def match_bands(self, displ, structure, amu):
"""
Match the phonon bands of neighboring q-points based on the scalar product of the eigenvectors
"""
eigenvectors = get_dyn_mat_eigenvec(displ, structure, amu)
ind = np.zeros(displ.shape[0:2], dtype=np.int)
ind[0] = range(displ.shape[1])
for i in range(1, len(eigenvectors)):
match = match_eigenvectors(eigenvectors[i - 1], eigenvectors[i])
ind[i] = [match[m] for m in ind[i - 1]]
return ind
def calculate_gruns_finite_differences(phfreqs, eig, iv0, volume, dv):
"""
Calculates the Gruneisen parameters from finite differences on the phonon frequencies.
Uses the eigenvectors to match the frequencies at different volumes.
Args:
phfreqs: numpy array with the phonon frequencies at different volumes. Shape (nvols, nqpts, 3*natoms)
eig: numpy array with the phonon eigenvectors at the different volumes. Shape (nvols, nqpts, 3*natoms, 3*natoms)
If None simple ordering will be used.
iv0: index of the 0 volume.
volume: volume of the structure at the central volume.
dv: volume variation.
Returns:
A numpy array with the gruneisen parameters. Shape (nqpts, 3*natoms)
"""
phfreqs = phfreqs.copy()
nvols = phfreqs.shape[0]
if eig is not None:
for i in range(nvols):
if i == iv0:
continue
for iq in range(phfreqs.shape[1]):
ind = match_eigenvectors(eig[iv0, iq], eig[i, iq])
phfreqs[i, iq] = phfreqs[i, iq][ind]
acc = nvols - 1
g = np.zeros_like(phfreqs[0])
for iq in range(phfreqs.shape[1]):
for im in range(phfreqs.shape[2]):
w = phfreqs[iv0, iq, im]
if w == 0:
g[iq, im] = 0
else:
g[iq, im] = -finite_diff(
phfreqs[:, iq, im], dv, order=1, acc=acc)[iv0] * volume / w
return g
def calculate_gruns_finite_differences(phfreqs, eig, iv0, volume, dv):
"""
Calculates the Gruneisen parameters from finite differences on the phonon frequencies. Uses the eigenvectors
to match the frequencies at different volumes.
Args:
phfreqs: numpy array with the phonon frequencies at different volumes. Shape (nvols, nqpts, 3*natoms)
eig: numpy array with the phonon eigenvectors at the different volumes. Shape (nvols, nqpts, 3*natoms, 3*natoms)
If None simple ordering will be used.
iv0: index of the 0 volume.
volume: volume of the structure at the central volume.
dv: volume variation.
Returns:
A numpy array with the gruneisen parameters. Shape (nqpts, 3*natoms)
"""
phfreqs = phfreqs.copy()
nvols = phfreqs.shape[0]
if eig is not None:
for i in range(nvols):
if i == iv0:
continue
for iq in range(phfreqs.shape[1]):
ind = match_eigenvectors(eig[iv0, iq], eig[i, iq])
phfreqs[i, iq] = phfreqs[i, iq][ind]
acc = nvols - 1
g = np.zeros_like(phfreqs[0])
for iq in range(phfreqs.shape[1]):
for im in range(phfreqs.shape[2]):
w = phfreqs[iv0, iq, im]
if w == 0:
g[iq, im] = 0
else:
g[iq, im] = - finite_diff(phfreqs[:, iq, im], dv, order=1, acc=acc)[iv0] * volume / w
return g
def from_phbst(cls, phbst_path, ignore_neg_freqs=True, labels=None):
"""
Creates an instance of the object starting interpolating the acoustic frequencies
from a PHBST netcdf file.
The file should contain a series of directions starting from gamma and with the
same number of points for each direction, as the one produced in the from_ddb method.
Args:
phbst_path: path to the PHBST netcdf file.
ignore_neg_freqs (bool): if True points with negative frequencies will not be
considered in the fit, in order to ignore inaccuracies in the long range
behavior.
labels (list): list of string with the name of the directions.
Returns:
an instance of SoundVelocity
"""
phb = PhononBands.from_file(phbst_path)
structure = phb.structure
rlatt = structure.lattice.reciprocal_lattice
# q points in cartesian coordinate in 1/bohr, the original units are 1/A
qpt_cart_coords = [
rlatt.get_cartesian_coords(c) * bohr_to_angstrom
for c in phb.qpoints.frac_coords
]
qpt_cart_norms = np.linalg.norm(qpt_cart_coords, axis=1)
# find the indices of the gamma points
gamma_ind = []
for i, q in enumerate(phb.qpoints.frac_coords):
if np.array_equal(q, [0, 0, 0]):
gamma_ind.append(i)
n_directions = len(gamma_ind)
n_points = len(phb.qpoints) / n_directions
if not n_points.is_integer():
raise ValueError(
'Error extracting information from {}'.format(phbst_path))
n_points = int(n_points)
phfreqs = phb.phfreqs
eigdisp = phb.phdispl_cart
sound_velocities = []
mode_types = []
directions = []
all_acoustic_freqs = []
all_qpts = []
for i in range(n_directions):
start = n_points * i
# index of the end point used for the slice
# (the position of the last point is actually end-1)
end = n_points * (i + 1)
dir_freqs = phfreqs[start:end]
dir_displ = eigdisp[start:end]
# matching bands
dir_eigv = get_dyn_mat_eigenvec(dir_displ, structure, amu=phb.amu)
n_freqs = 3 * len(structure)
ind_match = np.zeros((n_points, n_freqs), dtype=np.int)
ind_match[0] = range(n_freqs)
for j in range(1, n_points):
k = j - 1
match = match_eigenvectors(dir_eigv[k], dir_eigv[j])
ind_match[j] = [match[m] for m in ind_match[k]]
acoustic_freqs = (dir_freqs[np.arange(n_points)[:, None],
ind_match])[:, 0:3]
acoustic_displ = (dir_displ[np.arange(n_points)[:, None],
ind_match])[:, 0:3]
direction = phb.qpoints[end - 1].frac_coords
direction = np.array(direction) / np.linalg.norm(direction)
directions.append(direction)
# identify the first (not gamma) qpoint with all positive frequencies
first_positive_freq_ind = None
for j in range(1, n_points):
if min(acoustic_freqs[j]) > 0:
first_positive_freq_ind = j
break
if first_positive_freq_ind is None or first_positive_freq_ind - n_points / 2 > 0:
raise ValueError(
"too many negative frequencies along direction {}".format(
direction))
sv = []
mt = []
cart_versor = qpt_cart_coords[end - 1] / np.linalg.norm(
qpt_cart_coords[end - 1])
for k in range(3):
start_fit = 0
if ignore_neg_freqs and first_positive_freq_ind > 1:
start_fit = first_positive_freq_ind
slope, se, _, _ = np.linalg.lstsq(
qpt_cart_norms[start + start_fit:end][:, np.newaxis],
acoustic_freqs[start_fit:, k] * eV_to_Ha,
rcond=None)
sv.append(slope[0] * abu.velocity_at_to_si)
# identify the type of the mode (longitudinal/transversal) based on the
# scalar product between the eigendisplacement and the direction.
disp_0 = acoustic_displ[first_positive_freq_ind + 1, k, 0:3]
disp_0 = disp_0 / np.linalg.norm(disp_0)
scalar_prod = np.abs(np.dot(disp_0, cart_versor))
if scalar_prod > 0.9:
mt.append("longitudinal")
elif scalar_prod < 0.1:
mt.append("transversal")
else:
mt.append(None)
# sort the lists based on the sound velocites
sv, mt, freqs = zip(*sorted(zip(sv, mt, acoustic_freqs.T)))
sound_velocities.append(sv)
mode_types.append(mt)
all_acoustic_freqs.append(freqs)
all_qpts.append(phb.qpoints.frac_coords[start:end])
return cls(directions=directions,
sound_velocities=sound_velocities,
mode_types=mode_types,
structure=structure,
labels=labels,
phfreqs=all_acoustic_freqs,
qpts=all_qpts)