def subgroup(self, H=None, eps=0.05, idx=None, once=False):
"""
generate a structure with lower symmetry
Args:
H: space group number (int)
eps: pertubation term (float)
idx: list
once: generate only one structure, otherwise output all
Returns:
a list of pyxtal structures with lower symmetries
"""
#randomly choose a subgroup from the available list
Hs = self.group.get_max_t_subgroup()['subgroup']
if idx is None:
idx = range(len(Hs))
else:
for id in idx:
if id >= len(Hs):
raise ValueError(
"The idx exceeds the number of possible splits")
if H is not None:
idx = [id for id in idx if Hs[idx] == H]
if len(idx) == 0:
raise ValueError("The space group H is incompatible with idx")
sites = [
str(site.wp.multiplicity) + site.wp.letter
for site in self.atom_sites
]
valid_splitters = []
bad_splitters = []
for id in idx:
splitter = wyckoff_split(G=self.group.number, wp1=sites, idx=id)
if splitter.valid_split:
valid_splitters.append(splitter)
else:
bad_splitters.append(splitter)
if len(valid_splitters) == 0:
# do one more step
new_strucs = []
for splitter in bad_splitters:
trail_struc = self.subgroup_by_splitter(splitter)
new_strucs.append(trail_struc.subgroup(once=True))
return new_strucs
else:
if once:
return self.subgroup_by_splitter(choice(valid_splitters),
eps=eps)
else:
new_strucs = []
for splitter in valid_splitters:
new_strucs.append(
self.subgroup_by_splitter(splitter, eps=eps))
return new_strucs
def get_displacement(self, G, split_id, solution, d_tol):
"""
For a given solution, search for the possbile supergroup structure
Args:
G: group object
split_id (int): integer
solution (list): e.g., [['2d'], ['6h'], ['2c', '6h', '12i']]
d_tol (float): tolerance
Returns:
mae: mean absolute atomic displcement
disp: overall cell translation
"""
sites_G = []
elements = []
muls = []
for i, e in enumerate(self.elements):
sites_G.extend(solution[i])
elements.extend([e]*len(solution[i]))
muls.extend([int(sol[:-1]) for sol in solution[i]])
# resort the sites_G by multiplicity
ids = np.argsort(np.array(muls))
elements = [elements[id] for id in ids]
sites_G = [sites_G[id] for id in ids]
#print(G, self.struc.group.number, sites_G)
splitter = wyckoff_split(G, split_id, sites_G, self.group_type, elements)
mappings = find_mapping(self.struc.atom_sites, splitter)
dists = []
disps = []
masks = []
if len(mappings) > 0:
for mapping in mappings:
dist, disp, mask = self.symmetrize_dist(splitter, mapping, None, None, d_tol)
dists.append(dist)
disps.append(disp)
masks.append(mask)
dists = np.array(dists)
mae = np.min(dists)
id = np.argmin(dists)
disp = disps[id]
mask = masks[id]
if 0.2 < mae < d_tol:
# optimize disp further
if mask is None or len(mask)<3:
def fun(disp, mapping, splitter, mask):
return self.symmetrize_dist(splitter, mapping, disp, mask)[0]
res = minimize(fun, disps[id], args=(mappings[id], splitter, mask),
method='Nelder-Mead', options={'maxiter': 10})
if res.fun < mae:
mae = res.fun
disp = res.x
return mae, disp, mappings[id], splitter
else:
print("bug in findding the mappings", solution)
print(splitter.G.number, '->', splitter.H.number)
return 1000, None, None, None
def get_displacement(self, G, split_id, solution, d_tol):
"""
For a given solution, search for the possbile supergroup structure
Args:
G: supergroup number
split_id: integer
solution: e.g., [['2d'], ['6h'], ['2c', '6h', '12i']]
d_tol:
Returns:
mae: mean absolute atomic displcement
disp: overall cell translation
"""
sites_G = []
elements = []
muls = []
for i, e in enumerate(self.elements):
sites_G.extend(solution[i])
elements.extend([e] * len(solution[i]))
muls.extend([int(sol[:-1]) for sol in solution[i]])
# resort the sites_G by multiplicity
ids = np.argsort(np.array(muls))
elements = [elements[id] for id in ids]
sites_G = [sites_G[id] for id in ids]
#print(G, self.struc.group.number, sites_G)
splitter = wyckoff_split(G, split_id, sites_G, self.group_type,
elements)
mappings = self.find_mapping(splitter)
dists = []
disps = []
for mapping in mappings:
#disp = None #np.array([0.0, 0.0, 0.222222])
dist, disp, mask = self.symmetrize_dist(splitter, mapping, None,
None, d_tol)
dists.append(dist)
disps.append(disp)
dists = np.array(dists)
mae = np.min(dists)
id = np.argmin(dists)
disp = disps[id]
if (mae > 0.2) and (mae < d_tol):
# optimize further
def fun(disp, mapping, splitter, mask):
return self.symmetrize_dist(splitter, mapping, disp, mask)[0]
res = minimize(fun,
disps[id],
args=(mappings[id], splitter, mask),
method='Nelder-Mead',
options={'maxiter': 20})
if res.fun < mae:
mae = res.fun
disp = res.x
return mae, disp, mappings[id], splitter
def subgroup(self,
H=None,
eps=0.05,
idx=None,
once=False,
group_type='t',
max_index=4):
"""
generate a structure with lower symmetry
Args:
H: space group number (int)
eps: pertubation term (float)
idx: list
once: generate only one structure, otherwise output all
Returns:
a list of pyxtal structures with lower symmetries
"""
#randomly choose a subgroup from the available list
if group_type == 't':
dicts = self.group.get_max_t_subgroup() #['subgroup']
else:
dicts = self.group.get_max_k_subgroup() #['subgroup']
Hs = dicts['subgroup']
indices = dicts['index']
if idx is None:
idx = [i for i, id in enumerate(indices) if id <= max_index]
#idx = range(len(Hs))
else:
for id in idx:
if id >= len(Hs):
raise ValueError(
"The idx exceeds the number of possible splits")
if H is not None:
idx = [id for id in idx if Hs[id] == H]
if len(idx) == 0:
raise RuntimeError("No subgroup to perform the split")
if self.molecular:
struc_sites = self.mol_sites
else:
struc_sites = self.atom_sites
sites = [
str(site.wp.multiplicity) + site.wp.letter for site in struc_sites
]
valid_splitters = []
bad_splitters = []
for id in idx:
splitter = wyckoff_split(G=self.group.number,
wp1=sites,
idx=id,
group_type=group_type)
if splitter.valid_split:
valid_splitters.append(splitter)
else:
bad_splitters.append(splitter)
if len(valid_splitters) == 0:
# do one more step
new_strucs = []
for splitter in bad_splitters:
trail_struc = self.subgroup_by_splitter(splitter)
new_strucs.append(
trail_struc.subgroup(once=True, group_type=group_type))
return new_strucs
else:
if once:
return self.subgroup_by_splitter(choice(valid_splitters),
eps=eps)
else:
new_strucs = []
for splitter in valid_splitters:
new_strucs.append(
self.subgroup_by_splitter(splitter, eps=eps))
return new_strucs
def subgroup_once(self, eps=0.1, H=None, permutations=None, group_type='t', max_cell=4, mut_lat=True):
"""
generate a structure with lower symmetry (for atomic crystals only)
Args:
permutations: e.g., {"Si": "C"}
H: space group number (int)
idx: list
group_type: `t` or `k`
max_cell: maximum cell reconstruction (float)
Returns:
a list of pyxtal structures with lower symmetries
"""
idx, sites, t_types, k_types = self._get_subgroup_ids(H, group_type, None, max_cell)
# Try 100 times to see if a valid split can be found
count = 0
while count < 100:
id = choice(idx)
gtype = (t_types+k_types)[id]
if gtype == 'k':
id -= len(t_types)
#print(self.group.number, sites, id, gtype)
splitter = wyckoff_split(G=self.group.number, wp1=sites, idx=id, group_type=gtype)
if not splitter.error:
if permutations is not None:
if len(splitter.H_orbits) == 1:
if len(splitter.H_orbits[0]) > 1:
return self._apply_substitution(splitter, permutations)
else:
#print("try to find the next subgroup")
trail_struc = self._subgroup_by_splitter(splitter, eps=eps, mut_lat=mut_lat)
multiple = sum(trail_struc.numIons)/sum(self.numIons)
max_cell = max([1, max_cell/multiple])
ans = trail_struc.subgroup_once(eps, H, permutations, group_type, max_cell)
if ans.group.number > 1:
return ans
else:
return self._apply_substitution(splitter, permutations)
else:
if splitter.valid_split:
special = False
if self.molecular:
for i in range(len(self.mol_sites)):
for ops in splitter.H_orbits[i]:
if len(ops) < len(splitter.H[0]):
special = True
break
if not special:
return self._subgroup_by_splitter(splitter, eps=eps, mut_lat=mut_lat)
else:
#print("try to find the next subgroup")
trail_struc = self._subgroup_by_splitter(splitter, eps=eps, mut_lat=mut_lat)
multiple = sum(trail_struc.numIons)/sum(self.numIons)
max_cell = max([1, max_cell/multiple])
ans = trail_struc.subgroup_once(eps, H, None, group_type, max_cell)
if ans.group.number > 1:
return ans
count += 1
raise RuntimeError("Cannot find the splitter")
def subgroup(self, permutations=None, H=None, eps=0.05, idx=None, group_type='t', max_cell=4):
"""
generate a structure with lower symmetry
Args:
permutations: e.g., {"Si": "C"}
H: space group number (int)
eps: pertubation term (float)
idx: list
group_type: `t`, `k` or `t+k`
max_cell: maximum cell reconstruction (float)
Returns:
a list of pyxtal structures with lower symmetries
"""
#randomly choose a subgroup from the available list
idx, sites, t_types, k_types = self._get_subgroup_ids(H, group_type, idx, max_cell)
valid_splitters = []
bad_splitters = []
for id in idx:
gtype = (t_types+k_types)[id]
if gtype == 'k':
id -= len(t_types)
splitter = wyckoff_split(G=self.group.number, wp1=sites, idx=id, group_type=gtype)
if not splitter.error:
if permutations is None:
if splitter.valid_split:
special = False
if self.molecular:
for i in range(len(self.mol_sites)):
for ops in splitter.H_orbits[i]:
if len(ops) < len(splitter.H[0]):
special = True
break
if not special:
valid_splitters.append(splitter)
else:
bad_splitters.append(splitter)
else:
bad_splitters.append(splitter)
else:
# apply permuation
if len(splitter.H_orbits) == 1:
if len(splitter.H_orbits[0]) > 1:
valid_splitters.append(splitter)
else:
bad_splitters.append(splitter)
else:
valid_splitters.append(splitter)
if len(valid_splitters) == 0:
#print("try do one more step")
new_strucs = []
for splitter in bad_splitters:
trail_struc = self._subgroup_by_splitter(splitter, eps=eps)
new_strucs.extend(trail_struc.subgroup(permutations, group_type=group_type))
return new_strucs
else:
#print(len(valid_splitters), "valid_splitters are present")
new_strucs = []
for splitter in valid_splitters:
if permutations is None:
new_struc = self._subgroup_by_splitter(splitter, eps=eps)
else:
new_struc = self._apply_substitution(splitter, permutations)
new_strucs.append(new_struc)
return new_strucs