def __init__(self, cell, symprec=1e-5, is_symmetry=True):
self._cell = cell
self._symprec = symprec
self._symmetry_operations = None
self._international_table = None
self._dataset = None
self._wyckoff_letters = None
self._map_atoms = None
self._atomic_permutations = None
self._pointgroup_operations = None
self._pointgroup = None
self._independent_atoms = None
self._map_operations = None
magmom = cell.magnetic_moments
if type(magmom) is np.ndarray:
if (magmom < symprec).all():
magmom = None
if not is_symmetry:
self._set_nosym()
elif magmom is None:
self._set_symmetry_dataset()
else:
self._set_symmetry_operations_with_magmoms()
(self._pointgroup_operations,
self._reciprocal_operations) = get_pointgroup_operations(
self._symmetry_operations['rotations'])
ptg_symbol = spglib.get_pointgroup(self._pointgroup_operations)[0]
self._pointgroup = ptg_symbol.strip()
self._set_atomic_permutations()
self._set_independent_atoms()
self._map_operations = self._get_map_operations_from_permutations()
def _get_symmetry_yaml(cell, symmetry, phonopy_version=None):
rotations = symmetry.get_symmetry_operations()['rotations']
translations = symmetry.get_symmetry_operations()['translations']
atom_sets = symmetry.get_map_atoms()
independent_atoms = symmetry.get_independent_atoms()
wyckoffs = symmetry.get_Wyckoff_letters()
lines = []
if phonopy_version is not None:
lines.append("phonopy_version: '%s'" % phonopy_version)
if cell.get_magnetic_moments() is None:
spg_symbol, spg_number = symmetry.get_international_table().split()
spg_number = int(spg_number.replace('(', '').replace(')', ''))
lines.append("space_group_type: '%s'" % spg_symbol)
lines.append("space_group_number: %d" % spg_number)
lines.append("point_group_type: '%s'" % symmetry.get_pointgroup())
lines.append("space_group_operations:")
for i, (r, t) in enumerate(zip(rotations, translations)):
lines.append("- rotation: # %d" % (i + 1))
for vec in r:
lines.append(" - [%2d, %2d ,%2d]" % tuple(vec))
line = " translation: ["
for j, x in enumerate(t):
if abs(x - np.rint(x)) < 1e-5:
line += " 0.00000"
else:
line += "%8.5f" % x
if j < 2:
line += ", "
else:
line += " ]"
lines.append(line)
lines.append("atom_mapping:")
for i, atom_num in enumerate(atom_sets):
lines.append(" %d: %d" % (i + 1, atom_num + 1))
lines.append("site_symmetries:")
for i in independent_atoms:
sitesym = symmetry.get_site_symmetry(i)
lines.append("- atom: %d" % (i + 1))
if cell.get_magnetic_moments() is None:
lines.append(" Wyckoff: '%s'" % wyckoffs[i])
site_pointgroup = get_pointgroup(sitesym)
lines.append(" site_point_group: '%s'" % site_pointgroup[0].strip())
lines.append(" orientation:")
for v in site_pointgroup[2]:
lines.append(" - [%2d, %2d, %2d]" % tuple(v))
lines.append(" rotations:")
for j, r in enumerate(sitesym):
lines.append(" - # %d" % (j + 1))
for vec in r:
lines.append(" - [%2d, %2d, %2d]" % tuple(vec))
return "\n".join(lines)
def __init__(self, structure):
"""
Args:
structure: |Structure| object.
"""
# Get spacegroup from spglib if not available from Abinit.
if not structure.has_abi_spacegroup:
structure.spgset_abi_spacegroup(has_timerev=True, overwrite=False)
self._structure = structure
abispg = structure.abi_spacegroup
nsym = len(abispg.symrel)
indsym = self.structure.indsym
#self.eq_atoms = structure.spget_equivalent_atoms()
# Precompute sympy objects used to solve linear system of equations.
self.sp_symrel, self.sp_symrec = [], []
self.sp_tnons, self.sp_inv_symrel = [], []
from abipy.core.symmetries import mati3inv
for symr, symc, tau in zip(abispg.symrel, abispg.symrec, abispg.tnons):
self.sp_symrel.append(sp.Matrix((symr)))
inv_symr = mati3inv(symr, trans=False)
self.sp_inv_symrel.append(sp.Matrix((inv_symr)))
self.sp_symrec.append(sp.Matrix((symc)))
# FIXME: Should convert to rational numbers
# Permissible translations are unit cell translations or fractions thereof
# that are consistent with the rotational symmetry (e.g. 1/2, 1/3, 1/4, and 1/6), plus combinations.
tau = np.around(tau, decimals=5)
self.sp_tnons.append(sp.Matrix(tau))
#from abipy.core.symmetries import indsym_from_symrel
#other_indsym = indsym_from_symrel(abispg.symrel, abispg.tnons, self.structure, tolsym=1e-8)
#assert np.all(self.structure.indsym == other_indsym)
# Compute symmetry operations in Cartesian coordinates (numpy arrays)
a = self.structure.lattice.matrix.T
self.symcart = np.matmul(a, np.matmul(abispg.symrel, np.linalg.inv(a)))
import spglib
self.sitesym_labels = []
for iatom, site in enumerate(self.structure):
rotations = [
abispg.symrel[isym] for isym in range(nsym)
if indsym[iatom, isym, 3] == iatom and abispg.symafm[isym] == 1
]
# Passing a 0-length rotations list to spglib can segfault.
herm_symbol, ptg_num = "1", 1
if len(rotations) != 0:
herm_symbol, ptg_num, trans_mat = spglib.get_pointgroup(
rotations)
self.sitesym_labels.append(
"%s (#%d,nsym:%d)" %
(herm_symbol.strip(), ptg_num, len(rotations)))
def __init__(self, rotations):
self._ops = [LatticeRotation(rot) for rot in rotations]
# Call spglib to get the Herm symbol.
# Remove blanks from C string.
herm_symbol, ptg_num, trans_mat = spglib.get_pointgroup(rotations)
self.herm_symbol = herm_symbol.strip()
#print(self.herm_symbol, ptg_num, trans_mat)
if self.sch_symbol is None:
raise ValueError("Cannot detect point group symbol! Got sch_symbol = %s" % self.sch_symbol)
def get_point_group(self):
"""
Get the point group associated with the structure.
Returns:
(Pointgroup): Point group for structure.
"""
rotations = self._spacegroup_data["rotations"]
# passing a 0-length rotations list to spglib can segfault
if len(rotations) == 0:
return '1'
return spglib.get_pointgroup(rotations)[0].strip()
def get_point_group(self):
"""
Get the point group associated with the structure.
Returns:
(Pointgroup): Point group for structure.
"""
rotations = self._spacegroup_data["rotations"]
# passing a 0-length rotations list to spglib can segfault
if len(rotations) == 0:
return '1'
return spglib.get_pointgroup(rotations)[0].strip()
def spginfo(self):
cell = (self.a, self.frac, self.charges)
print("[get_spacegroup]")
print(" Spacegroup of cell is %s" % spg.get_spacegroup(cell))
print("[get_symmetry]")
print(" Symmetry operations of unitcell are")
symmetry = spg.get_symmetry(cell)
show_symmetry(symmetry)
print("[get_pointgroup]")
print(" Pointgroup of cell is %s" %
spg.get_pointgroup(symmetry['rotations'])[0])
dataset = spg.get_symmetry_dataset(cell)
print("[get_symmetry_dataset] ['international']")
print(" Spacegroup of cell is %s (%d)" %
(dataset['international'], dataset['number']))
print("[get_symmetry_dataset] ['pointgroup']")
print(" Pointgroup of cell is %s" % (dataset['pointgroup']))
print("[get_symmetry_dataset] ['hall']")
print(" Hall symbol of cell is %s (%d)." %
(dataset['hall'], dataset['hall_number']))
print("[get_symmetry_dataset] ['wyckoffs']")
alphabet = "abcdefghijklmnopqrstuvwxyz"
print(" Wyckoff letters of cell are ", dataset['wyckoffs'])
print("[get_symmetry_dataset] ['equivalent_atoms']")
print(" Mapping to equivalent atoms of cell ")
for i, x in enumerate(dataset['equivalent_atoms']):
print(" %d -> %d" % (i + 1, x + 1))
print("[get_symmetry_dataset] ['rotations'], ['translations']")
print(" Symmetry operations of unitcell are:")
for i, (rot, trans) in enumerate(
zip(dataset['rotations'], dataset['translations'])):
print(" --------------- %4d ---------------" % (i + 1))
print(" rotation:")
for x in rot:
print(" [%2d %2d %2d]" % (x[0], x[1], x[2]))
print(" translation:")
print(" (%8.5f %8.5f %8.5f)" % (trans[0], trans[1], trans[2]))
reduced_lattice = spg.niggli_reduce(self.a)
print("[niggli_reduce]")
print(" Original lattice")
show_lattice(self.a)
print(" Reduced lattice")
show_lattice(reduced_lattice)
mapping, grid = spg.get_ir_reciprocal_mesh([11, 11, 11],
cell,
is_shift=[0, 0, 0])
num_ir_kpt = len(numpy.unique(mapping))
print("[get_ir_reciprocal_mesh]")
print(" Number of irreducible k-points of primitive")
print(" 11x11x11 Monkhorst-Pack mesh is %d " % num_ir_kpt)
return self
def get_point_group(atoms, tol=1e-8):
"""Return the point group operations of a systems."""
rotations, translations = get_symmetry(atoms, tol=tol)
point_group = spglib.get_pointgroup(rotations)[0].strip()
laue = [
'-1', '2/m', 'mmm', '4/m', '4/mmm', '-3', '-3m', '6/m', '6/mmm', 'm-3',
'm-3m'
]
is_laue = point_group in laue
return point_group, is_laue
def __init__(self, rotations):
rotations = np.reshape(rotations, (-1, 3, 3))
self._ops = [LatticeRotation(rot) for rot in rotations]
# Call spglib to get the Herm symbol.
# (symbol, pointgroup_number, transformation_matrix)
herm_symbol, ptg_num, trans_mat = spglib.get_pointgroup(rotations)
# Remove blanks from C string.
self.herm_symbol = herm_symbol.strip()
#print(self.herm_symbol, ptg_num, trans_mat)
if self.sch_symbol is None:
raise ValueError("Cannot detect point group symbol! Got sch_symbol = %s" % self.sch_symbol)
def __init__(self, rotations):
self._ops = [LatticeRotation(rot) for rot in rotations]
# Call spglib to get the Herm symbol.
# Remove blanks from C string.
import spglib
herm_symbol, ptg_num, trans_mat = spglib.get_pointgroup(rotations)
self.herm_symbol = herm_symbol.strip()
#print(self.herm_symbol, ptg_num, trans_mat)
if self.sch_symbol is None:
raise ValueError(
"Cannot detect point group symbol! Got sch_symbol = %s" %
self.sch_symbol)
def _set_grid_matrix_by_input_cell(self, input_cell, length):
"""Grid generating matrix based on input cell."""
pointgroup = get_pointgroup(self._sym_dataset["rotations"])
# tmat: From input lattice to point group preserving lattice
tmat = pointgroup[2]
lattice = np.dot(input_cell.cell.T, tmat).T
num_cells = np.prod(length2mesh(length, lattice))
self._mesh_numbers = estimate_supercell_matrix_from_pointgroup(
pointgroup[1], lattice, num_cells)
# transpose in reciprocal space
self._grid_matrix = np.array(np.multiply(tmat, self._mesh_numbers).T,
dtype="int_",
order="C")
self._transformation_matrix = np.eye(3, dtype="double", order="C")
def test_standardize_cell_and_pointgroup(self):
for fname, spgnum in zip(self._filenames, self._spgnum_ref):
cell = read_vasp(fname)
if 'distorted' in fname:
symprec = 1e-1
else:
symprec = 1e-5
std_cell = standardize_cell(cell,
to_primitive=False,
no_idealize=True,
symprec=symprec)
dataset = get_symmetry_dataset(std_cell, symprec=symprec)
self.assertEqual(dataset['number'], spgnum, msg=("%s" % fname))
# The test for point group has to be done after standarization.
ptg_symbol, _, _ = get_pointgroup(dataset['rotations'])
self.assertEqual(dataset['pointgroup'],
ptg_symbol,
msg=("%s" % fname))
def test_standardize_cell_and_pointgroup(self):
for fname, spgnum in zip(self._filenames, self._spgnum_ref):
cell = read_vasp(fname)
if 'distorted' in fname:
symprec = 1e-1
else:
symprec = 1e-5
std_cell = standardize_cell(cell,
to_primitive=False,
no_idealize=True,
symprec=symprec)
dataset = get_symmetry_dataset(std_cell, symprec=symprec)
self.assertEqual(dataset['number'], spgnum,
msg=("%s" % fname))
# The test for point group has to be done after standarization.
ptg_symbol, _, _ = get_pointgroup(dataset['rotations'])
self.assertEqual(dataset['pointgroup'],
ptg_symbol,
msg=("%s" % fname))
def get_pointgroup(structure):
"""
Get the point group of the crystal structure.
Args:
structure: :class:`simulation.Structure` object with the crystal structure.
Returns:
List of point group symbol, point group number, and the
transformation matrix.
None if `spglib` fails to determine symmetry.
Raises:
ImportError: If `spglib` cannot be imported.
"""
_check_spglib_install()
data = get_structure_symmetry(structure)
if data is None:
return None
else:
return spglib.get_pointgroup(data['rotations'])
def get_pointgroup(self):
ro = self.get_symmetry_operations()['rotations']
if len(ro) == 0:
return '1'
return spglib.get_pointgroup(ro)[0]
print
print "[get_spacegroup]"
print " Spacegroup of Rutile is ", spglib.get_spacegroup(rutile)
print
print "[get_spacegroup]"
print " Spacegroup of MgB2 is ", spglib.get_spacegroup(MgB2)
print
print "[get_symmetry]"
print " Symmetry operations of Rutile unitcell are:"
print
symmetry = spglib.get_symmetry(rutile)
show_symmetry(symmetry)
print
print "[get_pointgroup]"
print " Pointgroup of Rutile is", spglib.get_pointgroup(
symmetry['rotations'])[0]
print
dataset = spglib.get_symmetry_dataset(rutile)
print "[get_symmetry_dataset] ['international']"
print " Spacegroup of Rutile is %s (%d) " % (dataset['international'],
dataset['number'])
print
print "[get_symmetry_dataset] ['pointgroup']"
print " Pointgroup of Rutile is %s (%d)" % (dataset['pointgroup'],
dataset['pointgroup_number'])
print
print "[get_symmetry_dataset] ['hall']"
print " Hall symbol of Rutile is %s (%d)" % (dataset['hall'],
dataset['hall_number'])
print
print('')
print("[get_symmetry]")
print(" Symmetry operations of Rutile unitcell are:")
print('')
symmetry = spglib.get_symmetry(rutile)
show_symmetry(symmetry)
print('')
print("[get_symmetry]")
print(" Symmetry operations of MgB2 are:")
print('')
symmetry = spglib.get_symmetry(MgB2)
show_symmetry(symmetry)
print('')
print("[get_pointgroup]")
print(" Pointgroup of Rutile is %s." %
spglib.get_pointgroup(symmetry['rotations'])[0])
print('')
dataset = spglib.get_symmetry_dataset( rutile )
print("[get_symmetry_dataset] ['international']")
print(" Spacegroup of Rutile is %s (%d)." % (dataset['international'],
dataset['number']))
print('')
print("[get_symmetry_dataset] ['pointgroup']")
print(" Pointgroup of Rutile is %s." % (dataset['pointgroup']))
print('')
print("[get_symmetry_dataset] ['hall']")
print(" Hall symbol of Rutile is %s (%d)." % (dataset['hall'],
dataset['hall_number']))
print('')
print '========================================================='
def get_rot_trans(myposwan):
Amat = myposwan.Amat
natom_pos = myposwan.natom_pos
atoms_frac = myposwan.atoms_frac
atoms_symbol= myposwan.atoms_symbol
natom_wan = myposwan.natom_wan
atom_num = myposwan.atom_num
crystal_ase = Atoms(symbols=atoms_symbol,cell=Amat.T, scaled_positions=atoms_frac.T,pbc=True)
symmetry = spglib.get_symmetry(crystal_ase)
ptgrp = spglib.get_pointgroup(symmetry['rotations'])
nsymm = symmetry['rotations'].shape[0]
rotmat = symmetry['rotations']
rottrn = symmetry['translations']
rmat0 = np.array(rotmat[0], dtype = np.float64)
# get the number of ptrans
nptrans = 0
for i in range(nsymm):
rmati = np.array(rotmat[i], dtype = np.float64)
diff = abs(rmati-rmat0).sum()
#print "i ", i+1, "diff", diff
if diff < 1.0E-9: nptrans = nptrans + 1
# get the number of distinct rotaions
nrot = nsymm/nptrans
print "--------------abstrac of symmetry------------------"
print("Spacegroup of this cell is %s." % spglib.get_spacegroup(crystal_ase))
print('Point group: ',ptgrp[0])
print "number of total symmetry operations: ", nsymm
print "number of distnct rot ", nrot
print "nptrans per rotation", nptrans
print "######### For details, see ./mysymmop.dat ########"
print ""
# check whether rotmat are put as typeI
# still need to be tested.
err="""
Opps, It seems that in spglib, the rotaions_matrix is not put as
----typeI-----
rot1/ptran_11
rot2/ptran_21
...
rotn/ptran_n1
...
...
...
rot1/ptran_1m
rot2/ptran_2m
...
rotn/ptran_nm
If put as above, I want to trans it as in vasp/OUTCAR
----typeII-----
rot1/ptran_11
rot1/ptran_12
...
rot1/ptran_1m
...
...
...
rotn/ptran_n1
rotn/ptran_n2
...
rotn/ptran_nm
"""
for isym in range(nrot):
rmat0 = np.array(rotmat[isym], dtype = np.float64)
diff = 0.0
for iptr in range(nptrans):
numb = isym + iptr*nrot
rmatt = np.array(rotmat[numb], dtype = np.float64)
diff = diff + abs(rmatt-rmat0).sum()
if diff>1.0E-5: print err
if diff>1.0E-5: sys.exit(0)
# To change code less, we use type I and set nptrans=1
nptrans = 1
wann_atom_rotmap=np.zeros((nsymm,nptrans,natom_wan), dtype=np.int32)
symop = []
f = open('mysymmop.dat', 'w')
for isym in range(nsymm):
print>>f, (" --------------- %4d ---------------" % (isym + 1))
rot = symmetry['rotations'][isym]
trans = symmetry['translations'][isym]
print>>f, (" rotation:")
for x in rot:
print>>f, (" %2d %2d %2d " % (x[0], x[1], x[2]))
print>>f, (" translation:")
print>>f, (" %8.5f %8.5f %8.5f " % (trans[0], trans[1], trans[2]))
print>>f, (" rotmap:")
gtrans = trans
ptrans = [np.zeros((3),dtype=np.float64)]
# rot map for POSCAR
rotmap = []
for iatom in range(natom_pos):
atoms_frac_new = np.dot(rotmat[isym],atoms_frac[:,iatom]) + rottrn[isym]
# find equiv loc as in original cell
for jatom in range(natom_pos):
frac_diff = atoms_frac[:,jatom]-atoms_frac_new
# determine the equivalent between two atoms before and after space group operation.
if abs(frac_diff-np.array([round(i) for i in frac_diff],dtype=np.float64)).sum() < 1.0E-3:
print>>f, " ", iatom+1, "->", jatom+1
rotmap.append([iatom+1,jatom+1])
# rot map for wann.in. here
for iatom in range(natom_wan):
target = rotmap[ atom_num[iatom]-1 ][1]
wann_atom_rotmap[isym,0,iatom]=atom_num.index(target)
symop.append((rotmat[isym],gtrans,rotmap,ptrans))
print>>f, "\n"
print>>f, "\n"
print>>f,"rotations as for atoms in wannier projection"
# rot map of atoms in wannier projection
for isymm in range(nsymm):
print >>f, "isymm", isymm+1, "---------"
for iptr in range(nptrans):
print>>f, "trans", 0, gtrans
for ii in range(natom_wan):
print>>f, "OUTCAR atom rot map:", atom_num[ii], "->", symop[isymm][2][atom_num[ii]-1][1], "=====>", "wannier atom rot map:", ii+1, "->", wann_atom_rotmap[isymm,iptr,ii]+1
f.close()
return nsymm, nptrans, symop, wann_atom_rotmap
print
print "[get_spacegroup]"
print " Spacegroup of Rutile is ", spglib.get_spacegroup(rutile)
print
print "[get_spacegroup]"
print " Spacegroup of MgB2 is ", spglib.get_spacegroup(MgB2)
print
print "[get_symmetry]"
print " Symmetry operations of Rutile unitcell are:"
print
symmetry = spglib.get_symmetry( rutile )
show_symmetry(symmetry)
print
print "[get_pointgroup]"
print " Pointgroup of Rutile is", spglib.get_pointgroup(symmetry['rotations'])[0]
print
dataset = spglib.get_symmetry_dataset( rutile )
print "[get_symmetry_dataset] ['international']"
print " Spacegroup of Rutile is %s (%d) " % (dataset['international'],
dataset['number'])
print
print "[get_symmetry_dataset] ['pointgroup']"
print " Pointgroup of Rutile is %s (%d)" % (dataset['pointgroup'],
dataset['pointgroup_number'])
print
print "[get_symmetry_dataset] ['hall']"
print " Hall symbol of Rutile is %s (%d)" % (dataset['hall'],
dataset['hall_number'])
print
print('')
print("[get_symmetry]")
print(" Symmetry operations of Rutile unitcell are:")
print('')
symmetry = spglib.get_symmetry(rutile)
show_symmetry(symmetry)
print('')
print("[get_symmetry]")
print(" Symmetry operations of MgB2 are:")
print('')
symmetry = spglib.get_symmetry(MgB2)
show_symmetry(symmetry)
print('')
print("[get_pointgroup]")
print(" Pointgroup of Rutile is %s." %
spglib.get_pointgroup(symmetry['rotations'])[0])
print('')
dataset = spglib.get_symmetry_dataset( rutile )
print("[get_symmetry_dataset] ['international']")
print(" Spacegroup of Rutile is %s (%d)." % (dataset['international'],
dataset['number']))
print('')
print("[get_symmetry_dataset] ['pointgroup']")
print(" Pointgroup of Rutile is %s." % (dataset['pointgroup']))
print('')
print("[get_symmetry_dataset] ['hall']")
print(" Hall symbol of Rutile is %s (%d)." % (dataset['hall'],
dataset['hall_number']))
print('')
print("[get_symmetry_dataset] ['wyckoffs']")
def get_pointgroup(rotations):
ptg = spglib.get_pointgroup(rotations)
return ptg[0].strip(), ptg[2]
