def GetPrimLattice(latt, pos, num, dictp):
is_prim = None
rot = np.identity(3)
tr = SymTrans(rot, dictp, num, pos, latt)
#print('tr:\n', tr)
if tr is not None:
if len(tr) == 1:
print('Input cell is primitive!')
is_prim = 1 # // primitive cell flag
#print('primitive lattice:\n', latt) # // delaunay of primitive lattice vec
#print('primitive numbers:\n', num)
#print('primitive cell positions:\n', pos) # atom postion
#return latt, num, pos
#// delaunay change part
flag, reduc_b, delauP = delaunay.Delaunay(latt, -1)
if flag:
new_pos = delaunay.ChangeOfBasis(pos, np.linalg.inv(delauP))
print('primitive lattice (delaunay):\n',
reduc_b) # // delaunay of primitive lattice vec
print('primitive cell positions:\n',
[list(i) for i in new_pos]) # atom postion
return reduc_b, num, new_pos, is_prim
else:
print('Input cell is not primitive! Changing...')
is_prim = 0 # // convetional cell flag
ori_tr = [
np.array([1.000000000, 0.0000000000, 0.0000000000]),
np.array([0.000000000, 1.0000000000, 0.0000000000]),
np.array([0.000000000, 0.0000000000, 1.0000000000])
]
#print('original:\n', ori_tr)
prim_vec = tr[1:] + ori_tr # delete the first vec in tr (ori-ori)
print('all primitive translations:\n', prim_vec)
#min_prim_latt = np.zeros((3, 3))
flag3, min_prim_latt = check_volume1(
prim_vec, latt) # // delaunay of primitive lattice vec
if flag3 == 'Found':
#print('final primitive lattice\n', min_prim_latt)
#prim_latt, new_num, new_pos = AtomPosConv2Prim(min_prim_latt, latt, pos, num)
#return prim_latt, new_num, new_pos
#print('new numbers:\n', new_num)
#print('new positions:\n', new_pos)
# // delaunay change part
flag, reduc_b, delaup = delaunay.Delaunay(min_prim_latt, -1)
if flag:
print('primitive lattice (delaunay):\n', reduc_b)
reduc_latt, new_num, new_pos = AtomPosConv2Prim(
reduc_b, latt, pos, num)
print('primitive cell positions:\n',
[list(i) for i in new_pos]) # atom postion
return reduc_latt, new_num, new_pos, is_prim
def GetStandardPos(std_latt, pos, num, trans_matrix, center, is_prim, origin, prim_flag=False):
# Get standard positions
tp_positions = []
positions = []
std_num = []
std_pos = []
if is_prim:
tp1_positions = delaunay.ChangeOfBasis(pos, np.linalg.inv(trans_matrix))
tp = np.zeros(3)
for i in tp1_positions:
tp_positions.append(np.array(i) + origin) # // Xc~ = Q * Xp + Pc
shift = [[0, 0, 0]]
if center == 'A_FACE':
shift.append([0, 0.5, 0.5])
elif center == 'B_FACE':
shift.append([0.5, 0, 0.5])
elif center == 'C_FACE':
shift.append([0.5, 0.5, 0])
elif center == 'BODY':
shift.append([0.5, 0.5, 0.5])
elif center == 'R_CENTER':
shift.append([2. / 3, 1. / 3, 1. / 3])
shift.append([1. / 3, 2. / 3, 2. / 3])
elif center == 'FACE':
shift.append([0, 0.5, 0.5])
shift.append([0.5, 0, 0.5])
shift.append([0.5, 0.5, 0])
# new_pos = np.zeros(3)
for j in range(len(tp_positions)):
for i in range(len(shift)):
new_pos = np.array(tp_positions[j]) + np.array(shift[i])
tp2 = new_pos.copy()
for k in range(3):
if tp2[k] < 0.0:
tp2[k] = int(tp2[k] - 0.5)
else:
tp2[k] = int(tp2[k] + 0.5)
new_pos = new_pos - tp2
for k in range(3):
if new_pos[k] < 0.0:
new_pos[k] += 1.0
positions.append(new_pos) # // Xc = Xc~ + shift vec
# print('cek1', positions)
for j in num:
for i in range(len(shift)):
std_num.append(j)
# adjust positions to list format
for i in positions:
tp = []
for j in i:
tp.append(j)
std_pos.append(tp)
else:
# input is conventional
tp_positions = delaunay.ChangeOfBasis(pos, np.linalg.inv(trans_matrix))
for i in tp_positions:
positions.append(np.array(i) + origin)
# adjust positions to list format
for i in positions:
tp = []
for j in i:
tp.append(j)
std_pos.append(tp)
std_num = num.copy()
# print('cek1', positions)
if is_prim or prim_flag:
print('standard conventional lattice:\n', std_latt)
print('standard conventional numbers:\n', std_num)
print('standard conventional positions:\n', std_pos)
return StandardPrimCell(std_latt, std_pos, std_num, center)
else:
return std_latt, std_num, std_pos
def AtomPosPrim2Conv(prim_latt, latt, pos, num, cel_size):
latt_vol = np.linalg.det(latt)
prim_vol = np.linalg.det(prim_latt)
ratio = latt_vol / prim_vol
print('ratio1:\n', ratio)
#cel_size = len(pos)
ratio = np.around(ratio, decimals=3)
ratio = abs(ratio)
print('ratio2:\n', ratio)
inv_tp_vec = np.linalg.inv(latt)
P = np.transpose(np.dot(prim_latt, inv_tp_vec)) # P, Q is a vertical vec
Q = np.linalg.inv(P)
print('check Q1: ', np.linalg.det(Q))
deterQ = np.around(np.linalg.det(Q), decimals=3)
print('check Q2: ', deterQ)
if abs(
deterQ
) != ratio: # P: big(conv) --> small(prim). so P is no larger than 1, Q is no smaller than 1
print('Error1')
return None, None, None
if (cel_size / ratio) * ratio != cel_size:
print('Error2')
return None, None, None
tp_new_pos = delaunay.ChangeOfBasis(pos, Q)
#print('temp_postion1:\n', tp_new_pos)
new_site = []
tolerance = 0.00001
for i in range(cel_size):
new_site.append(
i
) # // note: maybe index is out of range if it isn't intialized with len(cel_size)
for cnt in range(100):
for i in range(cel_size):
for j in range(cel_size):
if num[i] == num[j]:
if VecIsOverlap(np.array(tp_new_pos[i]),
np.array(tp_new_pos[j]), prim_latt,
tolerance):
if new_site[j] == j:
new_site[
i] = j # // change the equiv to the first showed one
break
#print('new site:\n', new_site)
new_num = []
for i in set(new_site):
new_num.append(num[i]) # // ['Zr', 'O', 'O']
print('check!', new_num)
tp_p = []
for i in new_site:
tp_p.append(
tp_new_pos[i]
) # // atom sites according to the new_site ['Zr', 'O', 'O']
#print('temp_postion2:\n', tp_p)
# // boundary trim
new_posi = []
for i in range(cel_size):
new_posi.append(np.zeros(3))
for i in range(cel_size):
for j in range(3):
if abs(tp_new_pos[i][j] - tp_p[i][j]) > 0.5:
if tp_new_pos[i][j] < tp_p[i][j]:
new_posi[new_site[i]][j] += tp_new_pos[i][j] + 1
else:
new_posi[new_site[i]][j] += tp_new_pos[i][j] - 1
else:
new_posi[new_site[i]][j] = tp_new_pos[i][j]
# // average of the overlapped two atoms
ave_pos = cel_size / len(new_posi)
for j in range(len(new_posi)):
#tp2 = np.zeros(3)
for k in range(3):
new_posi[j][k] = new_posi[j][k] / ave_pos
tp2 = new_posi[j].copy(
) # // Watch out! Don't use "tp2 = new_posi[j]", otherwise they will change at the same time
for k in range(3):
if tp2[k] < 0.0:
tp2[k] = int(tp2[k] - 0.5)
else:
tp2[k] = int(tp2[k] + 0.5)
new_posi[j] = new_posi[j] - tp2
for k in range(3):
if new_posi[j][k] < 0.0:
new_posi[j][k] += 1.0
new_pos = []
for i in set(new_site):
new_pos.append(new_posi[i])
print('new numbers:\n', new_num)
print('new positions:\n', [list(i) for i in new_pos])
return prim_latt, new_num, new_pos
def AtomPosConv2Prim(prim_latt, latt, pos, num):
"""
Conventional lattice changes to primitive lattice
Find correspoing new atomic positions (for primitive)
"""
latt_vol = np.linalg.det(latt)
prim_vol = np.linalg.det(prim_latt)
ratio = latt_vol / prim_vol
cel_size1 = len(pos)
if ratio < 0.0:
ratio = int(ratio - 0.5)
else:
ratio = int(ratio + 0.5)
ratio = abs(ratio)
#print('ratio2:\n', ratio)
inv_tp_vec = np.linalg.inv(latt)
P = np.transpose(np.dot(prim_latt, inv_tp_vec)) # P, Q : vertical vectors
Q = np.linalg.inv(P)
# print('check Q1: ', np.linalg.det(Q))
for i in range(3):
for j in range(3):
if Q[i, j] < 0.0:
Q[i, j] = int(Q[i, j] - 0.5)
else:
Q[i, j] = int(Q[i, j] + 0.5)
# print('check Q2: ', np.linalg.det(Q))
# P: big(conv) --> small(prim)
# P is no larger than 1, but Q is no smaller than 1
if abs(np.linalg.det(Q)) != ratio:
print('Error1')
return None, None, None
if (cel_size1 / ratio) * ratio != cel_size1:
print('Error2')
return None, None, None
tp_new_pos = delaunay.ChangeOfBasis(pos, Q)
#print('temp_postion1:\n', tp_new_pos)
new_site = []
tolerance = 0.00001
# note: index maybe out of range if it isn't initialized with len(cel_size)
for i in range(cel_size1):
new_site.append(i)
for cnt in range(100):
for i in range(cel_size1):
for j in range(cel_size1):
if num[i] == num[j]:
if VecIsOverlap(np.array(tp_new_pos[i]),
np.array(tp_new_pos[j]), prim_latt,
tolerance):
# change the equivalent to the first showed one
if new_site[j] == j:
new_site[i] = j
break
# print('new site:\n', new_site)
new_num = []
for i in sorted(set(new_site)):
new_num.append(num[i]) # test: ['Zr', 'O', 'O']
# print('check!', new_num)
tp_p = []
for i in new_site:
tp_p.append(
tp_new_pos[i]
) # test: atomic sites according to the new_site ['Zr', 'O', 'O']
# boundary trim
new_posi = []
for i in range(cel_size1):
new_posi.append(np.zeros(3))
for i in range(cel_size1):
for j in range(3):
if abs(tp_new_pos[i][j] - tp_p[i][j]) > 0.5:
if tp_new_pos[i][j] < tp_p[i][j]:
new_posi[new_site[i]][j] += tp_new_pos[i][j] + 1
else:
new_posi[new_site[i]][j] += tp_new_pos[i][j] - 1
else:
new_posi[new_site[i]][j] = tp_new_pos[i][j]
# average of the overlapped two atoms
ave_pos = cel_size1 / len(new_posi)
for j in range(len(new_posi)):
#tp2 = np.zeros(3)
for k in range(3):
new_posi[j][k] = new_posi[j][k] / ave_pos
# Note: Don't use "tp2 = new_posi[j]" (change at the same time)
tp2 = new_posi[j].copy()
for k in range(3):
if tp2[k] < 0.0:
tp2[k] = int(tp2[k] - 0.5)
else:
tp2[k] = int(tp2[k] + 0.5)
new_posi[j] = new_posi[j] - tp2
for k in range(3):
if new_posi[j][k] < 0.0:
new_posi[j][k] += 1.0
new_pos = []
for i in sorted(set(new_site)):
new_pos.append(new_posi[i])
print('new numbers:\n', new_num)
print('new positions:\n', [list(i) for i in new_pos])
return prim_latt, new_num, new_pos