_step / 2,
frequency_step)
ise.set_fpoints(fpoints)
ise.run()
gamma = ise.get_imag_self_energy()
for i, bi in enumerate(self._band_indices):
pos = 0
for j in range(i):
pos += len(self._band_indices[j])
write_damping_functions(
gp,
bi,
self._mesh,
fpoints,
gamma[:, pos:(pos + len(bi))].sum(axis=1) /
len(bi),
sigma=sigma,
temperature=t,
filename=filename)
class Conductivity_RTA(Conductivity):
def __init__(
self,
interaction,
symmetry,
grid_points=None,
temperatures=np.arange(0, 1001, 10, dtype='double'),
sigmas=None,
is_isotope=False,
mass_variances=None,
boundary_mfp=None, # in micrometre
use_ave_pp=False,
gamma_unit_conversion=None,
mesh_divisors=None,
coarse_mesh_shifts=None,
is_kappa_star=True,
gv_delta_q=None,
run_with_g=True,
is_full_pp=False,
log_level=0):
self._pp = None
self._temperatures = None
self._sigmas = None
self._is_kappa_star = None
self._gv_delta_q = None
self._run_with_g = run_with_g
self._is_full_pp = is_full_pp
self._log_level = None
self._primitive = None
self._dm = None
self._frequency_factor_to_THz = None
self._cutoff_frequency = None
self._boundary_mfp = None
self._symmetry = None
self._point_operations = None
self._rotations_cartesian = None
self._grid_points = None
self._grid_weights = None
self._grid_address = None
self._read_gamma = False
self._read_gamma_iso = False
self._frequencies = None
self._gv = None
self._gamma = None
self._gamma_iso = None
self._gamma_unit_conversion = gamma_unit_conversion
self._use_ave_pp = use_ave_pp
self._averaged_pp_interaction = None
self._num_ignored_phonon_modes = None
self._num_sampling_grid_points = None
self._mesh = None
self._mesh_divisors = None
self._coarse_mesh = None
self._coarse_mesh_shifts = None
self._conversion_factor = None
self._is_isotope = None
self._isotope = None
self._mass_variances = None
self._grid_point_count = None
Conductivity.__init__(self,
interaction,
symmetry,
grid_points=grid_points,
temperatures=temperatures,
sigmas=sigmas,
is_isotope=is_isotope,
mass_variances=mass_variances,
mesh_divisors=mesh_divisors,
coarse_mesh_shifts=coarse_mesh_shifts,
boundary_mfp=boundary_mfp,
is_kappa_star=is_kappa_star,
gv_delta_q=gv_delta_q,
log_level=log_level)
self._cv = None
if self._temperatures is not None:
self._allocate_values()
def set_kappa_at_sigmas(self):
num_band = self._primitive.get_number_of_atoms() * 3
self._num_sampling_grid_points = 0
for i, grid_point in enumerate(self._grid_points):
cv = self._cv[:, i, :]
gp = self._grid_points[i]
frequencies = self._frequencies[gp]
# Outer product of group velocities (v x v) [num_k*, num_freqs, 3, 3]
gv_by_gv_tensor, order_kstar = self._get_gv_by_gv(i)
self._num_sampling_grid_points += order_kstar
# Sum all vxv at k*
gv_sum2 = np.zeros((6, num_band), dtype='double')
for j, vxv in enumerate(
([0, 0], [1, 1], [2, 2], [1, 2], [0, 2], [0, 1])):
gv_sum2[j] = gv_by_gv_tensor[:, vxv[0], vxv[1]]
# Kappa
for j in range(len(self._sigmas)):
for k in range(len(self._temperatures)):
g_sum = self._get_main_diagonal(i, j, k)
for l in range(num_band):
if frequencies[l] < self._cutoff_frequency:
self._num_ignored_phonon_modes[j, k] += 1
continue
self._mode_kappa[j, k, i,
l] = (gv_sum2[:, l] * cv[k, l] /
(g_sum[l] * 2) *
self._conversion_factor)
self._mode_kappa /= self._num_sampling_grid_points
self._kappa = self._mode_kappa.sum(axis=2).sum(axis=2)
def get_mode_heat_capacities(self):
return self._cv
def get_number_of_ignored_phonon_modes(self):
return self._num_ignored_phonon_modes
def get_number_of_sampling_grid_points(self):
return self._num_sampling_grid_points
def get_averaged_pp_interaction(self):
return self._averaged_pp_interaction
def set_averaged_pp_interaction(self, ave_pp):
self._averaged_pp_interaction = ave_pp
def _run_at_grid_point(self):
i = self._grid_point_count
self._show_log_header(i)
grid_point = self._grid_points[i]
if self._read_gamma:
if self._use_ave_pp:
self._collision.set_grid_point(grid_point)
self._collision.set_averaged_pp_interaction(
self._averaged_pp_interaction[i])
self._set_gamma_at_sigmas(i)
else:
self._collision.set_grid_point(grid_point)
if self._log_level:
print("Number of triplets: %d" %
len(self._pp.get_triplets_at_q()[0]))
print("Calculating interaction...")
self._set_gamma_at_sigmas(i)
if self._isotope is not None and not self._read_gamma_iso:
self._set_gamma_isotope_at_sigmas(i)
freqs = self._frequencies[grid_point][self._pp.get_band_indices()]
self._cv[:, i, :] = self._get_cv(freqs)
self._set_gv(i)
if self._log_level:
self._show_log(self._qpoints[i], i)
def _allocate_values(self):
num_band0 = len(self._pp.get_band_indices())
num_band = self._primitive.get_number_of_atoms() * 3
num_grid_points = len(self._grid_points)
self._kappa = np.zeros((len(self._sigmas), len(self._temperatures), 6),
dtype='double')
self._mode_kappa = np.zeros((len(self._sigmas), len(
self._temperatures), num_grid_points, num_band0, 6),
dtype='double')
if not self._read_gamma:
self._gamma = np.zeros((len(self._sigmas), len(
self._temperatures), num_grid_points, num_band0),
dtype='double')
self._gv = np.zeros((num_grid_points, num_band0, 3), dtype='double')
self._cv = np.zeros(
(len(self._temperatures), num_grid_points, num_band0),
dtype='double')
if self._isotope is not None:
self._gamma_iso = np.zeros(
(len(self._sigmas), num_grid_points, num_band0),
dtype='double')
if self._is_full_pp or self._use_ave_pp:
self._averaged_pp_interaction = np.zeros(
(num_grid_points, num_band0), dtype='double')
self._num_ignored_phonon_modes = np.zeros(
(len(self._sigmas), len(self._temperatures)), dtype='intc')
self._collision = ImagSelfEnergy(
self._pp, unit_conversion=self._gamma_unit_conversion)
def _set_gamma_at_sigmas(self, i):
for j, sigma in enumerate(self._sigmas):
if self._log_level:
text = "Calculating Gamma of ph-ph with "
if sigma is None:
text += "tetrahedron method"
else:
text += "sigma=%s" % sigma
print(text)
self._collision.set_sigma(sigma)
if not self._use_ave_pp:
if sigma is None or self._run_with_g:
self._collision.set_integration_weights()
if self._is_full_pp and j != 0:
pass
else:
self._collision.run_interaction(
is_full_pp=self._is_full_pp)
if self._is_full_pp and j == 0:
self._averaged_pp_interaction[i] = (
self._pp.get_averaged_interaction())
for k, t in enumerate(self._temperatures):
self._collision.set_temperature(t)
self._collision.run()
self._gamma[j, k, i] = self._collision.get_imag_self_energy()
def _get_gv_by_gv(self, i):
rotation_map = get_grid_points_by_rotations(
self._grid_address[self._grid_points[i]], self._point_operations,
self._mesh)
gv_by_gv = np.zeros((len(self._gv[i]), 3, 3), dtype='double')
for r in self._rotations_cartesian:
gvs_rot = np.dot(self._gv[i], r.T)
gv_by_gv += [np.outer(r_gv, r_gv) for r_gv in gvs_rot]
gv_by_gv /= len(rotation_map) // len(np.unique(rotation_map))
order_kstar = len(np.unique(rotation_map))
if order_kstar != self._grid_weights[i]:
if self._log_level:
print("*" * 33 + "Warning" + "*" * 33)
print(" Number of elements in k* is unequal "
"to number of equivalent grid-points.")
print("*" * 73)
return gv_by_gv, order_kstar
def _get_cv(self, freqs):
cv = np.zeros((len(self._temperatures), len(freqs)), dtype='double')
# T/freq has to be large enough to avoid divergence.
# Otherwise just set 0.
for i, f in enumerate(freqs):
finite_t = (self._temperatures > f / 100)
if f > self._cutoff_frequency:
cv[:, i] = np.where(
finite_t,
get_mode_cv(np.where(finite_t, self._temperatures, 10000),
f * THzToEv), 0)
return cv
def _show_log(self, q, i):
gp = self._grid_points[i]
frequencies = self._frequencies[gp][self._pp.get_band_indices()]
gv = self._gv[i]
if self._is_full_pp or self._use_ave_pp:
ave_pp = self._averaged_pp_interaction[i]
if self._is_full_pp or self._use_ave_pp:
text = "Frequency group velocity (x, y, z) |gv| Pqj"
else:
text = "Frequency group velocity (x, y, z) |gv|"
if self._gv_delta_q is None:
pass
else:
text += " (dq=%3.1e)" % self._gv_delta_q
print(text)
if self._log_level > 1:
rotation_map = get_grid_points_by_rotations(
self._grid_address[gp], self._point_operations, self._mesh)
for i, j in enumerate(np.unique(rotation_map)):
for k, (rot, rot_c) in enumerate(
zip(self._point_operations,
self._rotations_cartesian)):
if rotation_map[k] != j:
continue
print(" k*%-2d (%5.2f %5.2f %5.2f)" %
((i + 1, ) + tuple(np.dot(rot, q))))
if self._is_full_pp or self._use_ave_pp:
for f, v, pp in zip(frequencies,
np.dot(rot_c, gv.T).T, ave_pp):
print("%8.3f (%8.3f %8.3f %8.3f) %8.3f %11.3e" %
(f, v[0], v[1], v[2], np.linalg.norm(v), pp))
else:
for f, v in zip(frequencies, np.dot(rot_c, gv.T).T):
print("%8.3f (%8.3f %8.3f %8.3f) %8.3f" %
(f, v[0], v[1], v[2], np.linalg.norm(v)))
print('')
else:
if self._is_full_pp or self._use_ave_pp:
for f, v, pp in zip(frequencies, gv, ave_pp):
print("%8.3f (%8.3f %8.3f %8.3f) %8.3f %11.3e" %
(f, v[0], v[1], v[2], np.linalg.norm(v), pp))
else:
for f, v in zip(frequencies, gv):
print("%8.3f (%8.3f %8.3f %8.3f) %8.3f" %
(f, v[0], v[1], v[2], np.linalg.norm(v)))
class conductivity_RTA(Conductivity):
def __init__(self,
interaction,
symmetry,
sigmas=[0.1],
asigma_step =1,
temperatures=None,
mesh_divisors=None,
coarse_mesh_shifts=None,
grid_points=None,
cutoff_lifetime=1e-4, # in second
diff_kappa = 1e-3, # W/m-K
nu=None, # is Normal or Umklapp
no_kappa_stars=False,
gv_delta_q=1e-4, # finite difference for group velocity
log_level=0,
write_tecplot=False,
kappa_write_step=None,
is_thm=False,
filename=None):
Conductivity.__init__(self,
interaction,
symmetry,
grid_points=grid_points,
temperatures=temperatures,
sigmas=sigmas,
mesh_divisors=mesh_divisors,
coarse_mesh_shifts=coarse_mesh_shifts,
no_kappa_stars=no_kappa_stars,
gv_delta_q=gv_delta_q,
log_level=log_level,
write_tecplot=write_tecplot)
self._ise = ImagSelfEnergy(self._pp, nu, is_thm=is_thm, cutoff_lifetime= cutoff_lifetime)
self._max_sigma_step=asigma_step
self._is_asigma = False if asigma_step==1 else True
self._sigma_iteration_step = 0
self._nu=nu
self._filename = filename
if asigma_step > 1:
if self._filename is not None:
self._filename ="-adapt" + self._filename
else:
self._filename = "-adapt"
self._cutoff_lifetime = cutoff_lifetime
self._diff_kappa = diff_kappa
self._is_converge = None
if self._no_kappa_stars:
self._kpoint_operations = np.eye(3,dtype="intc")
else:
self._kpoint_operations = get_pointgroup_operations(
self._pp.get_point_group_operations())
self._gamma_N = [None] * len(sigmas)
self._gamma_U = [None]*len(sigmas)
self._read_f = False
self._read_gv = False
self._cv = None
self._wstep=kappa_write_step
self._sum_num_kstar = 0
self._scale_bar = 0
if temperatures is not None:
self._allocate_values()
def get_mesh_divisors(self):
return self._mesh_divisors
def get_mesh_numbers(self):
return self._mesh
def get_group_velocities(self):
return self._gv
def get_mode_heat_capacities(self):
return self._cv
def get_frequencies(self):
return self._frequencies
def get_qpoints(self):
qpoints = np.double([self._grid_address[gp].astype(float) / self._mesh
for gp in self._grid_points])
return qpoints
def get_grid_points(self):
return self._grid_points
def get_grid_weights(self):
return self._grid_weights
def set_temperatures(self, temperatures):
self._temperatures = temperatures
def get_temperatures(self):
return self._temperatures
def set_gamma(self, gamma):
if not self._read_gamma:
self._gamma = gamma
self._read_gamma = True
def set_group_velocity(self, gv):
if not self._read_gv:
self._gv = gv
self._read_gv = True
def set_frequency(self, frequencies):
if not self._read_f:
self._frequencies = frequencies
for i, freq in enumerate(frequencies):
self.set_degenerate_at_grid(i)
self._read_f = True
def get_kappa(self):
return self._kappa
def print_calculation_progress_header(self):
self._scale_bar = 0 # used for marking the calculation progress
if self._sigma_iteration_step==0:
print "Calculation based on constant sigma value"
else:
print "Calculation for the %d iteration for sigmas" %self._sigma_iteration_step
print "Calculation progress..."
print "%9s%%"*10 %tuple(np.arange(1,11)*10)
def calculate_kappa(self,write_gamma=False):
self.set_pp_grid_points_all()
for self._sigma_iteration_step in np.arange(self._max_sigma_step+1):
#Avoid multiple writings
if self._sigma_iteration_step != 0 :
if self._pp.get_is_write_amplitude():
self._pp.set_is_write_amplitude(False)
self._pp.set_is_read_amplitude(True)
# self._gamma_prev[:] = self._gamma[:]
self._kappa_prev[:] = self._kappa.copy()
self.print_calculation_progress_header()
for i, grid_point in enumerate(self._grid_points):
self._qpoint = (self._grid_address[grid_point].astype('double') /
self._mesh)
self.print_log_information(i, grid_point)
if not self._read_f:
self._frequencies[i] = self._get_phonon_c()
self.set_degenerate_at_grid(i)
if (not self._read_gamma) or (self._max_sigma_step > 1):
if self._log_level > 0:
print "Number of triplets:",
self._ise.set_grid_point(grid_point, i)
if self._log_level > 0:
print len(self._pp.get_triplets_at_q()[0])
print "Calculating interaction..."
sys.stdout.flush()
log_level = self._log_level if self._sigma_iteration_step ==0 else 0
self._ise.run_interaction(log_level=log_level)
self._frequencies[i] = self._ise.get_phonon_at_grid_point()[0]
self.set_degenerate_at_grid(i)
if self._sigma_iteration_step == 0 and not self._read_gamma:
self._set_gamma_at_sigmas(i)
else:
self._set_gamma_at_sigmas(i, is_adapt_sigma=True)
self._set_kappa_at_sigmas(i)
if write_gamma:
self._write_gamma(i, grid_point)
self._kappa /= self._sum_num_kstar
if self._pp.get_is_write_amplitude() and self._ise._interaction._amplitude_all is not None:
write_amplitude_to_hdf5_all(self._ise._interaction._amplitude_all, self._mesh, is_nosym=self._pp.is_nosym())
print
if self._sigma_iteration_step==0:
print "Thermal conductivity from constant sigma values is calculated to be"
else:
print "After %d iterations for sigma, the thermal conducitvity is recalculated to be" %(self._sigma_iteration_step)
print_kappa(self._kappa, self._temperatures, self._sigmas)
if self._wstep is not None:
if self._sigma_iteration_step % self._wstep == 0:
self.write_kappa(filename="adapt-%d"%self._sigma_iteration_step)
if self.check_sigma_convergence().all() and self._max_sigma_step>0 and self._sigma_iteration_step > 0:
print "The iterations for adaptive sigma has converged"
break
if not self.check_sigma_convergence().all() and self._sigma_iteration_step>0:
print "The iteration for sigma has ended because it has reached the maximum step"
print "Note that the iterations has not fully converged"
def print_log_information(self, i, grid_point):
if self._log_level:
print ("===================== Grid point %d (%d/%d) "
"=====================" %
(grid_point, i + 1, len(self._grid_points)))
print "q-point: (%5.2f %5.2f %5.2f)" % tuple(self._qpoint)
print "Lifetime cutoff (sec): %-10.3e" % self._cutoff_lifetime
sys.stdout.flush()
else:
scale = 100./len(self._grid_points)
num = np.rint(scale)
self._scale_bar+=(scale-num)
sys.stdout.write("="*(num+int(self._scale_bar)))
self._scale_bar-=int(self._scale_bar)
sys.stdout.flush()
def check_sigma_convergence(self):
nsigma = self._kappa.shape[0]
ntemp = self._kappa.shape[2]
max_kappa = np.sum(self._kappa, axis=(1,3)).max(axis=-1)
diff_kappa=np.sum(np.abs(self._kappa - self._kappa_prev), axis=(1,3)) # sum over qpoints and bands
for i in range(nsigma):
for j in range(ntemp):
diff_kappa[i,j] /= max_kappa[i,j]
is_converge = (np.abs(diff_kappa) < self._diff_kappa)
self._is_converge = is_converge
return is_converge
def _allocate_values(self):
num_freqs = self._primitive.get_number_of_atoms() * 3
self._kappa = np.zeros((len(self._sigmas),
len(self._grid_points),
len(self._temperatures),
num_freqs,
6), dtype='double')
self._kappa_prev = np.zeros_like(self._kappa)
if not self._read_gamma:
self._gamma = np.zeros((len(self._sigmas),
len(self._grid_points),
len(self._temperatures),
num_freqs), dtype='double')
if self._nu:
self._gamma_N = np.zeros_like(self._gamma)
self._gamma_U = np.zeros_like(self._gamma)
# self._gamma_prev = self._gamma.copy()
self._is_converge = np.zeros((len(self._sigmas), len(self._temperatures), 6), dtype="bool")
if not self._read_gv:
self._gv = np.zeros((len(self._grid_points),
num_freqs,
3), dtype='double')
self._cv = np.zeros((len(self._grid_points),
len(self._temperatures),
num_freqs), dtype='double')
if not self._read_f:
self._frequencies = np.zeros((len(self._grid_points),
num_freqs), dtype='double')
def _set_gamma_at_sigmas(self, i, is_adapt_sigma=False):
freqs = self._frequencies[i]
if is_adapt_sigma:
bz_to_irr_map = self._irr_index_mapping[self._bz_to_pp_map]
triplets_irre_indices = bz_to_irr_map[self._ise._grid_point_triplets]
for j, sigma in enumerate(self._sigmas):
if self._is_converge[j].all():
continue
if self._log_level > 0:
print "Calculating Gamma with initial sigma=%s" % sigma
if not is_adapt_sigma:
self._ise.set_sigma(sigma)
for k, t in enumerate(self._temperatures):
if self._is_converge[j,k].all():
continue
if is_adapt_sigma:
self._ise.set_adaptive_sigma(triplets_irre_indices, self._gamma[j,:,k])
self._ise.set_temperature(t)
self._ise.run()
self._gamma[j, i, k] = self._ise.get_imag_self_energy()
if self._nu:
self._gamma_N[j,i,k]=self._ise.get_imag_self_energy_N()
self._gamma_U[j,i,k]=self._ise.get_imag_self_energy_U()
def get_gamma(self):
return np.where(self._gamma< 0.5 / self._cutoff_lifetime / THz, -1, self._gamma)
def write_kappa(self, filename):
temperatures = self.get_temperatures()
for i, sigma in enumerate(self._sigmas):
kappa = self._kappa[i]
write_kappa_to_hdf5(self._gamma[i],
temperatures,
self.get_mesh_numbers(),
frequency=self.get_frequencies(),
group_velocity=self.get_group_velocities(),
heat_capacity=self.get_mode_heat_capacities(),
kappa=kappa,
qpoint=self.get_qpoints(),
weight=self.get_grid_weights(),
mesh_divisors=self.get_mesh_divisors(),
sigma=sigma,
filename=filename,
gnu=(self._gamma_N[i],self._gamma_U[i]))
if self._write_tecplot:
for j,temp in enumerate(temperatures):
write_kappa_to_tecplot_BZ(np.where(self._gamma[i,:,j]>1e-8, self._gamma[i,:,j],0),
temp,
self.get_mesh_numbers(),
bz_q_address=self._bz_grid_address / self.get_mesh_numbers().astype(float),
tetrahedrdons=self._unique_vertices,
bz_to_pp_mapping=self._bz_to_pp_map,
rec_lattice=np.linalg.inv(self._primitive.get_cell()),
spg_indices_mapping=self._irr_index_mapping,
spg_rotation_mapping=self._rot_mappings,
frequency=self.get_frequencies(),
group_velocity=self.get_group_velocities(),
heat_capacity=self.get_mode_heat_capacities()[:,j],
kappa=kappa[:,j],
weight=self.get_grid_weights(),
sigma=sigma,
filename=filename+"-bz")
def _set_kappa_at_sigmas(self, i):
freqs = self._frequencies[i]
# Group velocity [num_freqs, 3]
if not self._read_gv:
gv = get_group_velocity(
self._qpoint,
self._dm,
self._symmetry,
q_length=self._gv_delta_q,
frequency_factor_to_THz=self._frequency_factor_to_THz)
self._gv[i] = gv
# self._gv[i] = self._get_degenerate_gv(i)
# Heat capacity [num_temps, num_freqs]
cv = self._get_cv(freqs)
self._cv[i] = cv
num_kstar_counted = False
try:
import anharmonic._phono3py as phono3c
rec_lat = np.linalg.inv(self._primitive.get_cell())
kpt_rotations_at_q = self._get_rotations_for_star(i)
if self._sigma_iteration_step == 0:
self._sum_num_kstar += len(kpt_rotations_at_q)
num_kstar_counted = True
deg = degenerate_sets(self._frequencies[i])
degeneracy = np.zeros(len(self._frequencies[i]), dtype="intc")
for ele in deg:
for sub_ele in ele:
degeneracy[sub_ele]=ele[0]
for j, sigma in enumerate(self._sigmas):
kappa_at_qs = np.zeros_like(self._kappa[j,i])
mfp = np.zeros((len(self._temperatures), self._frequencies.shape[1], 3), dtype="double")
for t, temp in enumerate(self._temperatures):
for k in range(3):
mfp[t,:,k] = np.where(self._gamma[j,i,t] > 0.5 / self._cutoff_lifetime / THz,
self._gv[i,:,k] / self._gamma[j,i,t],
0)
phono3c.thermal_conductivity_at_grid(kappa_at_qs,
kpt_rotations_at_q.astype("intc").copy(),
rec_lat.copy(),
cv.copy(),
mfp.copy(),
self._gv[i].copy(),
degeneracy.copy())
self._kappa[j,i] = kappa_at_qs / 2 * self._conversion_factor
except ImportError:
print "Warning: kappa calculation (the final step) went wrong in the C implementation. Changing to python instead..."
# Outer product of group velocities (v x v) [num_k*, num_freqs, 3, 3]
gv_by_gv_tensor = self._get_gv_by_gv(i)
if self._sigma_iteration_step == 0 and num_kstar_counted == False:
self._sum_num_kstar += len(gv_by_gv_tensor)
# Sum all vxv at k*
gv_sum2 = np.zeros((6, len(freqs)), dtype='double')
for j, vxv in enumerate(
([0, 0], [1, 1], [2, 2], [1, 2], [0, 2], [0, 1])):
gv_sum2[j] = gv_by_gv_tensor[:, :, vxv[0], vxv[1]].sum(axis=0)
# Kappa
for j, sigma in enumerate(self._sigmas):
for k, l in list(np.ndindex(len(self._temperatures), len(freqs))):
if self._gamma[j, i, k, l] < 0.5 / self._cutoff_lifetime / THz:
continue
self._kappa[j, i, k, l, :] = (
gv_sum2[:, l] * cv[k, l] / (self._gamma[j, i, k, l] * 2) *
self._conversion_factor)
def _get_degenerate_gv(self, i):
deg_sets = degenerate_sets(self._frequencies[i])
gv = self._gv[i]
gvs = np.zeros_like(gv)
for deg in deg_sets:
gv_ave = gv[deg].sum(axis=0) / len(deg)
for j in deg:
gvs[j] = gv_ave
return gvs
def set_degenerate_at_grid(self, i):
deg_sets = degenerate_sets(self._frequencies[i])
for ele in deg_sets:
for sub_ele in ele:
self._degeneracies[i, sub_ele]=ele[0]
def _get_rotations_for_star(self, i):
if self._no_kappa_stars:
rotations = np.array([np.eye(3, dtype=int)])
else:
grid_point = self._grid_points[i]
rotations = self._kpoint_operations[self._rot_mappings[np.where(self._mappings==grid_point)]]
if self._grid_weights is not None:
assert len(rotations) == self._grid_weights[i], \
"Num rotations %d, weight %d" % (len(rotations), self._grid_weights[i])
return rotations
def _get_phonon_c(self):
import anharmonic._phono3py as phono3c
dm = self._dm
svecs, multiplicity = dm.get_shortest_vectors()
masses = np.double(dm.get_primitive().get_masses())
rec_lattice = np.double(
np.linalg.inv(dm.get_primitive().get_cell())).copy()
if dm.is_nac():
born = dm.get_born_effective_charges()
nac_factor = dm.get_nac_factor()
dielectric = dm.get_dielectric_constant()
else:
born = None
nac_factor = 0
dielectric = None
uplo = self._pp.get_lapack_zheev_uplo()
num_freqs = len(masses) * 3
frequencies = np.zeros(num_freqs, dtype='double')
eigenvectors = np.zeros((num_freqs, num_freqs), dtype='complex128')
phono3c.phonon(frequencies,
eigenvectors,
np.double(self._qpoint),
dm.get_force_constants(),
svecs,
multiplicity,
masses,
dm.get_primitive_to_supercell_map(),
dm.get_supercell_to_primitive_map(),
self._frequency_factor_to_THz,
born,
dielectric,
rec_lattice,
None,
nac_factor,
uplo)
# dm.set_dynamical_matrix(self._qpoint)
# dynmat = dm.get_dynamical_matrix()
# eigvals = np.linalg.eigvalsh(dynmat).real
# frequencies = (np.sqrt(np.abs(eigvals)) * np.sign(eigvals) *
# self._frequency_factor_to_THz)
return frequencies
def _show_log(self,
grid_point,
frequencies,
group_velocity,
rotations,
rotations_cartesian):
print "----- Partial kappa at grid address %d -----" % grid_point
print "Frequency, projected group velocity (x, y, z), norm at k-stars",
if self._gv_delta_q is None:
print
else:
print " (dq=%3.1e)" % self._gv_delta_q
q = self._grid_address[grid_point].astype(float) / self._mesh
for i, (rot, rot_c) in enumerate(zip(rotations, rotations_cartesian)):
q_rot = np.dot(rot, q)
q_rot -= np.rint(q_rot)
print " k*%-2d (%5.2f %5.2f %5.2f)" % ((i + 1,) + tuple(q_rot))
for f, v in zip(frequencies, np.dot(rot_c, group_velocity.T).T):
print "%8.3f (%8.3f %8.3f %8.3f) %8.3f" % (
f, v[0], v[1], v[2], np.linalg.norm(v))
print
def print_kappa(self):
temperatures = self.get_temperatures()
if self._log_level==2:
directions=['xx', 'yy','zz','xy','yz','zx']
else:
directions=['xx']
for i, sigma in enumerate(self._sigmas):
kappa = self._kappa[i]
band = ['band'+str(b+1) for b in range(kappa.shape[2])]
print "----------- Thermal conductivity (W/m-k) for",
print "sigma=%s -----------" % sigma
for j, direction in enumerate(directions):
print"*direction:%s" %direction
print ("#%6s%10s" + " %9s" * len(band)) % (("T(K)","Total")+ tuple(band))
for t, k in zip(temperatures, kappa[...,j].sum(axis=0)):
print ("%7.1f%10.3f" + " %9.3f" * len(band)) % ((t,k.sum()) + tuple(k))
print
sys.stdout.flush()
def _write_gamma(self, i, grid_point):
for j, sigma in enumerate(self._sigmas):
write_kappa_to_hdf5(
self._gamma[j, i],
self._temperatures,
self._mesh,
frequency=self._frequencies[i],
group_velocity=self._gv[i],
heat_capacity=self._cv[i],
kappa=self._kappa[j, i],
mesh_divisors=self._mesh_divisors,
grid_point=grid_point,
sigma=sigma,
filename=self._filename)
def _write_triplets(self, grid_point):
triplets, weights = self._pp.get_triplets_at_q()
grid_address = self._pp.get_grid_address()
write_triplets(triplets,
weights,
self._mesh,
grid_address,
grid_point=grid_point,
filename=self._filename)
class Conductivity_RTA(Conductivity):
def __init__(
self,
interaction,
symmetry,
grid_points=None,
temperatures=np.arange(0, 1001, 10, dtype='double'),
sigmas=[],
is_isotope=False,
mass_variances=None,
mesh_divisors=None,
coarse_mesh_shifts=None,
cutoff_mfp=None, # in micrometre
no_kappa_stars=False,
gv_delta_q=None, # finite difference for group veolocity
log_level=0):
self._pp = None
self._temperatures = None
self._sigmas = None
self._no_kappa_stars = None
self._gv_delta_q = None
self._log_level = None
self._primitive = None
self._dm = None
self._frequency_factor_to_THz = None
self._cutoff_frequency = None
self._cutoff_mfp = None
self._symmetry = None
self._point_operations = None
self._rotations_cartesian = None
self._grid_points = None
self._grid_weights = None
self._grid_address = None
self._gamma = None
self._read_gamma = False
self._read_gamma_iso = False
self._frequencies = None
self._gv = None
self._gamma_iso = None
self._mean_square_pp_strength = None
self._mesh = None
self._mesh_divisors = None
self._coarse_mesh = None
self._coarse_mesh_shifts = None
self._conversion_factor = None
self._is_isotope = None
self._isotope = None
self._mass_variances = None
self._grid_point_count = None
Conductivity.__init__(self,
interaction,
symmetry,
grid_points=grid_points,
temperatures=temperatures,
sigmas=sigmas,
is_isotope=is_isotope,
mass_variances=mass_variances,
mesh_divisors=mesh_divisors,
coarse_mesh_shifts=coarse_mesh_shifts,
cutoff_mfp=cutoff_mfp,
no_kappa_stars=no_kappa_stars,
gv_delta_q=gv_delta_q,
log_level=log_level)
self._cv = None
if self._temperatures is not None:
self._allocate_values()
def set_kappa_at_sigmas(self):
num_band = self._primitive.get_number_of_atoms() * 3
num_sampling_points = 0
for i, grid_point in enumerate(self._grid_points):
cv = self._cv[i]
# Outer product of group velocities (v x v) [num_k*, num_freqs, 3, 3]
gv_by_gv_tensor, order_kstar = self._get_gv_by_gv(i)
num_sampling_points += order_kstar
# Sum all vxv at k*
gv_sum2 = np.zeros((6, num_band), dtype='double')
for j, vxv in enumerate(
([0, 0], [1, 1], [2, 2], [1, 2], [0, 2], [0, 1])):
gv_sum2[j] = gv_by_gv_tensor[:, vxv[0], vxv[1]]
# Kappa
for j in range(len(self._sigmas)):
for k in range(len(self._temperatures)):
g_sum = self._get_main_diagonal(i, j, k)
for l in range(num_band):
if i == 0 and l < 3: # Exclude acoustic modes at Gamma
continue
self._mode_kappa[j, k, i,
l] = (gv_sum2[:, l] * cv[k, l] /
(g_sum[l] * 2) *
self._conversion_factor)
self._mode_kappa /= num_sampling_points
self._kappa = self._mode_kappa.sum(axis=2).sum(axis=2)
def get_mode_heat_capacities(self):
return self._cv
def _run_at_grid_point(self):
i = self._grid_point_count
self._show_log_header(i)
grid_point = self._grid_points[i]
if not self._read_gamma:
self._collision.set_grid_point(grid_point)
if self._log_level:
print "Number of triplets:",
print len(self._pp.get_triplets_at_q()[0])
print "Calculating interaction..."
self._collision.run_interaction()
self._set_gamma_at_sigmas(i)
self._mean_square_pp_strength[i] = (
self._pp.get_mean_square_strength())
if self._isotope is not None and not self._read_gamma_iso:
self._set_gamma_isotope_at_sigmas(i)
self._cv[i] = self._get_cv(self._frequencies[grid_point])
self._set_gv(i)
if self._log_level:
self._show_log(self._qpoints[i], i)
def _allocate_values(self):
num_band = self._primitive.get_number_of_atoms() * 3
num_grid_points = len(self._grid_points)
self._kappa = np.zeros((len(self._sigmas), len(self._temperatures), 6),
dtype='double')
self._mode_kappa = np.zeros((len(self._sigmas), len(
self._temperatures), num_grid_points, num_band, 6),
dtype='double')
if not self._read_gamma:
self._gamma = np.zeros((len(self._sigmas), len(
self._temperatures), num_grid_points, num_band),
dtype='double')
self._gv = np.zeros((num_grid_points, num_band, 3), dtype='double')
self._cv = np.zeros(
(num_grid_points, len(self._temperatures), num_band),
dtype='double')
if self._isotope is not None:
self._gamma_iso = np.zeros(
(len(self._sigmas), num_grid_points, num_band), dtype='double')
self._mean_square_pp_strength = np.zeros((num_grid_points, num_band),
dtype='double')
self._collision = ImagSelfEnergy(self._pp)
def _set_gamma_at_sigmas(self, i):
for j, sigma in enumerate(self._sigmas):
if self._log_level:
print "Calculating Gamma of ph-ph with",
if sigma is None:
print "tetrahedron method"
else:
print "sigma=%s" % sigma
self._collision.set_sigma(sigma)
if not sigma:
self._collision.set_integration_weights()
for k, t in enumerate(self._temperatures):
self._collision.set_temperature(t)
self._collision.run()
self._gamma[j, k, i] = self._collision.get_imag_self_energy()
def _get_gv_by_gv(self, i):
rotation_map = get_grid_points_by_rotations(
self._grid_address[self._grid_points[i]], self._point_operations,
self._mesh)
gv_by_gv = np.zeros((len(self._gv[i]), 3, 3), dtype='double')
for r in self._rotations_cartesian:
gvs_rot = np.dot(self._gv[i], r.T)
gv_by_gv += [np.outer(r_gv, r_gv) for r_gv in gvs_rot]
gv_by_gv /= len(rotation_map) / len(np.unique(rotation_map))
order_kstar = len(np.unique(rotation_map))
if order_kstar != self._grid_weights[i]:
if self._log_level:
print "*" * 33 + "Warning" + "*" * 33
print(
" Number of elements in k* is unequal "
"to number of equivalent grid-points.")
print "*" * 73
return gv_by_gv, order_kstar
def _get_cv(self, freqs):
cv = np.zeros((len(self._temperatures), len(freqs)), dtype='double')
# T/freq has to be large enough to avoid divergence.
# Otherwise just set 0.
for i, f in enumerate(freqs):
finite_t = (self._temperatures > f / 100)
if f > self._cutoff_frequency:
cv[:, i] = np.where(
finite_t,
get_mode_cv(np.where(finite_t, self._temperatures, 10000),
f * THzToEv), 0)
return cv
def _show_log(self, q, i):
gp = self._grid_points[i]
frequencies = self._frequencies[gp]
gv = self._gv[i]
mspp = self._mean_square_pp_strength[i]
print "Frequency group velocity (x, y, z) |gv| mspp",
if self._gv_delta_q is None:
print
else:
print " (dq=%3.1e)" % self._gv_delta_q
if self._log_level > 1:
rotation_map = get_grid_points_by_rotations(
self._grid_address[gp], self._point_operations, self._mesh)
for i, j in enumerate(np.unique(rotation_map)):
for k, (rot, rot_c) in enumerate(
zip(self._point_operations,
self._rotations_cartesian)):
if rotation_map[k] != j:
continue
print " k*%-2d (%5.2f %5.2f %5.2f)" % (
(i + 1, ) + tuple(np.dot(rot, q)))
for f, v, pp in zip(frequencies,
np.dot(rot_c, gv.T).T, mspp):
print "%8.3f (%8.3f %8.3f %8.3f) %8.3f %11.3e" % (
f, v[0], v[1], v[2], np.linalg.norm(v), pp)
print
else:
for f, v, pp in zip(frequencies, gv, mspp):
print "%8.3f (%8.3f %8.3f %8.3f) %8.3f %11.3e" % (
f, v[0], v[1], v[2], np.linalg.norm(v), pp)
class Conductivity_RTA(Conductivity):
def __init__(self,
interaction,
symmetry,
grid_points=None,
temperatures=np.arange(0, 1001, 10, dtype='double'),
sigmas=[],
mass_variances=None,
mesh_divisors=None,
coarse_mesh_shifts=None,
cutoff_lifetime=1e-4, # in second
no_kappa_stars=False,
gv_delta_q=None, # finite difference for group veolocity
log_level=0):
self._pp = None
self._temperatures = None
self._sigmas = None
self._no_kappa_stars = None
self._gv_delta_q = None
self._log_level = None
self._primitive = None
self._dm = None
self._frequency_factor_to_THz = None
self._cutoff_frequency = None
self._cutoff_lifetime = None
self._symmetry = None
self._point_operations = None
self._rotations_cartesian = None
self._grid_points = None
self._grid_weights = None
self._grid_address = None
self._gamma = None
self._read_gamma = False
self._read_gamma_iso = False
self._frequencies = None
self._gv = None
self._gamma_iso = None
self._mesh = None
self._mesh_divisors = None
self._coarse_mesh = None
self._coarse_mesh_shifts = None
self._conversion_factor = None
self._sum_num_kstar = None
self._isotope = None
self._mass_variances = None
self._grid_point_count = None
Conductivity.__init__(self,
interaction,
symmetry,
grid_points=grid_points,
temperatures=temperatures,
sigmas=sigmas,
mass_variances=mass_variances,
mesh_divisors=mesh_divisors,
coarse_mesh_shifts=coarse_mesh_shifts,
cutoff_lifetime=cutoff_lifetime,
no_kappa_stars=no_kappa_stars,
gv_delta_q=gv_delta_q,
log_level=log_level)
self._cv = None
if self._temperatures is not None:
self._allocate_values()
def set_kappa_at_sigmas(self):
num_band = self._primitive.get_number_of_atoms() * 3
num_sampling_points = 0
for i, grid_point in enumerate(self._grid_points):
cv = self._cv[i]
# Outer product of group velocities (v x v) [num_k*, num_freqs, 3, 3]
gv_by_gv_tensor, order_kstar = self._get_gv_by_gv(i)
num_sampling_points += order_kstar
# Sum all vxv at k*
gv_sum2 = np.zeros((6, num_band), dtype='double')
for j, vxv in enumerate(
([0, 0], [1, 1], [2, 2], [1, 2], [0, 2], [0, 1])):
gv_sum2[j] = gv_by_gv_tensor[:, vxv[0], vxv[1]]
# Kappa
for j in range(len(self._sigmas)):
for k, l in list(np.ndindex(len(self._temperatures), num_band)):
g_phph = self._gamma[j, k, i, l]
if g_phph < 0.5 / self._cutoff_lifetime / THz:
continue
if self._isotope is None:
g_sum = g_phph
else:
g_iso = self._gamma_iso[j, i, l]
g_sum = g_phph + g_iso
self._kappa[j, k] += (
gv_sum2[:, l] * cv[k, l] / (g_sum * 2) *
self._conversion_factor)
self._kappa /= num_sampling_points
def get_mode_heat_capacities(self):
return self._cv
def _run_at_grid_point(self):
i = self._grid_point_count
self._show_log_header(i)
grid_point = self._grid_points[i]
if not self._read_gamma:
self._collision.set_grid_point(grid_point)
if self._log_level:
print "Number of triplets:",
print len(self._pp.get_triplets_at_q()[0])
print "Calculating interaction..."
self._collision.run_interaction()
self._set_gamma_at_sigmas(i)
if self._isotope is not None and not self._read_gamma_iso:
self._set_gamma_isotope_at_sigmas(i)
self._cv[i] = self._get_cv(self._frequencies[grid_point])
self._set_gv(i)
if self._log_level:
self._show_log(self._qpoints[i], i)
def _allocate_values(self):
num_band = self._primitive.get_number_of_atoms() * 3
num_grid_points = len(self._grid_points)
self._kappa = np.zeros((len(self._sigmas),
len(self._temperatures),
6), dtype='double')
if not self._read_gamma:
self._gamma = np.zeros((len(self._sigmas),
len(self._temperatures),
num_grid_points,
num_band), dtype='double')
self._gv = np.zeros((num_grid_points,
num_band,
3), dtype='double')
self._cv = np.zeros((num_grid_points,
len(self._temperatures),
num_band), dtype='double')
if self._isotope is not None:
self._gamma_iso = np.zeros((len(self._sigmas),
num_grid_points,
num_band), dtype='double')
self._collision = ImagSelfEnergy(self._pp)
def _set_gamma_at_sigmas(self, i):
for j, sigma in enumerate(self._sigmas):
if self._log_level:
print "Calculating Gamma of ph-ph with",
if sigma is None:
print "tetrahedron method"
else:
print "sigma=%s" % sigma
self._collision.set_sigma(sigma)
if not sigma:
self._collision.set_integration_weights()
for k, t in enumerate(self._temperatures):
self._collision.set_temperature(t)
self._collision.run()
self._gamma[j, k, i] = self._collision.get_imag_self_energy()
def _get_gv_by_gv(self, i):
rotation_map = get_grid_points_by_rotations(
self._grid_points[i], self._point_operations, self._mesh)
gv_by_gv = np.zeros((len(self._gv[i]), 3, 3), dtype='double')
if self._no_kappa_stars:
count = 0
for r, r_gp in zip(self._rotations_cartesian, rotation_map):
if r_gp == rotation_map[0]:
gvs_rot = np.dot(r, self._gv[i].T).T
gv_by_gv += [np.outer(r_gv, r_gv) for r_gv in gvs_rot]
count += 1
gv_by_gv /= count
order_kstar = 1
else:
for r in self._rotations_cartesian:
gvs_rot = np.dot(r, self._gv[i].T).T
gv_by_gv += [np.outer(r_gv, r_gv) for r_gv in gvs_rot]
gv_by_gv /= len(rotation_map) / len(np.unique(rotation_map))
order_kstar = len(np.unique(rotation_map))
# check if the number of rotations is correct.
if self._grid_weights is not None:
if len(set(rotation_map)) != self._grid_weights[i]:
if self._log_level:
print "*" * 33 + "Warning" + "*" * 33
print (" Number of elements in k* is unequal "
"to number of equivalent grid-points.")
print "*" * 73
# assert len(rotations) == self._grid_weights[i], \
# "Num rotations %d, weight %d" % (
# len(rotations), self._grid_weights[i])
return gv_by_gv, order_kstar
def _get_cv(self, freqs):
cv = np.zeros((len(self._temperatures), len(freqs)), dtype='double')
# T/freq has to be large enough to avoid divergence.
# Otherwise just set 0.
for i, f in enumerate(freqs):
finite_t = (self._temperatures > f / 100)
if f > self._cutoff_frequency:
cv[:, i] = np.where(
finite_t, get_mode_cv(
np.where(finite_t, self._temperatures, 10000),
f * THzToEv), 0)
return cv
def _show_log(self, q, i):
gp = self._grid_points[i]
frequencies = self._frequencies[gp]
gv = self._gv[i]
print "Frequency group velocity (x, y, z) |gv|",
if self._gv_delta_q is None:
print
else:
print " (dq=%3.1e)" % self._gv_delta_q
if self._log_level > 1:
rotation_map = get_grid_points_by_rotations(
gp, self._point_operations, self._mesh)
for i, j in enumerate(np.unique(rotation_map)):
for k, (rot, rot_c) in enumerate(zip(self._point_operations,
self._rotations_cartesian)):
if rotation_map[k] != j:
continue
print " k*%-2d (%5.2f %5.2f %5.2f)" % ((i + 1,) +
tuple(np.dot(rot, q)))
for f, v in zip(frequencies,
np.dot(rot_c, gv.T).T):
print "%8.3f (%8.3f %8.3f %8.3f) %8.3f" % (
f, v[0], v[1], v[2], np.linalg.norm(v))
print
else:
for f, v in zip(frequencies, gv):
print "%8.3f (%8.3f %8.3f %8.3f) %8.3f" % (
f, v[0], v[1], v[2], np.linalg.norm(v))
def get_imag_self_energy(self,
grid_points,
frequency_step=1.0,
sigmas=[None],
temperatures=[0.0],
filename=None):
ise = ImagSelfEnergy(self._interaction, is_thm = self._is_thm)
for gp in grid_points:
ise.set_grid_point(gp)
ise.run_interaction()
for sigma in sigmas:
ise.set_sigma(sigma)
for t in temperatures:
ise.set_temperature(t)
max_freq = (np.amax(self._interaction.get_phonons()[0]) * 2
+ sigma * 4)
fpoints = np.arange(0, max_freq + frequency_step / 2,
frequency_step)
ise.set_fpoints(fpoints)
ise.run()
gamma = ise.get_imag_self_energy()
for i, bi in enumerate(self._band_indices):
pos = 0
for j in range(i):
pos += len(self._band_indices[j])
write_damping_functions(
gp,
bi,
self._mesh,
fpoints,
gamma[:, pos:(pos + len(bi))].sum(axis=1) / len(bi),
sigma=sigma,
temperature=t,
filename=filename)