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)
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=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,
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))
