def symmetrize_2nd_rank_tensor(tensor, symmetry_operations, lattice):
sym_cart = [similarity_transformation(lattice.T, r)
for r in symmetry_operations]
sum_tensor = np.zeros_like(tensor)
for sym in sym_cart:
sum_tensor += similarity_transformation(sym, tensor)
return sum_tensor / len(symmetry_operations)
def symmetrize_borns_and_epsilon(borns,
epsilon,
ucell,
symprec=1e-5,
is_symmetry=True):
lattice = ucell.get_cell()
positions = ucell.get_scaled_positions()
u_sym = Symmetry(ucell, is_symmetry=is_symmetry, symprec=symprec)
rotations = u_sym.get_symmetry_operations()['rotations']
translations = u_sym.get_symmetry_operations()['translations']
ptg_ops = u_sym.get_pointgroup_operations()
epsilon_ = _symmetrize_2nd_rank_tensor(epsilon, ptg_ops, lattice)
for i, Z in enumerate(borns):
site_sym = u_sym.get_site_symmetry(i)
Z = _symmetrize_2nd_rank_tensor(Z, site_sym, lattice)
borns_ = np.zeros_like(borns)
for i in range(len(borns)):
count = 0
for r, t in zip(rotations, translations):
count += 1
diff = np.dot(positions, r.T) + t - positions[i]
diff -= np.rint(diff)
dist = np.sqrt(np.sum(np.dot(diff, lattice)**2, axis=1))
j = np.nonzero(dist < symprec)[0][0]
r_cart = similarity_transformation(lattice.T, r)
borns_[i] += similarity_transformation(r_cart, borns[j])
borns_[i] /= count
return borns_, epsilon_
def get_born_OUTCAR(poscar_filename="POSCAR",
outcar_filename="OUTCAR",
primitive_axis=np.eye(3),
is_symmetry=True,
symmetrize_tensors=False):
cell = read_vasp(poscar_filename)
primitive = Primitive(cell, primitive_axis)
p2p = primitive.get_primitive_to_primitive_map()
symmetry = Symmetry(primitive, is_symmetry=is_symmetry)
independent_atoms = symmetry.get_independent_atoms()
prim_lat = primitive.get_cell().T
outcar = open(outcar_filename)
borns = []
while True:
line = outcar.readline()
if not line:
break
if "NIONS" in line:
num_atom = int(line.split()[11])
if "MACROSCOPIC STATIC DIELECTRIC TENSOR" in line:
epsilon = []
outcar.readline()
epsilon.append([float(x) for x in outcar.readline().split()])
epsilon.append([float(x) for x in outcar.readline().split()])
epsilon.append([float(x) for x in outcar.readline().split()])
if "BORN" in line:
outcar.readline()
line = outcar.readline()
if "ion" in line:
for i in range(num_atom):
born = []
born.append([float(x) for x in outcar.readline().split()][1:])
born.append([float(x) for x in outcar.readline().split()][1:])
born.append([float(x) for x in outcar.readline().split()][1:])
outcar.readline()
borns.append(born)
reduced_borns = []
for p_i, u_i in enumerate(p2p):
if p_i in independent_atoms:
if symmetrize_tensors:
site_sym = [similarity_transformation(prim_lat, rot)
for rot in symmetry.get_site_symmetry(p_i)]
reduced_borns.append(symmetrize_tensor(borns[u_i], site_sym))
else:
reduced_borns.append(borns[u_i])
if symmetrize_tensors:
point_sym = [similarity_transformation(prim_lat, rot)
for rot in symmetry.get_pointgroup_operations()]
epsilon = symmetrize_tensor(epsilon, point_sym)
else:
epsilon = np.array(epsilon)
return np.array(reduced_borns), epsilon
def _symmetrize_borns(borns, u_sym, lattice, positions, symprec):
borns_orig = borns.copy()
for i, Z in enumerate(borns):
site_sym = [similarity_transformation(lattice, r)
for r in u_sym.get_site_symmetry(i)]
Z = _symmetrize_tensor(Z, site_sym)
rotations = u_sym.get_symmetry_operations()['rotations']
translations = u_sym.get_symmetry_operations()['translations']
map_atoms = u_sym.get_map_atoms()
borns_copy = np.zeros_like(borns)
for i in range(len(borns)):
count = 0
for r, t in zip(rotations, translations):
count += 1
diff = np.dot(positions, r.T) + t - positions[i]
diff -= np.rint(diff)
j = np.nonzero((np.abs(diff) < symprec).all(axis=1))[0][0]
r_cart = similarity_transformation(lattice, r)
borns_copy[i] += similarity_transformation(r_cart, borns[j])
borns_copy[i] /= count
borns = borns_copy
sum_born = borns.sum(axis=0) / len(borns)
borns -= sum_born
if (np.abs(borns_orig - borns) > 0.1).any():
sys.stderr.write(
"Born effective charge symmetrization might go wrong.\n")
return borns
def _symmetrize_2nd_rank_tensor(tensor, symmetry_operations, lattice):
sym_cart = [similarity_transformation(lattice.T, r)
for r in symmetry_operations]
sum_tensor = np.zeros_like(tensor)
for sym in sym_cart:
sum_tensor += similarity_transformation(sym, tensor)
return sum_tensor / len(symmetry_operations)
def symmetrize_borns_and_epsilon(borns,
epsilon,
ucell,
symprec=1e-5,
is_symmetry=True):
lattice = ucell.get_cell()
positions = ucell.get_scaled_positions()
u_sym = Symmetry(ucell, is_symmetry=is_symmetry, symprec=symprec)
rotations = u_sym.get_symmetry_operations()['rotations']
translations = u_sym.get_symmetry_operations()['translations']
ptg_ops = u_sym.get_pointgroup_operations()
epsilon_ = _symmetrize_2nd_rank_tensor(epsilon, ptg_ops, lattice)
for i, Z in enumerate(borns):
site_sym = u_sym.get_site_symmetry(i)
Z = _symmetrize_2nd_rank_tensor(Z, site_sym, lattice)
borns_ = np.zeros_like(borns)
for i in range(len(borns)):
count = 0
for r, t in zip(rotations, translations):
count += 1
diff = np.dot(positions, r.T) + t - positions[i]
diff -= np.rint(diff)
dist = np.sqrt(np.sum(np.dot(diff, lattice) ** 2, axis=1))
j = np.nonzero(dist < symprec)[0][0]
r_cart = similarity_transformation(lattice.T, r)
borns_[i] += similarity_transformation(r_cart, borns[j])
borns_[i] /= count
sum_born = borns_.sum(axis=0) / len(borns_)
borns_ -= sum_born
return borns_, epsilon_
def _symmetrize_borns(borns, u_sym, lattice, positions, symprec):
borns_orig = borns.copy()
for i, Z in enumerate(borns):
site_sym = [
similarity_transformation(lattice, r)
for r in u_sym.get_site_symmetry(i)
]
Z = _symmetrize_tensor(Z, site_sym)
rotations = u_sym.get_symmetry_operations()['rotations']
translations = u_sym.get_symmetry_operations()['translations']
map_atoms = u_sym.get_map_atoms()
borns_copy = np.zeros_like(borns)
for i in range(len(borns)):
count = 0
for r, t in zip(rotations, translations):
count += 1
diff = np.dot(positions, r.T) + t - positions[i]
diff -= np.rint(diff)
j = np.nonzero((np.abs(diff) < symprec).all(axis=1))[0][0]
r_cart = similarity_transformation(lattice, r)
borns_copy[i] += similarity_transformation(r_cart, borns[j])
borns_copy[i] /= count
borns = borns_copy
sum_born = borns.sum(axis=0) / len(borns)
borns -= sum_born
if (np.abs(borns_orig - borns) > 0.1).any():
sys.stderr.write(
"Born effective charge symmetrization might go wrong.\n")
return borns
def get_born_parameters(f, primitive, symmetry):
from phonopy.harmonic.force_constants import similarity_transformation
# Read unit conversion factor, damping factor, ...
line_arr = f.readline().split()
if len(line_arr) < 1:
print("BORN file format of line 1 is incorrect")
return False
if len(line_arr) > 0:
try:
factor = float(line_arr[0])
except (ValueError, TypeError):
factor = None
# Read dielectric constant
line = f.readline().split()
if not len(line) == 9:
print("BORN file format of line 2 is incorrect")
return False
dielectric = np.reshape([float(x) for x in line], (3, 3))
# Read Born effective charge
independent_atoms = symmetry.get_independent_atoms()
born = np.zeros((primitive.get_number_of_atoms(), 3, 3), dtype=float)
for i in independent_atoms:
line = f.readline().split()
if len(line) == 0:
print("Number of lines for Born effect charge is not enough.")
return False
if not len(line) == 9:
print("BORN file format of line %d is incorrect" % (i + 3))
return False
born[i] = np.reshape([float(x) for x in line], (3, 3))
# Check that the number of atoms in the BORN file was correct
line = f.readline().split()
if len(line) > 0:
print(
"Too many atoms in the BORN file (it should only contain symmetry-independent atoms)"
)
return False
# Expand Born effective charges to all atoms in the primitive cell
rotations = symmetry.get_symmetry_operations()['rotations']
map_operations = symmetry.get_map_operations()
map_atoms = symmetry.get_map_atoms()
for i in range(primitive.get_number_of_atoms()):
# R_cart = L R L^-1
rot_cartesian = similarity_transformation(
primitive.get_cell().transpose(), rotations[map_operations[i]])
# R_cart^T B R_cart^-T (inverse rotation is required to transform)
born[i] = similarity_transformation(rot_cartesian.transpose(),
born[map_atoms[i]])
non_anal = {'born': born, 'factor': factor, 'dielectric': dielectric}
return non_anal
def get_born_parameters(f, primitive, symmetry):
from phonopy.harmonic.force_constants import similarity_transformation
# Read unit conversion factor, damping factor, ...
line_arr = f.readline().split()
if len(line_arr) < 1:
print("BORN file format of line 1 is incorrect")
return False
if len(line_arr) > 0:
try:
factor = float(line_arr[0])
except (ValueError, TypeError):
factor = None
# Read dielectric constant
line = f.readline().split()
if not len(line) == 9:
print("BORN file format of line 2 is incorrect")
return False
dielectric = np.reshape([float(x) for x in line], (3, 3))
# Read Born effective charge
independent_atoms = symmetry.get_independent_atoms()
born = np.zeros((primitive.get_number_of_atoms(), 3, 3), dtype=float)
for i in independent_atoms:
line = f.readline().split()
if len(line) == 0:
print("Number of lines for Born effect charge is not enough.")
return False
if not len(line) == 9:
print("BORN file format of line %d is incorrect" % (i + 3))
return False
born[i] = np.reshape([float(x) for x in line], (3, 3))
# Expand Born effective charges to all atoms in the primitive cell
rotations = symmetry.get_symmetry_operations()['rotations']
map_operations = symmetry.get_map_operations()
map_atoms = symmetry.get_map_atoms()
for i in range(primitive.get_number_of_atoms()):
# R_cart = L R L^-1
rot_cartesian = similarity_transformation(
primitive.get_cell().transpose(), rotations[map_operations[i]])
# R_cart^T B R_cart^-T (inverse rotation is required to transform)
born[i] = similarity_transformation(rot_cartesian.transpose(),
born[map_atoms[i]])
non_anal = {'born': born,
'factor': factor,
'dielectric': dielectric }
return non_anal
def _expand_borns(borns, primitive, prim_symmetry):
# Expand Born effective charges to all atoms in the primitive cell
rotations = prim_symmetry.get_symmetry_operations()['rotations']
map_operations = prim_symmetry.get_map_operations()
map_atoms = prim_symmetry.get_map_atoms()
for i in range(primitive.get_number_of_atoms()):
# R_cart = L R L^-1
rot_cartesian = similarity_transformation(
primitive.get_cell().transpose(), rotations[map_operations[i]])
# R_cart^T B R_cart^-T (inverse rotation is required to transform)
borns[i] = similarity_transformation(rot_cartesian.transpose(),
borns[map_atoms[i]])
def _expand_borns(borns, primitive: PhonopyAtoms, prim_symmetry: Symmetry):
# Expand Born effective charges to all atoms in the primitive cell
rotations = prim_symmetry.symmetry_operations["rotations"]
map_operations = prim_symmetry.get_map_operations()
map_atoms = prim_symmetry.get_map_atoms()
for i in range(len(primitive)):
# R_cart = L R L^-1
rot_cartesian = similarity_transformation(primitive.cell.T,
rotations[map_operations[i]])
# R_cart^T B R_cart^-T (inverse rotation is required to transform)
borns[i] = similarity_transformation(rot_cartesian.T,
borns[map_atoms[i]])
def get_born_parameters(f, primitive, is_symmetry):
# Read unit conversion factor, damping factor, ...
factors = [float(x) for x in f.readline().split()]
if len(factors) < 1:
print "BORN file format of line 1 is incorrect"
return False
if len(factors) < 2:
factors = factors[0]
# Read dielectric constant
line = f.readline().split()
if not len(line) == 9:
print "BORN file format of line 2 is incorrect"
return False
dielectric = np.reshape([float(x) for x in line], (3, 3))
# Read Born effective charge
symmetry = Symmetry(primitive, is_symmetry=is_symmetry)
independent_atoms = symmetry.get_independent_atoms()
born = np.zeros((primitive.get_number_of_atoms(), 3, 3), dtype=float)
for i in independent_atoms:
line = f.readline().split()
if len(line) == 0:
print "Number of lines for Born effect charge is not enough."
return False
if not len(line) == 9:
print "BORN file format of line %d is incorrect" % (i + 3)
return False
born[i] = np.reshape([float(x) for x in line], (3, 3))
# Expand Born effective charges to all atoms in the primitive cell
rotations = symmetry.get_symmetry_operations()['rotations']
map_operations = symmetry.get_map_operations()
map_atoms = symmetry.get_map_atoms()
for i in range(primitive.get_number_of_atoms()):
# R_cart = L R L^-1
rot_cartesian = similarity_transformation(
primitive.get_cell().transpose(), rotations[map_operations[i]])
# R_cart^T B R_cart^-T (inverse rotation is required to transform)
born[i] = similarity_transformation(rot_cartesian.transpose(),
born[map_atoms[i]])
non_anal = {'born': born,
'factor': factors,
'dielectric': dielectric }
return non_anal
def _expand_borns(borns, primitive, prim_symmetry):
from phonopy.harmonic.force_constants import similarity_transformation
# Expand Born effective charges to all atoms in the primitive cell
rotations = prim_symmetry.get_symmetry_operations()['rotations']
map_operations = prim_symmetry.get_map_operations()
map_atoms = prim_symmetry.get_map_atoms()
for i in range(primitive.get_number_of_atoms()):
# R_cart = L R L^-1
rot_cartesian = similarity_transformation(
primitive.get_cell().transpose(), rotations[map_operations[i]])
# R_cart^T B R_cart^-T (inverse rotation is required to transform)
borns[i] = similarity_transformation(rot_cartesian.transpose(),
borns[map_atoms[i]])
def _distribute_3(self, disps_3, forces_3, second_atom_num, third_atom_num,
reduced_bond_sym):
positions = self._positions.copy() - self._positions[second_atom_num]
rot_map_syms = get_positions_sent_by_rot_inv(positions,
reduced_bond_sym,
self._symprec)
sym_cart = None
rot_atom_map = None
for i, sym in enumerate(reduced_bond_sym):
if disps_3[rot_map_syms[i, third_atom_num]] is not None:
sym_cart = similarity_transformation(self._lattice, sym)
rot_atom_map = rot_map_syms[i, :]
break
assert sym_cart is not None, "Something is wrong."
forces = [
np.dot(f[rot_atom_map], sym_cart.T)
for f in forces_3[rot_atom_map[third_atom_num]]
]
disps = [[d3[0], d3[1], np.dot(sym_cart, d3[2])]
for d3 in disps_3[rot_atom_map[third_atom_num]]]
disps_3[third_atom_num] = disps
forces_3[third_atom_num] = forces
def _distribute_2(self, disps, forces, first_atom_num, second_atom_num,
reduced_site_sym):
positions = self._positions.copy() - self._positions[first_atom_num]
rot_map_syms = get_positions_sent_by_rot_inv(positions,
reduced_site_sym,
self._symprec)
sym_cart = None
rot_atom_map = None
for i, sym in enumerate(reduced_site_sym):
if disps[rot_map_syms[i, second_atom_num]] is not None:
sym_cart = similarity_transformation(self._lattice, sym)
rot_atom_map = rot_map_syms[i, :]
break
assert sym_cart is not None, "Something is wrong."
forces[second_atom_num] = []
disps[second_atom_num] = []
for i in range(self._num_atom):
forces_2 = [
np.dot(f[rot_atom_map], sym_cart.T)
for f in forces[rot_atom_map[second_atom_num]][rot_atom_map[i]]
]
disps_2 = [[
d3[0], np.dot(sym_cart, d3[1]),
np.dot(sym_cart, d3[2])
] for d3 in disps[rot_atom_map[second_atom_num]][rot_atom_map[i]]]
forces[second_atom_num].append(forces_2)
disps[second_atom_num].append(disps_2)
def solve_fc3(fc3,
first_atom_num,
supercell,
site_symmetry,
displacements_first,
delta_fc2s,
symprec,
pinv="numpy"):
lattice = supercell.get_cell().T
site_sym_cart = [similarity_transformation(lattice, sym)
for sym in site_symmetry]
num_atom = supercell.get_number_of_atoms()
positions = supercell.get_scaled_positions()
pos_center = positions[first_atom_num].copy()
positions -= pos_center
rot_map_syms = get_positions_sent_by_rot_inv(positions,
site_symmetry,
symprec)
rot_disps = get_rotated_displacement(displacements_first, site_sym_cart)
if pinv == "numpy":
inv_U = np.linalg.pinv(rot_disps)
else:
try:
import anharmonic._phono3py as phono3c
inv_U = np.zeros((rot_disps.shape[1], rot_disps.shape[0]),
dtype='double')
phono3c.pinv(inv_U, rot_disps, 1e-13)
except ImportError:
inv_U = np.linalg.pinv(rot_disps)
for (i, j) in list(np.ndindex(num_atom, num_atom)):
fc3[first_atom_num, i, j] = np.dot(inv_U, _get_rotated_fc2s(
i, j, delta_fc2s, rot_map_syms, site_sym_cart)).reshape(3, 3, 3)
def distribute_fc3(fc3,
first_disp_atoms,
lattice,
positions,
rotations,
translations,
symprec,
verbose):
num_atom = len(positions)
for i in range(num_atom):
if i in first_disp_atoms:
continue
for atom_index_done in first_disp_atoms:
rot_num = get_atom_mapping_by_symmetry(positions,
i,
atom_index_done,
rotations,
translations,
symprec)
if rot_num > -1:
i_rot = atom_index_done
rot = rotations[rot_num]
trans = translations[rot_num]
break
if rot_num < 0:
print "Position or symmetry may be wrong."
raise ValueError
if verbose > 2:
print " [ %d, x, x ] to [ %d, x, x ]" % (i_rot + 1, i + 1)
sys.stdout.flush()
atom_mapping = np.zeros(num_atom, dtype='intc')
for j in range(num_atom):
atom_mapping[j] = get_atom_by_symmetry(positions,
rot,
trans,
j,
symprec)
rot_cart_inv = np.double(
similarity_transformation(lattice, rot).T.copy())
try:
import anharmonic._phono3py as phono3c
phono3c.distribute_fc3(fc3,
i,
atom_mapping,
rot_cart_inv)
except ImportError:
for j in range(num_atom):
j_rot = atom_mapping[j]
for k in range(num_atom):
k_rot = atom_mapping[k]
fc3[i, j, k] = third_rank_tensor_rotation(
rot_cart_inv, fc3[i_rot, j_rot, k_rot])
def get_gv_by_sr0_at_stars(self, s, i, t):
deg_sets = degenerate_sets(self._frequencies[i])
grid_point = self._grid_points[i]
orig_address = self._grid_address[grid_point]
rotations = get_rotations_for_star(orig_address, self._mesh,
self._kpoint_operations)
# self._get_group_veclocities_at_star(i, gv)
gv_by_F_tensor = []
rec_lat = np.linalg.inv(self._primitive.get_cell())
rotations_cartesian = [
similarity_transformation(rec_lat, r) for r in rotations
]
for rot_c in rotations_cartesian:
gvs_rot = np.dot(rot_c, self._gv[i].T).T
F_rot = np.dot(rot_c, self._F0[s, i, t].T).T
# Take average of group veclocities of degenerate phonon modes
# and then calculate gv x gv to preserve symmetry
gvs = np.zeros_like(gvs_rot)
Fs = np.zeros_like(F_rot)
for deg in deg_sets:
gv_ave = gvs_rot[deg].sum(axis=0) / len(deg)
F_ave = F_rot[deg].sum(axis=0) / len(deg)
for j in deg:
gvs[j] = gv_ave
Fs[j] = F_ave
gv_by_F_tensor.append(
[np.outer(gvs[b], Fs[b]) for b in range(len(gvs))])
return np.array(gv_by_F_tensor)
def _solve_fc4(fc4,
first_atom_num,
supercell,
site_symmetry,
displacements_first,
delta_fc3s,
symprec):
lattice = supercell.get_cell().T
site_sym_cart = np.double([similarity_transformation(lattice, sym)
for sym in site_symmetry])
num_atom = supercell.get_number_of_atoms()
positions = supercell.get_scaled_positions()
pos_center = positions[first_atom_num].copy()
positions -= pos_center
rot_map_syms = get_positions_sent_by_rot_inv(positions,
site_symmetry,
symprec)
rot_disps = get_rotated_displacement(displacements_first, site_sym_cart)
inv_U = np.linalg.pinv(rot_disps)
for (i, j, k) in list(np.ndindex(num_atom, num_atom, num_atom)):
fc4[first_atom_num, i, j, k] = np.dot(
inv_U, _rotate_delta_fc3s(
i, j, k, delta_fc3s, rot_map_syms, site_sym_cart)
).reshape(3, 3, 3, 3)
def _distribute_2(self,
disps,
forces,
first_atom_num,
second_atom_num,
reduced_site_sym):
positions = self._positions.copy() - self._positions[first_atom_num]
rot_map_syms = get_positions_sent_by_rot_inv(positions,
reduced_site_sym,
self._symprec)
sym_cart = None
rot_atom_map = None
for i, sym in enumerate(reduced_site_sym):
if disps[rot_map_syms[i, second_atom_num]] is not None:
sym_cart = similarity_transformation(self._lattice, sym)
rot_atom_map = rot_map_syms[i, :]
break
assert sym_cart is not None, "Something is wrong."
forces[second_atom_num] = []
disps[second_atom_num] = []
for i in range(self._num_atom):
forces_2 = [
np.dot(f[rot_atom_map], sym_cart.T)
for f in forces[rot_atom_map[second_atom_num]][rot_atom_map[i]]]
disps_2 = [
[d3[0], np.dot(sym_cart, d3[1]), np.dot(sym_cart, d3[2])]
for d3 in disps[rot_atom_map[second_atom_num]][rot_atom_map[i]]]
forces[second_atom_num].append(forces_2)
disps[second_atom_num].append(disps_2)
def _distribute_3(self,
disps_3,
forces_3,
second_atom_num,
third_atom_num,
reduced_bond_sym):
positions = self._positions.copy() - self._positions[second_atom_num]
rot_map_syms = get_positions_sent_by_rot_inv(positions,
reduced_bond_sym,
self._symprec)
sym_cart = None
rot_atom_map = None
for i, sym in enumerate(reduced_bond_sym):
if disps_3[rot_map_syms[i, third_atom_num]] is not None:
sym_cart = similarity_transformation(self._lattice, sym)
rot_atom_map = rot_map_syms[i, :]
break
assert sym_cart is not None, "Something is wrong."
forces = [np.dot(f[rot_atom_map], sym_cart.T)
for f in forces_3[rot_atom_map[third_atom_num]]]
disps = [[d3[0], d3[1], np.dot(sym_cart, d3[2])]
for d3 in disps_3[rot_atom_map[third_atom_num]]]
disps_3[third_atom_num] = disps
forces_3[third_atom_num] = forces
def _create_displacement_matrix(self, disp_pairs, site_symmetry,
rot_atom_map):
rot_disp1s = []
rot_disp2s = []
rot_pair12 = []
rot_pair21 = []
rot_pair11 = []
rot_pair22 = []
for disp_pairs_u1 in disp_pairs:
for rot_atom_num, ssym in zip(rot_atom_map, site_symmetry):
ssym_c = similarity_transformation(self._lattice, ssym)
for (u1, u2) in disp_pairs_u1[rot_atom_num]:
Su1 = np.dot(ssym_c, u1)
Su2 = np.dot(ssym_c, u2)
rot_disp1s.append(Su1)
rot_disp2s.append(Su2)
rot_pair12.append(np.outer(Su1, Su2).flatten() / 2)
rot_pair21.append(np.outer(Su2, Su1).flatten() / 2)
rot_pair11.append(np.outer(Su1, Su1).flatten() / 2)
rot_pair22.append(np.outer(Su2, Su2).flatten() / 2)
ones = np.ones(len(rot_disp1s)).reshape((-1, 1))
return np.hstack((ones, rot_disp1s, rot_disp2s, rot_pair12, rot_pair21,
rot_pair11, rot_pair22))
def get_born_OUTCAR(
poscar_filename="POSCAR",
outcar_filename="OUTCAR",
primitive_axis=np.eye(3),
supercell_matrix=np.eye(3, dtype="intc"),
is_symmetry=True,
symmetrize_tensors=False,
symprec=1e-5,
):
ucell = read_vasp(poscar_filename)
outcar = open(outcar_filename)
borns, epsilon = _read_born_and_epsilon(outcar)
num_atom = len(borns)
assert num_atom == ucell.get_number_of_atoms()
if symmetrize_tensors:
lattice = ucell.get_cell().T
positions = ucell.get_scaled_positions()
u_sym = Symmetry(ucell, is_symmetry=is_symmetry, symprec=symprec)
point_sym = [similarity_transformation(lattice, r) for r in u_sym.get_pointgroup_operations()]
epsilon = _symmetrize_tensor(epsilon, point_sym)
borns = _symmetrize_borns(borns, u_sym, lattice, positions, symprec)
inv_smat = np.linalg.inv(supercell_matrix)
scell = get_supercell(ucell, supercell_matrix, symprec=symprec)
pcell = get_primitive(scell, np.dot(inv_smat, primitive_axis), symprec=symprec)
p2s = np.array(pcell.get_primitive_to_supercell_map(), dtype="intc")
p_sym = Symmetry(pcell, is_symmetry=is_symmetry, symprec=symprec)
s_indep_atoms = p2s[p_sym.get_independent_atoms()]
u2u = scell.get_unitcell_to_unitcell_map()
u_indep_atoms = [u2u[x] for x in s_indep_atoms]
reduced_borns = borns[u_indep_atoms].copy()
return reduced_borns, epsilon
def _copy_dataset_2nd(self, second_atom_num, set_of_disps, sets_of_forces,
unique_second_atom_nums, reduced_site_sym,
rot_map_syms):
sym_cart = None
rot_atom_map = None
for i, sym in enumerate(reduced_site_sym):
if rot_map_syms[i, second_atom_num] in unique_second_atom_nums:
sym_cart = similarity_transformation(self._lattice, sym)
rot_atom_map = rot_map_syms[i, :]
break
assert sym_cart is not None, "Something is wrong."
forces = []
disps = []
for set_of_forces_orig in sets_of_forces[
rot_atom_map[second_atom_num]]:
forces.append(np.dot(set_of_forces_orig[rot_atom_map], sym_cart.T))
disps = [
np.dot(sym_cart, d)
for d in set_of_disps[rot_atom_map[second_atom_num]]
]
return forces, disps
def get_gv_by_sr0_at_stars(self, s,i,t):
deg_sets = degenerate_sets(self._frequencies[i])
grid_point = self._grid_points[i]
orig_address = self._grid_address[grid_point]
rotations=get_rotations_for_star(orig_address, self._mesh, self._kpoint_operations)
# self._get_group_veclocities_at_star(i, gv)
gv_by_F_tensor = []
rec_lat = np.linalg.inv(self._primitive.get_cell())
rotations_cartesian = [similarity_transformation(rec_lat, r)
for r in rotations]
for rot_c in rotations_cartesian:
gvs_rot = np.dot(rot_c, self._gv[i].T).T
F_rot = np.dot(rot_c, self._F0[s,i,t].T).T
# Take average of group veclocities of degenerate phonon modes
# and then calculate gv x gv to preserve symmetry
gvs = np.zeros_like(gvs_rot)
Fs = np.zeros_like(F_rot)
for deg in deg_sets:
gv_ave = gvs_rot[deg].sum(axis=0) / len(deg)
F_ave = F_rot[deg].sum(axis=0)/len(deg)
for j in deg:
gvs[j] = gv_ave
Fs[j]=F_ave
gv_by_F_tensor.append([np.outer(gvs[b], Fs[b]) for b in range(len(gvs))])
return np.array(gv_by_F_tensor)
def _create_displacement_matrix(self,
disp_pairs,
site_symmetry,
rot_atom_map):
rot_disp1s = []
rot_disp2s = []
rot_pair12 = []
rot_pair21 = []
rot_pair11 = []
rot_pair22 = []
for disp_pairs_u1 in disp_pairs:
for rot_atom_num, ssym in zip(rot_atom_map, site_symmetry):
ssym_c = similarity_transformation(self._lattice, ssym)
for (u1, u2) in disp_pairs_u1[rot_atom_num]:
Su1 = np.dot(ssym_c, u1)
Su2 = np.dot(ssym_c, u2)
rot_disp1s.append(Su1)
rot_disp2s.append(Su2)
rot_pair12.append(np.outer(Su1, Su2).flatten() / 2)
rot_pair21.append(np.outer(Su2, Su1).flatten() / 2)
rot_pair11.append(np.outer(Su1, Su1).flatten() / 2)
rot_pair22.append(np.outer(Su2, Su2).flatten() / 2)
ones = np.ones(len(rot_disp1s)).reshape((-1, 1))
return np.hstack((ones, rot_disp1s, rot_disp2s,
rot_pair12, rot_pair21, rot_pair11, rot_pair22))
def _copy_dataset_2nd(self,
second_atom_num,
set_of_disps,
sets_of_forces,
unique_second_atom_nums,
reduced_site_sym,
rot_map_syms):
sym_cart = None
rot_atom_map = None
for i, sym in enumerate(reduced_site_sym):
if rot_map_syms[i, second_atom_num] in unique_second_atom_nums:
sym_cart = similarity_transformation(self._lattice, sym)
rot_atom_map = rot_map_syms[i, :]
break
assert sym_cart is not None, "Something is wrong."
forces = []
disps = []
for set_of_forces_orig in sets_of_forces[rot_atom_map[second_atom_num]]:
forces.append(np.dot(set_of_forces_orig[rot_atom_map], sym_cart.T))
disps = [np.dot(sym_cart, d)
for d in set_of_disps[rot_atom_map[second_atom_num]]]
return forces, disps
def _get_rotated_fc2s(i, j, fc2s, rot_map_syms, site_sym_cart):
rotated_fc2s = []
for fc2 in fc2s:
for sym, map_sym in zip(site_sym_cart, rot_map_syms):
fc2_rot = fc2[map_sym[i], map_sym[j]]
rotated_fc2s.append(similarity_transformation(sym, fc2_rot))
return np.reshape(rotated_fc2s, (-1, 9))
def _symmetrize_group_velocity_matrix(self, gvm, q):
"""Symmetrize obtained group velocity matrices.
The following symmetries are applied:
1. site symmetries
2. band hermicity
"""
# site symmetries
rotations = []
for r in self._symmetry.reciprocal_operations:
q_in_BZ = q - np.rint(q)
diff = q_in_BZ - np.dot(r, q_in_BZ)
if (np.abs(diff) < self._symmetry.tolerance).all():
rotations.append(r)
gvm_sym = np.zeros_like(gvm)
for r in rotations:
r_cart = similarity_transformation(self._reciprocal_lattice, r)
gvm_sym += np.einsum("ij,jkl->ikl", r_cart, gvm)
gvm_sym = gvm_sym / len(rotations)
# band hermicity
gvm_sym = (gvm_sym + gvm_sym.transpose(0, 2, 1).conj()) / 2
return gvm_sym
def get_born_parameters(f, primitive, is_symmetry):
# Read unit conversion factor, damping factor, ...
factors = [float(x) for x in f.readline().split()]
if len(factors) < 1:
print "BORN file format of line 1 is incorrect"
return False
if len(factors) < 2:
factors = factors[0]
# Read dielectric constant
line = f.readline().split()
if not len(line) == 9:
print "BORN file format of line 2 is incorrect"
return False
dielectric = np.reshape([float(x) for x in line], (3, 3))
# Read Born effective charge
symmetry = Symmetry(primitive, is_symmetry=is_symmetry)
independent_atoms = symmetry.get_independent_atoms()
born = np.zeros((primitive.get_number_of_atoms(), 3, 3), dtype=float)
for i in independent_atoms:
line = f.readline().split()
if len(line) == 0:
print "Number of lines for Born effect charge is not enough."
return False
if not len(line) == 9:
print "BORN file format of line %d is incorrect" % (i + 3)
return False
born[i] = np.reshape([float(x) for x in line], (3, 3))
# Expand Born effective charges to all atoms in the primitive cell
rotations = symmetry.get_symmetry_operations()['rotations']
map_operations = symmetry.get_map_operations()
map_atoms = symmetry.get_map_atoms()
for i in range(primitive.get_number_of_atoms()):
# R_cart = L R L^-1
rot_cartesian = similarity_transformation(
primitive.get_cell().transpose(), rotations[map_operations[i]])
# R_cart^T B R_cart^-T (inverse rotation is required to transform)
born[i] = similarity_transformation(rot_cartesian.transpose(),
born[map_atoms[i]])
non_anal = {'born': born, 'factor': factors, 'dielectric': dielectric}
return non_anal
def distribute_fc3(fc3,
first_disp_atoms,
lattice,
positions,
rotations,
translations,
symprec,
verbose):
num_atom = len(positions)
for i in range(num_atom):
if i in first_disp_atoms:
continue
for atom_index_done in first_disp_atoms:
rot_num = get_atom_mapping_by_symmetry(positions,
i,
atom_index_done,
rotations,
translations,
symprec)
if rot_num > -1:
i_rot = atom_index_done
rot = rotations[rot_num]
trans = translations[rot_num]
break
if rot_num < 0:
print "Position or symmetry may be wrong."
raise ValueError
if verbose > 2:
print " [ %d, x, x ] to [ %d, x, x ]" % (i_rot + 1, i + 1)
sys.stdout.flush()
atom_mapping = np.zeros(num_atom, dtype='intc')
for j in range(num_atom):
atom_mapping[j] = get_atom_by_symmetry(positions,
rot,
trans,
j,
symprec)
rot_cart_inv = np.double(
similarity_transformation(lattice, rot).T.copy())
try:
import anharmonic._phono3py as phono3c
phono3c.distribute_fc3(fc3,
i,
atom_mapping,
rot_cart_inv)
except ImportError:
for j in range(num_atom):
j_rot = atom_mapping[j]
for k in range(num_atom):
k_rot = atom_mapping[k]
fc3[i, j, k] = third_rank_tensor_rotation(
rot_cart_inv, fc3[i_rot, j_rot, k_rot])
def distribute_fc3(
fc3_least_atoms,
first_disp_atoms,
lattice,
positions,
rotations,
translations,
symprec,
overwrite=True,
verbose=False,
):
num_atom = len(positions)
atom_mapping = np.zeros(num_atom, dtype="intc")
if overwrite:
fc3 = fc3_least_atoms
else:
fc3 = np.zeros((num_atom, num_atom, num_atom, 3, 3, 3), dtype="double")
for i in range(num_atom):
# if i in first_disp_atoms:
# continue
for atom_index_done in first_disp_atoms:
rot_num = get_atom_mapping_by_symmetry(positions, i, atom_index_done, rotations, translations, symprec)
if rot_num > -1:
i_rot = atom_index_done
rot = rotations[rot_num]
trans = translations[rot_num]
break
if rot_num < 0:
print "Position or symmetry may be wrong."
raise ValueError
for j in range(num_atom):
atom_mapping[j] = get_atom_by_symmetry(positions, rot, trans, j, symprec)
rot_cart_inv = np.array(similarity_transformation(lattice, rot).T, dtype="double", order="C")
if not (overwrite and i == i_rot):
if verbose > 2:
print " [ %d, x, x ] to [ %d, x, x ]" % (i_rot + 1, i + 1)
sys.stdout.flush()
try:
import anharmonic._phono3py as phono3c
phono3c.distribute_fc3(fc3, fc3_least_atoms, i, atom_mapping, rot_cart_inv)
except ImportError:
for j in range(num_atom):
j_rot = atom_mapping[j]
for k in range(num_atom):
k_rot = atom_mapping[k]
fc3[i, j, k] = third_rank_tensor_rotation(rot_cart_inv, fc3_least_atoms[i_rot, j_rot, k_rot])
if not overwrite:
return fc3
def _distribute_forces(supercell, disp, forces, filename, symprec):
natom = supercell.get_number_of_atoms()
lattice = supercell.get_cell()
symbols = supercell.get_chemical_symbols()
positions = supercell.get_positions()
positions[disp[0]] += disp[1]
cell = Atoms(cell=lattice, positions=positions, symbols=symbols, pbc=True)
symmetry = Symmetry(cell, symprec)
independent_atoms = symmetry.get_independent_atoms()
# Rotation matrices in Cartesian
rotations = []
for r in symmetry.get_symmetry_operations()["rotations"]:
rotations.append(similarity_transformation(lattice.T, r))
map_operations = symmetry.get_map_operations()
map_atoms = symmetry.get_map_atoms()
atoms_in_dot_scf = _get_independent_atoms_in_dot_scf(filename)
if len(forces) != len(atoms_in_dot_scf):
print("%s does not contain necessary information." % filename)
print('Plese check if there are "FGL" lines with')
print('"total forces" are required.')
return False
if len(atoms_in_dot_scf) == natom:
print("It is assumed that there is no symmetrically-equivalent " "atoms in ")
print("'%s' at wien2k calculation." % filename)
force_set = forces
elif len(forces) != len(independent_atoms):
print("Non-equivalent atoms of %s could not be recognized by phonopy." % filename)
return False
else:
# 1. Transform wien2k forces to those on independent atoms
indep_atoms_to_wien2k = []
forces_remap = []
for i, pos_wien2k in enumerate(atoms_in_dot_scf):
for j, pos in enumerate(cell.get_scaled_positions()):
diff = pos_wien2k - pos
diff -= np.rint(diff)
if (abs(diff) < symprec).all():
forces_remap.append(np.dot(rotations[map_operations[j]], forces[i]))
indep_atoms_to_wien2k.append(map_atoms[j])
break
if len(forces_remap) != len(forces):
print("Atomic position mapping between Wien2k and phonopy failed.")
print("If you think this is caused by a bug of phonopy")
print("please report it in the phonopy mainling list.")
return False
# 2. Distribute forces from independent to dependent atoms.
force_set = []
for i in range(natom):
j = indep_atoms_to_wien2k.index(map_atoms[i])
force_set.append(np.dot(rotations[map_operations[i]].T, forces_remap[j]))
return force_set
def _transform_rotations(self, tmat, rotations):
trans_rots = []
for r in rotations:
r_conv = similarity_transformation(np.linalg.inv(tmat), r)
trans_rots.append(np.rint(r_conv).astype(int))
return np.array(trans_rots)
def _get_rotated_fc2s(i, j, fc2s, rot_map_syms, site_sym_cart):
num_sym = len(site_sym_cart)
rotated_fc2s = []
for fc2 in fc2s:
for sym, map_sym in zip(site_sym_cart, rot_map_syms):
fc2_rot = fc2[map_sym[i], map_sym[j]]
rotated_fc2s.append(similarity_transformation(sym, fc2_rot))
return np.reshape(rotated_fc2s, (-1, 9))
def symmetrize_borns(borns,
rotations,
translations,
lattice,
positions,
symprec):
borns_orig = borns.copy()
for i, Z in enumerate(borns):
site_sym = get_site_symmetry(i,
lattice,
positions,
rotations,
translations,
symprec)
Z = symmetrize_2nd_rank_tensor(Z, site_sym, lattice)
borns_copy = np.zeros_like(borns)
for i in range(len(borns)):
count = 0
for r, t in zip(rotations, translations):
count += 1
diff = np.dot(positions, r.T) + t - positions[i]
diff -= np.rint(diff)
dist = np.sqrt(np.sum(np.dot(diff, lattice) ** 2, axis=1))
j = np.nonzero(dist < symprec)[0][0]
r_cart = similarity_transformation(lattice.T, r)
borns_copy[i] += similarity_transformation(r_cart, borns[j])
borns_copy[i] /= count
borns = borns_copy
sum_born = borns.sum(axis=0) / len(borns)
borns -= sum_born
if (np.abs(borns_orig - borns) > 0.1).any():
sys.stderr.write(
"Born effective charge symmetrization might go wrong.\n")
sys.stderr.write("Sum of Born charges:\n")
sys.stderr.write(str(borns_orig.sum(axis=0)))
sys.stderr.write("\n")
# for b_o, b in zip(borns_orig, borns):
# sys.stderr.write(str(b - b_o))
# sys.stderr.write("\n")
return borns
def _transform_rotations(self, tmat, rotations):
trans_rots = []
for r in rotations:
r_conv = similarity_transformation(np.linalg.inv(tmat), r)
trans_rots.append(np.rint(r_conv).astype(int))
return np.array(trans_rots)
def _fit(self, first_atom_num, disp_triplets, sets_of_forces):
site_symmetry = self._symmetry.get_site_symmetry(first_atom_num)
positions = self._positions.copy() - self._positions[first_atom_num]
rot_map_syms = get_positions_sent_by_rot_inv(positions,
site_symmetry,
self._symprec)
site_syms_cart = np.array([similarity_transformation(self._lattice, sym)
for sym in site_symmetry],
dtype='double')
(disp_triplets_rearranged,
num_triplets) = self._create_displacement_triplets_for_c(disp_triplets)
max_num_disp = np.amax(num_triplets[:, :, :, 1])
for second_atom_num in range(self._num_atom):
print second_atom_num + 1
rot_disps_set = []
for third_atom_num in range(self._num_atom):
try:
import anharmonic._forcefit as forcefit
rot_disps_set.append(self._create_displacement_matrix_c(
second_atom_num,
third_atom_num,
disp_triplets_rearranged,
num_triplets,
site_syms_cart,
rot_map_syms,
max_num_disp))
except ImportError:
rot_disps_set.append(self._create_displacement_matrix(
second_atom_num,
third_atom_num,
disp_triplets,
site_syms_cart,
rot_map_syms))
print third_atom_num + 1, rot_disps_set[third_atom_num].shape
inv_disps_set = self._invert_displacements(rot_disps_set)
for third_atom_num in range(self._num_atom):
rot_forces = self._create_force_matrix(
second_atom_num,
third_atom_num,
sets_of_forces,
site_syms_cart,
rot_map_syms)
fc = self._solve(inv_disps_set[third_atom_num], rot_forces)
# For elements with index exchange symmetry
fc2 = fc[:, 7:10, :].reshape((self._num_atom, 3, 3))
fc3 = fc[:, 46:55, :].reshape((self._num_atom, 3, 3, 3))
fc4 = fc[:, 172:199, :].reshape((self._num_atom, 3, 3, 3, 3))
self._fc2[third_atom_num] = fc2
self._fc3[second_atom_num, third_atom_num] = fc3
self._fc4[first_atom_num, second_atom_num, third_atom_num] = fc4
def _take_average_of_borns(borns, rotations, translations, cell, symprec):
lattice = cell.cell
positions = cell.scaled_positions
borns_ = np.zeros_like(borns)
for i in range(len(borns)):
for r, t in zip(rotations, translations):
diff = np.dot(positions, r.T) + t - positions[i]
diff -= np.rint(diff)
dist = np.sqrt(np.sum(np.dot(diff, lattice)**2, axis=1))
j = np.nonzero(dist < symprec)[0][0]
r_cart = similarity_transformation(lattice.T, r)
borns_[i] += similarity_transformation(r_cart, borns[j])
borns_[i] /= len(rotations)
sum_born = borns_.sum(axis=0) / len(borns_)
borns_ -= sum_born
return borns_
def solve_fc3(fc3,
first_atom_num,
supercell,
site_symmetry,
displacements_first,
delta_fc2s,
symprec,
pinv="numpy",
verbose=False):
if verbose:
text = "Solving fc3[ %d, x, x ] with " % (first_atom_num + 1)
if len(displacements_first) > 1:
text += "displacements:"
else:
text += "a displacement:"
print(text)
for i, v in enumerate(displacements_first):
print(" [%7.4f %7.4f %7.4f]" % tuple(v))
sys.stdout.flush()
if verbose > 2:
print(" Site symmetry:")
for i, v in enumerate(site_symmetry):
print(" [%2d %2d %2d] #%2d" % tuple(list(v[0]) + [i + 1]))
print(" [%2d %2d %2d]" % tuple(v[1]))
print(" [%2d %2d %2d]\n" % tuple(v[2]))
sys.stdout.flush()
lattice = supercell.get_cell().T
site_sym_cart = [
similarity_transformation(lattice, sym) for sym in site_symmetry
]
num_atom = supercell.get_number_of_atoms()
positions = supercell.get_scaled_positions()
pos_center = positions[first_atom_num].copy()
positions -= pos_center
rot_map_syms = get_positions_sent_by_rot_inv(positions, site_symmetry,
symprec)
rot_disps = get_rotated_displacement(displacements_first, site_sym_cart)
if pinv == "numpy":
inv_U = np.linalg.pinv(rot_disps)
else:
try:
import phonopy._lapackepy as lapackepy
inv_U = np.zeros((rot_disps.shape[1], rot_disps.shape[0]),
dtype='double')
lapackepy.pinv(inv_U, rot_disps, 1e-13)
except ImportError:
inv_U = np.linalg.pinv(rot_disps)
for (i, j) in list(np.ndindex(num_atom, num_atom)):
fc3[first_atom_num, i, j] = np.dot(
inv_U,
_get_rotated_fc2s(i, j, delta_fc2s, rot_map_syms,
site_sym_cart)).reshape(3, 3, 3)
def solve_fc3(fc3,
first_atom_num,
supercell,
site_symmetry,
displacements_first,
delta_fc2s,
symprec,
pinv="numpy",
verbose=False):
if verbose:
text = "Solving fc3[ %d, x, x ] with " % (first_atom_num + 1)
if len(displacements_first) > 1:
text += "displacements:"
else:
text += "a displacement:"
print(text)
for i, v in enumerate(displacements_first):
print(" [%7.4f %7.4f %7.4f]" % tuple(v))
sys.stdout.flush()
if verbose > 2:
print(" Site symmetry:")
for i, v in enumerate(site_symmetry):
print(" [%2d %2d %2d] #%2d" % tuple(list(v[0])+[i + 1]))
print(" [%2d %2d %2d]" % tuple(v[1]))
print(" [%2d %2d %2d]\n" % tuple(v[2]))
sys.stdout.flush()
lattice = supercell.get_cell().T
site_sym_cart = [similarity_transformation(lattice, sym)
for sym in site_symmetry]
num_atom = supercell.get_number_of_atoms()
positions = supercell.get_scaled_positions()
pos_center = positions[first_atom_num].copy()
positions -= pos_center
rot_map_syms = get_positions_sent_by_rot_inv(positions,
site_symmetry,
symprec)
rot_disps = get_rotated_displacement(displacements_first, site_sym_cart)
if pinv == "numpy":
inv_U = np.linalg.pinv(rot_disps)
else:
try:
import phonopy._lapackepy as lapackepy
inv_U = np.zeros((rot_disps.shape[1], rot_disps.shape[0]),
dtype='double')
lapackepy.pinv(inv_U, rot_disps, 1e-13)
except ImportError:
inv_U = np.linalg.pinv(rot_disps)
for (i, j) in list(np.ndindex(num_atom, num_atom)):
fc3[first_atom_num, i, j] = np.dot(inv_U, _get_rotated_fc2s(
i, j, delta_fc2s, rot_map_syms, site_sym_cart)).reshape(3, 3, 3)
def _fit(self, first_atom_num, disp_triplets, sets_of_forces):
site_symmetry = self._symmetry.get_site_symmetry(first_atom_num)
positions = self._positions.copy() - self._positions[first_atom_num]
rot_map_syms = get_positions_sent_by_rot_inv(self._lattice, positions,
site_symmetry,
self._symprec)
site_syms_cart = np.array([
similarity_transformation(self._lattice, sym)
for sym in site_symmetry
],
dtype='double')
(disp_triplets_rearranged, num_triplets
) = self._create_displacement_triplets_for_c(disp_triplets)
max_num_disp = np.amax(num_triplets[:, :, :, 1])
for second_atom_num in range(self._num_atom):
print second_atom_num + 1
rot_disps_set = []
for third_atom_num in range(self._num_atom):
try:
import anharmonic._forcefit as forcefit
rot_disps_set.append(
self._create_displacement_matrix_c(
second_atom_num, third_atom_num,
disp_triplets_rearranged, num_triplets,
site_syms_cart, rot_map_syms, max_num_disp))
except ImportError:
rot_disps_set.append(
self._create_displacement_matrix(
second_atom_num, third_atom_num, disp_triplets,
site_syms_cart, rot_map_syms))
print third_atom_num + 1, rot_disps_set[third_atom_num].shape
inv_disps_set = self._invert_displacements(rot_disps_set)
for third_atom_num in range(self._num_atom):
rot_forces = self._create_force_matrix(second_atom_num,
third_atom_num,
sets_of_forces,
site_syms_cart,
rot_map_syms)
fc = self._solve(inv_disps_set[third_atom_num], rot_forces)
# For elements with index exchange symmetry
fc2 = fc[:, 7:10, :].reshape((self._num_atom, 3, 3))
fc3 = fc[:, 46:55, :].reshape((self._num_atom, 3, 3, 3))
fc4 = fc[:, 172:199, :].reshape((self._num_atom, 3, 3, 3, 3))
self._fc2[third_atom_num] = fc2
self._fc3[second_atom_num, third_atom_num] = fc3
self._fc4[first_atom_num, second_atom_num,
third_atom_num] = fc4
def _get_ground_matrix(self):
matrices = []
for (r, t) in zip(self._rotations_at_q, self._translations_at_q):
lat = self._primitive.get_cell().T
r_cart = similarity_transformation(lat, r)
perm_mat = self._get_modified_permutation_matrix(r, t)
matrices.append(np.kron(perm_mat, r_cart))
return np.array(matrices)
def __init__(self,
interaction,
point_operations=None,
ir_grid_points=None,
rot_grid_points=None,
temperature=None,
sigma=None,
is_reducible_collision_matrix=False,
log_level=0,
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
self._log_level = log_level
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 = rot_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 _get_ground_matrix(self):
matrices = []
for (r, t) in zip(self._rotations_at_q,
self._translations_at_q):
lat = self._primitive.get_cell().T
r_cart = similarity_transformation(lat, r)
perm_mat = self._get_modified_permutation_matrix(r, t)
matrices.append(np.kron(perm_mat, r_cart))
return np.array(matrices)
def _symmetrize_group_velocity(self, gv, q):
rotations = []
for r in self._symmetry.get_reciprocal_operations():
q_in_BZ = q - np.rint(q)
diff = q_in_BZ - np.dot(r, q_in_BZ)
if (np.abs(diff) < self._symmetry.get_symmetry_tolerance()).all():
rotations.append(r)
gv_sym = np.zeros_like(gv)
for r in rotations:
r_cart = similarity_transformation(self._reciprocal_lattice, r)
gv_sym += np.dot(r_cart, gv.T).T
return gv_sym / len(rotations)
def _symmetrize_group_velocity(self, gv, q):
rotations = []
for r in self._symmetry.get_reciprocal_operations():
q_in_BZ = q - np.rint(q)
diff = q_in_BZ - np.dot(r, q_in_BZ)
if (np.abs(diff) < self._symmetry.get_symmetry_tolerance()).all():
rotations.append(r)
gv_sym = np.zeros_like(gv)
for r in rotations:
r_cart = similarity_transformation(self._reciprocal_lattice, r)
gv_sym += np.dot(r_cart, gv.T).T
return gv_sym / len(rotations)
def _set_kappa(self, i_sigma, i_temp, X):
num_band = self._primitive.get_number_of_atoms() * 3
if self._is_reducible_collision_matrix:
num_mesh_points = np.prod(self._mesh)
num_grid_points = num_mesh_points
from phonopy.harmonic.force_constants import similarity_transformation
point_operations = self._symmetry.get_reciprocal_operations()
rec_lat = np.linalg.inv(self._primitive.get_cell())
rotations_cartesian = np.array(
[similarity_transformation(rec_lat, r)
for r in point_operations], dtype='double')
inv_col_mat = np.kron(
self._collision_matrix[i_sigma, i_temp].reshape(
num_mesh_points * num_band,
num_mesh_points * num_band), np.eye(3))
else:
num_ir_grid_points = len(self._ir_grid_points)
num_grid_points = num_ir_grid_points
rotations_cartesian = self._rotations_cartesian
inv_col_mat = self._collision_matrix[i_sigma, i_temp].reshape(
num_ir_grid_points * num_band * 3,
num_ir_grid_points * num_band * 3)
Y = np.dot(inv_col_mat, X.ravel()).reshape(-1, 3)
for i, (v_gp, f_gp) in enumerate(zip(X.reshape(num_grid_points,
num_band, 3),
Y.reshape(num_grid_points,
num_band, 3))):
for j, (v, f) in enumerate(zip(v_gp, f_gp)):
sum_k = np.zeros((3, 3), dtype='double')
for r in rotations_cartesian:
sum_k += np.outer(np.dot(r, v), np.dot(r, f))
sum_k = sum_k + sum_k.T
for k, vxf in enumerate(
((0, 0), (1, 1), (2, 2), (1, 2), (0, 2), (0, 1))):
self._mode_kappa[i_sigma, i_temp, i, j, k] = sum_k[vxf]
t = self._temperatures[i_temp]
self._mode_kappa *= (self._conversion_factor * Kb * t ** 2
/ np.prod(self._mesh))
if self._is_reducible_collision_matrix:
self._mode_kappa /= len(point_operations)
self._kappa[i_sigma, i_temp] = (
self._mode_kappa[i_sigma, i_temp].sum(axis=0).sum(axis=0))
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 _set_kappa(self, i_sigma, i_temp, X):
num_band = self._primitive.get_number_of_atoms() * 3
if self._is_reducible_collision_matrix:
num_mesh_points = np.prod(self._mesh)
num_grid_points = num_mesh_points
from phonopy.harmonic.force_constants import similarity_transformation
point_operations = self._symmetry.get_reciprocal_operations()
rec_lat = np.linalg.inv(self._primitive.get_cell())
rotations_cartesian = np.array(
[similarity_transformation(rec_lat, r)
for r in point_operations], dtype='double')
inv_col_mat = np.kron(
self._collision_matrix[i_sigma, i_temp].reshape(
num_mesh_points * num_band,
num_mesh_points * num_band), np.eye(3))
else:
num_ir_grid_points = len(self._ir_grid_points)
num_grid_points = num_ir_grid_points
rotations_cartesian = self._rotations_cartesian
inv_col_mat = self._collision_matrix[i_sigma, i_temp].reshape(
num_ir_grid_points * num_band * 3,
num_ir_grid_points * num_band * 3)
Y = np.dot(inv_col_mat, X.ravel()).reshape(-1, 3)
for i, (v_gp, f_gp) in enumerate(zip(X.reshape(num_grid_points,
num_band, 3),
Y.reshape(num_grid_points,
num_band, 3))):
for j, (v, f) in enumerate(zip(v_gp, f_gp)):
sum_k = np.zeros((3, 3), dtype='double')
for r in rotations_cartesian:
sum_k += np.outer(np.dot(r, v), np.dot(r, f))
sum_k = sum_k + sum_k.T
for k, vxf in enumerate(
((0, 0), (1, 1), (2, 2), (1, 2), (0, 2), (0, 1))):
self._mode_kappa[i_sigma, i_temp, i, j, k] = sum_k[vxf]
t = self._temperatures[i_temp]
self._mode_kappa *= (self._conversion_factor * Kb * t ** 2
/ np.prod(self._mesh))
if self._is_reducible_collision_matrix:
self._mode_kappa /= len(point_operations)
self._kappa[i_sigma, i_temp] = (
self._mode_kappa[i_sigma, i_temp].sum(axis=0).sum(axis=0))
def _get_matrices(self, first_atom_num):
disps = []
sets_of_forces = []
for dataset_1st in self._dataset["first_atoms"]:
if first_atom_num != dataset_1st["number"]:
continue
disps.append(dataset_1st["displacement"])
sets_of_forces.append(dataset_1st["forces"])
site_symmetry = self._symmetry.get_site_symmetry(first_atom_num)
positions = self._positions.copy() - self._positions[first_atom_num]
rot_map_syms = get_positions_sent_by_rot_inv(positions, site_symmetry, self._symprec)
site_sym_cart = [similarity_transformation(self._lattice, sym) for sym in site_symmetry]
rot_disps = self._create_displacement_matrix(disps, site_sym_cart)
rot_forces = self._create_force_matrix(sets_of_forces, site_sym_cart, rot_map_syms)
return rot_disps, rot_forces
def can_use_std_lattice(conv_lat, tmat, std_lattice, rotations, symprec=1e-5):
"""Inspect if std_lattice can be used as conv_lat.
r_s is the rotation matrix of conv_lat.
Return if conv_lat rotated by det(r_s)*r_s and std_lattice are equivalent.
det(r_s) is necessary to make improper rotation to proper rotation.
"""
for r in rotations:
r_s = similarity_transformation(tmat, r)
if np.allclose(
np.linalg.det(r_s) * np.dot(np.transpose(conv_lat), r_s),
np.transpose(std_lattice),
atol=symprec,
):
return True
return False
def _create_force_matrix(self,
sets_of_forces,
site_symmetry,
rot_atom_map,
rot_map_syms):
site_syms_cart = [similarity_transformation(self._lattice, sym)
for sym in site_symmetry]
force_matrix = []
for i in range(self._num_atom):
force_matrix_atom = []
for sets_of_forces_u1 in sets_of_forces:
for map_sym, rot_atom_num, sym in zip(
rot_map_syms, rot_atom_map, site_syms_cart):
for forces in sets_of_forces_u1[rot_atom_num]:
force_matrix_atom.append(
np.dot(sym, forces[map_sym[i]]))
force_matrix.append(force_matrix_atom)
return np.array(force_matrix, dtype='double', order='C')
def _create_force_matrix(self, sets_of_forces, site_symmetry, rot_atom_map,
rot_map_syms):
site_syms_cart = [
similarity_transformation(self._lattice, sym)
for sym in site_symmetry
]
force_matrix = []
for i in range(self._num_atom):
force_matrix_atom = []
for sets_of_forces_u1 in sets_of_forces:
for map_sym, rot_atom_num, sym in zip(rot_map_syms,
rot_atom_map,
site_syms_cart):
for forces in sets_of_forces_u1[rot_atom_num]:
force_matrix_atom.append(
np.dot(sym, forces[map_sym[i]]))
force_matrix.append(force_matrix_atom)
return np.array(force_matrix, dtype='double', order='C')
def get_born_OUTCAR(poscar_filename="POSCAR",
outcar_filename="OUTCAR",
primitive_matrix=None,
supercell_matrix=None,
is_symmetry=True,
symmetrize_tensors=False,
symprec=1e-5):
if primitive_matrix is None:
pmat = np.eye(3)
else:
pmat = primitive_matrix
if supercell_matrix is None:
smat = np.eye(3, dtype='intc')
else:
smat = supercell_matrix
ucell = read_vasp(poscar_filename)
outcar = open(outcar_filename)
borns, epsilon = _read_born_and_epsilon(outcar)
num_atom = len(borns)
assert num_atom == ucell.get_number_of_atoms()
if symmetrize_tensors:
lattice = ucell.get_cell().T
positions = ucell.get_scaled_positions()
u_sym = Symmetry(ucell, is_symmetry=is_symmetry, symprec=symprec)
point_sym = [
similarity_transformation(lattice, r)
for r in u_sym.get_pointgroup_operations()
]
epsilon = _symmetrize_tensor(epsilon, point_sym)
borns = _symmetrize_borns(borns, u_sym, lattice, positions, symprec)
inv_smat = np.linalg.inv(smat)
scell = get_supercell(ucell, smat, symprec=symprec)
pcell = get_primitive(scell, np.dot(inv_smat, pmat), symprec=symprec)
p2s = np.array(pcell.get_primitive_to_supercell_map(), dtype='intc')
p_sym = Symmetry(pcell, is_symmetry=is_symmetry, symprec=symprec)
s_indep_atoms = p2s[p_sym.get_independent_atoms()]
u2u = scell.get_unitcell_to_unitcell_map()
u_indep_atoms = [u2u[x] for x in s_indep_atoms]
reduced_borns = borns[u_indep_atoms].copy()
return reduced_borns, epsilon, s_indep_atoms
def get_gv_by_gv(self,i):
deg_sets = degenerate_sets(self._frequency[i])
orbits, rotations = self._reverse_mapping[i], self._kpt_rotations_at_stars[i]
# self._get_group_veclocities_at_star(i, gv)
gv2_tensor = []
rec_lat = np.linalg.inv(self._cell.get_cell())
rotations_cartesian = [similarity_transformation(rec_lat, r)
for r in rotations]
for rot_c in rotations_cartesian:
gvs_rot = np.dot(rot_c, self._gv[i].T).T
# Take average of group veclocities of degenerate phonon modes
# and then calculate gv x gv to preserve symmetry
gvs = np.zeros_like(gvs_rot)
for deg in deg_sets:
gv_ave = gvs_rot[deg].sum(axis=0) / len(deg)
for j in deg:
gvs[j] = gv_ave
gv2_tensor.append([np.outer(gv, gv) for gv in gvs])
return np.array(gv2_tensor)
def _get_matrices(self, first_atom_num):
disps = []
sets_of_forces = []
for dataset_1st in self._dataset['first_atoms']:
if first_atom_num != dataset_1st['number']:
continue
disps.append(dataset_1st['displacement'])
sets_of_forces.append(dataset_1st['forces'])
site_symmetry = self._symmetry.get_site_symmetry(first_atom_num)
positions = (self._positions.copy() - self._positions[first_atom_num])
rot_map_syms = get_positions_sent_by_rot_inv(positions, site_symmetry,
self._symprec)
site_sym_cart = [
similarity_transformation(self._lattice, sym)
for sym in site_symmetry
]
rot_disps = self._create_displacement_matrix(disps, site_sym_cart)
rot_forces = self._create_force_matrix(sets_of_forces, site_sym_cart,
rot_map_syms)
return rot_disps, rot_forces
def _get_kappa(self, i_sigma, i_temp, X):
num_ir_grid_points = len(self._ir_grid_points)
num_band = self._primitive.get_number_of_atoms() * 3
if self._is_reducible_collision_matrix:
num_mesh_points = np.prod(self._mesh)
inv_col_mat = np.kron(
self._collision_matrix[i_sigma, i_temp].reshape(
num_mesh_points * num_band,
num_mesh_points * num_band), np.eye(3))
else:
inv_col_mat = self._collision_matrix[i_sigma, i_temp].reshape(
num_ir_grid_points * num_band * 3,
num_ir_grid_points * num_band * 3)
Y = np.dot(inv_col_mat, X.ravel()).reshape(-1, 3)
if self._is_reducible_collision_matrix:
from phonopy.harmonic.force_constants import similarity_transformation
point_operations = self._symmetry.get_reciprocal_operations()
rec_lat = np.linalg.inv(self._primitive.get_cell())
rotations_cartesian = np.array(
[similarity_transformation(rec_lat, r)
for r in point_operations], dtype='double')
else:
rotations_cartesian = self._rotations_cartesian
# Acoustic mode at Gamma is not summed.
RX = np.dot(X[3:], rotations_cartesian.reshape(-1, 3).T)
RY = np.dot(Y[3:], rotations_cartesian.reshape(-1, 3).T)
sum_outer = np.zeros((3, 3), dtype='double')
for v, f in zip(RX.reshape(-1, 3), RY.reshape(-1, 3)):
sum_outer += np.outer(v, f)
t = self._temperatures[i_temp]
if self._is_reducible_collision_matrix:
return ((sum_outer + sum_outer.T) * self._conversion_factor *
Kb * t ** 2 / np.prod(self._mesh) / len(point_operations))
else:
return ((sum_outer + sum_outer.T) * self._conversion_factor *
Kb * t ** 2 / np.prod(self._mesh))
def _symmetrize_tensor(tensor, symmetry_operations):
sum_tensor = np.zeros_like(tensor)
for sym in symmetry_operations:
sum_tensor += similarity_transformation(sym, tensor)
return sum_tensor / len(symmetry_operations)