def get_fc2_translational_invariance(supercell,
trans,
coeff,
ifc_map,
precision=1e-6):
natom = supercell.get_number_of_atoms()
unit_atoms = np.unique(supercell.get_supercell_to_unitcell_map())
num_irred = trans.shape[-1]
ti_transforms = [np.zeros(num_irred)]
for i, atom1 in enumerate(unit_atoms):
ti_transform = np.zeros((9, num_irred))
for atom2 in np.arange(natom):
irred_doublet = ifc_map[atom1, atom2]
ti_transform += np.dot(coeff[atom1, atom2], trans[irred_doublet])
for k in range(9):
if not (np.abs(ti_transform[k]) < precision).all():
# ti_transform_row = ti_transform[k] / np.abs(ti_transform[k]).max()
# ti_transforms.append(ti_transform_row)
argmax = np.argmax(np.abs(ti_transform[k]))
ti_transform[k] /= ti_transform[k, argmax]
is_exist = np.all(np.abs(ti_transform[k] -
np.array(ti_transforms)) < precision,
axis=1)
if (is_exist == False).all():
ti_transforms.append(ti_transform[k] /
ti_transform[k, argmax])
print "Number of constraints of fc2 from translational invariance:%d" % (
len(ti_transforms) - 1)
CC, transform, independent = gaussian(np.array(ti_transforms), precision)
return independent, transform
def get_trim_fc2(supercell,
trans,
coeff,
ifc_map,
symprec,
precision=1e-5,
pairs_included=None,
is_trim_boundary=False):
unit_atoms = np.unique(supercell.get_supercell_to_unitcell_map())
natom = supercell.get_number_of_atoms()
num_irred = trans.shape[-1]
ti_transforms =[np.zeros(num_irred)]
for i, atom1 in enumerate(unit_atoms):
for atom2 in np.arange(natom):
is_trim = False
if pairs_included is not None and not pairs_included[ifc_map[atom1, atom2]]:
is_trim = True
if is_trim_boundary:
dist = get_equivalent_smallest_vectors(atom2, atom1, supercell, supercell.get_cell(), symprec=symprec)
if len(dist) > 1:
is_trim = True
if is_trim:
irred_doublet = ifc_map[atom1, atom2]
ti_transform = np.dot(coeff[atom1, atom2], trans[irred_doublet])
for k in range(9):
if not (np.abs(ti_transform[k])< precision).all():
argmax = np.argmax(np.abs(ti_transform[k]))
ti_transform[k] /= ti_transform[k, argmax]
is_exist = np.all(np.abs(ti_transform[k] - np.array(ti_transforms)) < precision, axis=1)
if (is_exist == False).all():
ti_transforms.append(ti_transform[k] / ti_transform[k, argmax])
print "Number of constraints of fc2 from a cutoff of interaction distance:%d"%len(ti_transforms)
CC, transform, independent = gaussian(np.array(ti_transforms), precision)
return independent, transform
def get_trim_fc2(supercell,
trans,
coeff,
ifc_map,
symprec,
precision=1e-5,
pairs_included=None,
is_trim_boundary=False):
unit_atoms = np.unique(supercell.get_supercell_to_unitcell_map())
natom = supercell.get_number_of_atoms()
num_irred = trans.shape[-1]
ti_transforms = [np.zeros(num_irred)]
for i, atom1 in enumerate(unit_atoms):
for atom2 in np.arange(natom):
is_trim = False
if pairs_included is not None and not pairs_included[ifc_map[
atom1, atom2]]:
is_trim = True
if is_trim_boundary:
dist = get_equivalent_smallest_vectors(atom2,
atom1,
supercell,
supercell.get_cell(),
symprec=symprec)
if len(dist) > 1:
is_trim = True
if is_trim:
irred_doublet = ifc_map[atom1, atom2]
ti_transform = np.dot(coeff[atom1, atom2],
trans[irred_doublet])
for k in range(9):
if not (np.abs(ti_transform[k]) < precision).all():
argmax = np.argmax(np.abs(ti_transform[k]))
ti_transform[k] /= ti_transform[k, argmax]
is_exist = np.all(
np.abs(ti_transform[k] - np.array(ti_transforms)) <
precision,
axis=1)
if (is_exist == False).all():
ti_transforms.append(ti_transform[k] /
ti_transform[k, argmax])
print "Number of constraints of fc2 from a cutoff of interaction distance:%d" % len(
ti_transforms)
CC, transform, independent = gaussian(np.array(ti_transforms), precision)
return independent, transform
def get_fc2_translational_invariance(supercell, trans, coeff, ifc_map, precision=1e-6):
natom = supercell.get_number_of_atoms()
unit_atoms = np.unique(supercell.get_supercell_to_unitcell_map())
num_irred = trans.shape[-1]
ti_transforms =[np.zeros(num_irred)]
for i, atom1 in enumerate(unit_atoms):
ti_transform = np.zeros((9, num_irred))
for atom2 in np.arange(natom):
irred_doublet = ifc_map[atom1, atom2]
ti_transform += np.dot(coeff[atom1, atom2], trans[irred_doublet])
for k in range(9):
if not (np.abs(ti_transform[k])< precision).all():
# ti_transform_row = ti_transform[k] / np.abs(ti_transform[k]).max()
# ti_transforms.append(ti_transform_row)
argmax = np.argmax(np.abs(ti_transform[k]))
ti_transform[k] /= ti_transform[k, argmax]
is_exist = np.all(np.abs(ti_transform[k] - np.array(ti_transforms)) < precision, axis=1)
if (is_exist == False).all():
ti_transforms.append(ti_transform[k] / ti_transform[k, argmax])
print "Number of constraints of fc2 from translational invariance:%d"% (len(ti_transforms) - 1)
CC, transform, independent = gaussian(np.array(ti_transforms), precision)
return independent, transform
def get_fc2_rotational_invariance(supercell,
trans,
coeff,
ifc_map,
symprec,
precision=1e-8,
is_Huang=True): #Gazis-Wallis invariance
positions = supercell.get_scaled_positions()
unit_atoms = np.unique(supercell.get_supercell_to_unitcell_map())
natom = supercell.get_number_of_atoms()
num_irred2 = trans.shape[-1]
lattice = supercell.get_cell()
eijk = np.zeros((3,3,3), dtype="intc")
eijk[0,1,2] = eijk[1,2,0] = eijk[2,0,1] = 1
eijk[0,2,1] = eijk[2,1,0] = eijk[1,0,2] = -1 # epsion matrix, which is an antisymmetric 3 * 3 * 3 tensor
torques =[np.zeros(num_irred2)]
for i, patom_num in enumerate(unit_atoms):
force = np.zeros((27, num_irred2), dtype='double')
for j in range(natom):
fc_temp = np.dot(coeff[patom_num, j], trans[ifc_map[patom_num, j]]).reshape(3,3,-1)
vectors = get_equivalent_smallest_vectors(j,
patom_num,
supercell,
lattice,
symprec)
r_frac = np.array(vectors).sum(axis=0) / len(vectors)
r = np.dot(r_frac, lattice)
force_tmp = np.einsum('abN, c->abcN', fc_temp, r) - np.einsum('acN, b->abcN', fc_temp, r)
force += force_tmp.reshape(27, -1)
for k in range(27):
if not (np.abs(force[k])< precision).all():
argmax = np.argmax(np.abs(force[k]))
force[k] /= force[k, argmax]
is_exist = np.all(np.abs(force[k] - np.array(torques)) < precision, axis=1)
if (is_exist == False).all():
torques.append(force[k] / force[k, argmax])
print "Number of constraints of fc2 from rotational invariance:%d"%(len(torques)-1)
CC, transform, independent = gaussian(np.array(torques), precision)
if is_Huang:
precision *= 1e2
print "The Born-Huang invariance condition is also included in rotational symmetry"
trans2 = mat_dot_product(trans, transform, is_sparse=True)
num_irred2 = trans2.shape[-1]
torques =[np.zeros(num_irred2)]
unit_atoms = np.unique(supercell.get_supercell_to_unitcell_map())
torque_tmp = np.zeros((9, 9, num_irred2), dtype='double')
for patom_num in unit_atoms:
for j in range(natom):
fc_temp = np.dot(coeff[patom_num, j], trans2[ifc_map[patom_num, j]])
vectors12 = get_equivalent_smallest_vectors(j,
patom_num,
supercell,
lattice,
symprec)
for r12 in vectors12:
v12 = np.dot(r12, lattice)
v12_outer = np.kron(v12, v12)
torque_tmp += np.einsum('iN, j->ijN', fc_temp, v12_outer) / len(vectors12)
torque_tmp = torque_tmp - np.swapaxes(torque_tmp, 0, 1)
torque_tmp = torque_tmp.reshape(-1, num_irred2)
for i in range(81):
if not (np.abs(torque_tmp[i])< precision).all():
argmax = np.argmax(np.abs(torque_tmp[i]))
torque_tmp[i] /= torque_tmp[i, argmax]
is_exist = np.all(np.abs(torque_tmp[i] - np.array(torques)) < precision, axis=1)
if (is_exist == False).all():
torques.append(torque_tmp[i] / torque_tmp[i, argmax])
print "Number of constraints of fc2 from Born-Huang invariance condition:%d"%(len(torques)-1)
CC, transform_gw, independent_gw = gaussian(np.array(torques), precision)
independent = np.array([independent[i] for i in independent_gw])
transform = np.dot(transform,transform_gw)
return independent, transform
def get_fc2_spg_invariance(pairs_orig,
positions,
rotations1,
translations1,
mappings1,
rotations2,
num_rotations2,
mappings2,
lattice,
symprec):
indatoms1 = np.unique(mappings1)
doublets_dict = []
for index_pair,pair in enumerate(pairs_orig):
doublet_dict = {}
CC = [np.zeros(9)]
for permute in list(permutations([0,1])):
rot_all = []
atom1, atom2= [pair[i] for i in permute]
if not mappings1[atom1] == pair[0]:
continue
for numope in get_all_operations_at_star(rotations1,
translations1,
positions,
atom1,
mappings1,
symprec):
#get all the symmetry operation that keeps atom1 unchanged
rot1, tran = rotations1[numope], translations1[numope]
atom1_1 = mappings1[atom1]
index1 = np.where(indatoms1 == atom1_1)[0][0] # index of the first irreducible atom
atom2_1 = get_atom_sent_by_operation(atom2, positions, rot1, tran, symprec=symprec)
site_syms = rotations2[index1][:num_rotations2[index1]]
if mappings2[index1, atom2_1] != pair[1]:
continue
for rot2 in get_rotations_at_star(site_syms, positions, atom1_1, atom2_1, mappings2[index1], symprec):
rot = np.dot(rot2, rot1)
isfound = False
for r in rot_all:
if (np.abs(r-rot) < symprec).all():
isfound = True
break
if not isfound:
rot_all.append(rot)
else:
continue
rot_cart = np.double(similarity_transformation(lattice, rot))
seq = "".join(["ik"[i] for i in permute])
PP = np.einsum("ij,kl -> %sjl"%seq, rot_cart, rot_cart).reshape(9, 9).T
BB = PP - np.eye(9)
for i in np.arange(9):
is_found = False
if not (np.abs(BB[i]) < symprec).all():
for j in np.arange(len(CC)):
if (np.abs(BB[i] - CC[j]) < symprec).all():
is_found = True
break
if not is_found:
CC.append(BB[i])
CC, transform, independent = gaussian(np.array(CC))
doublet_dict['independent'] = [ind + index_pair * 9 for ind in independent] # independent ele
doublet_dict['transform'] = transform
doublets_dict.append(doublet_dict)
num_irred = [len(dic['independent']) for dic in doublets_dict]
trans = np.zeros((len(doublets_dict), 9, sum(num_irred)), dtype="float")
for i, doub in enumerate(doublets_dict):
start = sum(num_irred[:i])
length = num_irred[i]
trans[i,:, start:start + length] = doub['transform']
return np.hstack((dic['independent'] for dic in doublets_dict)), trans
def get_fc3_spg_invariance(triplets,
positions,
rotations1,
translations1,
mappings1,
rotations2,
num_rotations2,
mappings2,
rotations3,
num_rotations3,
mappings3,
lattice,
symprec,
is_disperse=False):
"Find all spg symmetries that map the triplet to itself and thus the symmetry would act as constraints"
triplets_dict = []
iatoms1 = np.unique(mappings1)
for itriplet, triplet in enumerate(triplets):
triplet_dict = {}
triplet_dict["triplet"] = triplet
CC = [np.zeros(27)]
for permute in list(permutations(
[0, 1, 2])): # Leave out the original triplet
rot_all = []
atom1, atom2, atom3 = [triplet[i] for i in permute]
if not mappings1[atom1] == triplet[0]:
continue
for numope in get_all_operations_at_star(rotations1, translations1,
positions, atom1,
mappings1, symprec):
#get all the symmetry operations that keep atom1 unchanged
rot1, tran = rotations1[numope], translations1[numope]
atom1_1 = mappings1[atom1]
index1 = np.where(iatoms1 == atom1_1)[0][
0] # index of the first irreducible atom
atom2_1 = get_atom_sent_by_operation(atom2,
positions,
rot1,
tran,
symprec=symprec)
atom3_1 = get_atom_sent_by_operation(atom3,
positions,
rot1,
tran,
symprec=symprec)
site_syms = rotations2[index1, :num_rotations2[index1]]
mapping2 = mappings2[
index1] # now atom1 would be fixed under its site symmetries
iatoms2 = np.unique(mapping2)
if mapping2[atom2_1] != triplet[1]:
continue
for rot2 in get_rotations_at_star(site_syms, positions,
atom1_1, atom2_1, mapping2,
symprec):
#get all the symmetry operations that keep both atom1 and atom2 unchanged
atom2_2 = mapping2[atom2_1]
atom3_2 = get_atom_sent_by_site_sym(
atom3_1, atom1_1, positions, rot2,
symprec=symprec) #no matter atom1_1 or atom2_1
index2 = np.where(iatoms2 == atom2_2)[0][
0] # index of the second irreducible atom
site_syms3 = rotations3[index1,
index2, :num_rotations3[index1,
index2]]
mapping3 = mappings3[index1, index2]
if not mapping3[atom3_2] == triplet[2]:
continue
for rot3 in get_rotations_at_star(site_syms3, positions,
atom2_2, atom3_2,
mapping3, symprec):
rot = np.dot(rot3, np.dot(rot2, rot1))
isfound = False
for r in rot_all:
if (np.abs(r - rot) < symprec).all():
isfound = True
break
if not isfound:
rot_all.append(rot)
else:
continue
# rot_cart = np.double(similarity_transformation(lattice, rot))
# seq = "".join(["ikm"[i] for i in permute])
# PP = np.einsum("ij,kl,mn -> %sjln"%seq, rot_cart, rot_cart, rot_cart).reshape(27, 27).T
rot_cart = np.double(
similarity_transformation(lattice, rot)).T
seq = "".join([
'ikm'[permute.index(i)] for i in range(3)
]) # find the original index before permutation
PP = np.einsum("ij,kl,mn -> %sjln" % seq, rot_cart,
rot_cart, rot_cart).reshape(27, 27)
BB = PP - np.eye(27)
for i in np.arange(27):
is_found = False
if not (np.abs(BB[i]) < symprec).all():
row = BB[i] / np.abs(BB[i]).max()
for j in np.arange(len(CC)):
if (np.abs(row - CC[j]) < symprec).all():
is_found = True
break
if not is_found:
CC.append(row)
DD = np.array(CC, dtype='double')
CC, transform, independent = gaussian(DD)
triplet_dict['independent'] = [
ind + itriplet * 27 for ind in independent
] # independent ele
triplet_dict['transform'] = transform
triplets_dict.append(triplet_dict)
num_irred = [len(dic['independent']) for dic in triplets_dict]
ind_elements = np.hstack((dic['independent'] for dic in triplets_dict))
if is_disperse:
from scipy.sparse import coo_matrix
trans = []
for i, trip in enumerate(triplets_dict):
start = sum(num_irred[:i])
length = num_irred[i]
transform_tmp = np.zeros((27, sum(num_irred)), dtype="float")
transform_tmp[:, start:start + length] = trip['transform']
non_zero = np.where(np.abs(transform_tmp) > symprec)
transform_tmp_sparse = coo_matrix(
(transform_tmp[non_zero], non_zero), shape=transform_tmp.shape)
trans.append(transform_tmp_sparse)
else:
trans = np.zeros((len(triplets_dict), 27, sum(num_irred)),
dtype="float")
for i, trip in enumerate(triplets_dict):
start = sum(num_irred[:i])
length = num_irred[i]
trans[i, :, start:start + length] = trip['transform']
return ind_elements, trans
def get_fc2_rotational_invariance(supercell,
trans,
coeff,
ifc_map,
symprec,
precision=1e-8,
is_Huang=True): #Gazis-Wallis invariance
positions = supercell.get_scaled_positions()
unit_atoms = np.unique(supercell.get_supercell_to_unitcell_map())
natom = supercell.get_number_of_atoms()
num_irred2 = trans.shape[-1]
lattice = supercell.get_cell()
eijk = np.zeros((3, 3, 3), dtype="intc")
eijk[0, 1, 2] = eijk[1, 2, 0] = eijk[2, 0, 1] = 1
eijk[0, 2, 1] = eijk[2, 1, 0] = eijk[
1, 0,
2] = -1 # epsion matrix, which is an antisymmetric 3 * 3 * 3 tensor
torques = [np.zeros(num_irred2)]
for i, patom_num in enumerate(unit_atoms):
force = np.zeros((27, num_irred2), dtype='double')
for j in range(natom):
fc_temp = np.dot(coeff[patom_num, j],
trans[ifc_map[patom_num, j]]).reshape(3, 3, -1)
vectors = get_equivalent_smallest_vectors(j, patom_num, supercell,
lattice, symprec)
r_frac = np.array(vectors).sum(axis=0) / len(vectors)
r = np.dot(r_frac, lattice)
force_tmp = np.einsum('abN, c->abcN', fc_temp, r) - np.einsum(
'acN, b->abcN', fc_temp, r)
force += force_tmp.reshape(27, -1)
for k in range(27):
if not (np.abs(force[k]) < precision).all():
argmax = np.argmax(np.abs(force[k]))
force[k] /= force[k, argmax]
is_exist = np.all(
np.abs(force[k] - np.array(torques)) < precision, axis=1)
if (is_exist == False).all():
torques.append(force[k] / force[k, argmax])
print "Number of constraints of fc2 from rotational invariance:%d" % (
len(torques) - 1)
CC, transform, independent = gaussian(np.array(torques), precision)
if is_Huang:
precision *= 1e2
print "The Born-Huang invariance condition is also included in rotational symmetry"
trans2 = mat_dot_product(trans, transform, is_sparse=True)
num_irred2 = trans2.shape[-1]
torques = [np.zeros(num_irred2)]
unit_atoms = np.unique(supercell.get_supercell_to_unitcell_map())
torque_tmp = np.zeros((9, 9, num_irred2), dtype='double')
for patom_num in unit_atoms:
for j in range(natom):
fc_temp = np.dot(coeff[patom_num, j], trans2[ifc_map[patom_num,
j]])
vectors12 = get_equivalent_smallest_vectors(
j, patom_num, supercell, lattice, symprec)
for r12 in vectors12:
v12 = np.dot(r12, lattice)
v12_outer = np.kron(v12, v12)
torque_tmp += np.einsum('iN, j->ijN', fc_temp,
v12_outer) / len(vectors12)
torque_tmp = torque_tmp - np.swapaxes(torque_tmp, 0, 1)
torque_tmp = torque_tmp.reshape(-1, num_irred2)
for i in range(81):
if not (np.abs(torque_tmp[i]) < precision).all():
argmax = np.argmax(np.abs(torque_tmp[i]))
torque_tmp[i] /= torque_tmp[i, argmax]
is_exist = np.all(
np.abs(torque_tmp[i] - np.array(torques)) < precision,
axis=1)
if (is_exist == False).all():
torques.append(torque_tmp[i] / torque_tmp[i, argmax])
print "Number of constraints of fc2 from Born-Huang invariance condition:%d" % (
len(torques) - 1)
CC, transform_gw, independent_gw = gaussian(np.array(torques),
precision)
independent = np.array([independent[i] for i in independent_gw])
transform = np.dot(transform, transform_gw)
return independent, transform
def get_fc2_spg_invariance(pairs_orig, positions, rotations1, translations1,
mappings1, rotations2, num_rotations2, mappings2,
lattice, symprec):
indatoms1 = np.unique(mappings1)
doublets_dict = []
for index_pair, pair in enumerate(pairs_orig):
doublet_dict = {}
CC = [np.zeros(9)]
for permute in list(permutations([0, 1])):
rot_all = []
atom1, atom2 = [pair[i] for i in permute]
if not mappings1[atom1] == pair[0]:
continue
for numope in get_all_operations_at_star(rotations1, translations1,
positions, atom1,
mappings1, symprec):
#get all the symmetry operation that keeps atom1 unchanged
rot1, tran = rotations1[numope], translations1[numope]
atom1_1 = mappings1[atom1]
index1 = np.where(indatoms1 == atom1_1)[0][
0] # index of the first irreducible atom
atom2_1 = get_atom_sent_by_operation(atom2,
positions,
rot1,
tran,
symprec=symprec)
site_syms = rotations2[index1][:num_rotations2[index1]]
if mappings2[index1, atom2_1] != pair[1]:
continue
for rot2 in get_rotations_at_star(site_syms, positions,
atom1_1, atom2_1,
mappings2[index1], symprec):
rot = np.dot(rot2, rot1)
isfound = False
for r in rot_all:
if (np.abs(r - rot) < symprec).all():
isfound = True
break
if not isfound:
rot_all.append(rot)
else:
continue
rot_cart = np.double(
similarity_transformation(lattice, rot))
seq = "".join(["ik"[i] for i in permute])
PP = np.einsum("ij,kl -> %sjl" % seq, rot_cart,
rot_cart).reshape(9, 9).T
BB = PP - np.eye(9)
for i in np.arange(9):
is_found = False
if not (np.abs(BB[i]) < symprec).all():
for j in np.arange(len(CC)):
if (np.abs(BB[i] - CC[j]) < symprec).all():
is_found = True
break
if not is_found:
CC.append(BB[i])
CC, transform, independent = gaussian(np.array(CC))
doublet_dict['independent'] = [
ind + index_pair * 9 for ind in independent
] # independent ele
doublet_dict['transform'] = transform
doublets_dict.append(doublet_dict)
num_irred = [len(dic['independent']) for dic in doublets_dict]
trans = np.zeros((len(doublets_dict), 9, sum(num_irred)), dtype="float")
for i, doub in enumerate(doublets_dict):
start = sum(num_irred[:i])
length = num_irred[i]
trans[i, :, start:start + length] = doub['transform']
return np.hstack((dic['independent'] for dic in doublets_dict)), trans
def get_fc3_spg_invariance(triplets,
positions,
rotations1,
translations1,
mappings1,
rotations2,
num_rotations2,
mappings2,
rotations3,
num_rotations3,
mappings3,
lattice,
symprec,
is_disperse=False):
"Find all spg symmetries that map the triplet to itself and thus the symmetry would act as constraints"
triplets_dict = []
iatoms1 = np.unique(mappings1)
for itriplet, triplet in enumerate(triplets):
triplet_dict = {}
triplet_dict["triplet"] = triplet
CC = [np.zeros(27)]
for permute in list(permutations([0,1,2])): # Leave out the original triplet
rot_all = []
atom1, atom2, atom3 = [triplet[i] for i in permute]
if not mappings1[atom1] == triplet[0]:
continue
for numope in get_all_operations_at_star(rotations1,
translations1,
positions,
atom1,
mappings1,
symprec):
#get all the symmetry operations that keep atom1 unchanged
rot1, tran = rotations1[numope], translations1[numope]
atom1_1 = mappings1[atom1]
index1 = np.where(iatoms1 == atom1_1)[0][0] # index of the first irreducible atom
atom2_1 = get_atom_sent_by_operation(atom2, positions, rot1, tran, symprec=symprec)
atom3_1 = get_atom_sent_by_operation(atom3, positions, rot1, tran, symprec=symprec)
site_syms = rotations2[index1, :num_rotations2[index1]]
mapping2 = mappings2[index1] # now atom1 would be fixed under its site symmetries
iatoms2 = np.unique(mapping2)
if mapping2[atom2_1] != triplet[1]:
continue
for rot2 in get_rotations_at_star(site_syms, positions, atom1_1, atom2_1, mapping2, symprec):
#get all the symmetry operations that keep both atom1 and atom2 unchanged
atom2_2 = mapping2[atom2_1]
atom3_2 = get_atom_sent_by_site_sym(atom3_1, atom1_1, positions, rot2, symprec=symprec) #no matter atom1_1 or atom2_1
index2 = np.where(iatoms2 == atom2_2)[0][0]# index of the second irreducible atom
site_syms3 = rotations3[index1, index2, :num_rotations3[index1, index2]]
mapping3 = mappings3[index1, index2]
if not mapping3[atom3_2] == triplet[2]:
continue
for rot3 in get_rotations_at_star(site_syms3, positions, atom2_2, atom3_2, mapping3, symprec):
rot = np.dot(rot3, np.dot(rot2, rot1))
isfound = False
for r in rot_all:
if (np.abs(r-rot) < symprec).all():
isfound = True
break
if not isfound:
rot_all.append(rot)
else:
continue
# rot_cart = np.double(similarity_transformation(lattice, rot))
# seq = "".join(["ikm"[i] for i in permute])
# PP = np.einsum("ij,kl,mn -> %sjln"%seq, rot_cart, rot_cart, rot_cart).reshape(27, 27).T
rot_cart = np.double(similarity_transformation(lattice, rot)).T
seq = "".join(['ikm'[permute.index(i)] for i in range(3)]) # find the original index before permutation
PP = np.einsum("ij,kl,mn -> %sjln"%seq, rot_cart, rot_cart, rot_cart).reshape(27, 27)
BB = PP - np.eye(27)
for i in np.arange(27):
is_found = False
if not (np.abs(BB[i]) < symprec).all():
row = BB[i] / np.abs(BB[i]).max()
for j in np.arange(len(CC)):
if (np.abs(row - CC[j]) < symprec).all():
is_found = True
break
if not is_found:
CC.append(row)
DD = np.array(CC, dtype='double')
CC, transform, independent = gaussian(DD)
triplet_dict['independent'] = [ind + itriplet * 27 for ind in independent] # independent ele
triplet_dict['transform'] = transform
triplets_dict.append(triplet_dict)
num_irred = [len(dic['independent']) for dic in triplets_dict]
ind_elements = np.hstack((dic['independent'] for dic in triplets_dict))
if is_disperse:
from scipy.sparse import coo_matrix
trans = []
for i, trip in enumerate(triplets_dict):
start = sum(num_irred[:i])
length = num_irred[i]
transform_tmp = np.zeros((27, sum(num_irred)), dtype="float")
transform_tmp[:, start:start + length] = trip['transform']
non_zero = np.where(np.abs(transform_tmp) > symprec)
transform_tmp_sparse = coo_matrix((transform_tmp[non_zero], non_zero), shape=transform_tmp.shape)
trans.append(transform_tmp_sparse)
else:
trans = np.zeros((len(triplets_dict), 27, sum(num_irred)), dtype="float")
for i, trip in enumerate(triplets_dict):
start = sum(num_irred[:i])
length = num_irred[i]
trans[i,:, start:start + length] = trip['transform']
return ind_elements, trans