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getBCsymmetry.py
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getBCsymmetry.py
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#!/usr/bin/env python3
# -*- coding: UTF-8 -*-
#------------------by Gui-Bin Liu [email protected]
#-------------- 2020-02-07 15:09:47 ---------------
#-------------- 2020-04-13 03:15:00 --------------- fix a problem of np.select in write_poscar
#-------------- 2020-05-14 02:24:00 --------------- add get_BZ_type
import os, sys, argparse, re
import numpy as np
from numpy import sin,cos,tan,sqrt
from numpy.linalg import det
from CifFile import ReadCif
import spglib as spg
atom_label2number={'N/A':0}; atom_number2label={}
i=1
for j in \
( 'H', 'He', 'Li', 'Be', 'B', 'C', 'N', 'O', 'F', 'Ne',
'Na', 'Mg', 'Al', 'Si', 'P', 'S', 'Cl', 'Ar', 'K', 'Ca',
'Sc', 'Ti', 'V', 'Cr', 'Mn', 'Fe', 'Co', 'Ni', 'Cu', 'Zn',
'Ga', 'Ge', 'As', 'Se', 'Br', 'Kr', 'Rb', 'Sr', 'Y', 'Zr',
'Nb', 'Mo', 'Tc', 'Ru', 'Rh', 'Pd', 'Ag', 'Cd', 'In', 'Sn',
'Sb', 'Te', 'I', 'Xe', 'Cs', 'Ba', 'La', 'Ce', 'Pr', 'Nd',
'Pm', 'Sm', 'Eu', 'Gd', 'Tb', 'Dy', 'Ho', 'Er', 'Tm', 'Yb',
'Lu', 'Hf', 'Ta', 'W', 'Re', 'Os', 'Ir', 'Pt', 'Au', 'Hg',
'Tl', 'Pb', 'Bi', 'Po', 'At', 'Rn', 'Fr', 'Ra', 'Ac', 'Th',
'Pa', 'U', 'Np', 'Pu', 'Am', 'Cm', 'Bk', 'Cf', 'Es', 'Fm',
'Md', 'No', 'Lr', 'Rf', 'Db', 'Sg', 'Bh', 'Hs', 'Mt', 'Ds'):
atom_label2number[j]=i
atom_number2label[i]=j; i+=1
atom_label2number['D']=1
JonesHex={}
JonesCub={}
JonesCub['[[1,0,0],[0,1,0],[0,0,1]]']='E'
JonesCub['[[1,0,0],[0,-1,0],[0,0,-1]]']='C2x'
JonesCub['[[-1,0,0],[0,1,0],[0,0,-1]]']='C2y'
JonesCub['[[-1,0,0],[0,-1,0],[0,0,1]]']='C2z'
JonesCub['[[0,0,1],[1,0,0],[0,1,0]]']='C31+'
JonesCub['[[0,0,-1],[1,0,0],[0,-1,0]]']='C32+'
JonesCub['[[0,0,-1],[-1,0,0],[0,1,0]]']='C33+'
JonesCub['[[0,0,1],[-1,0,0],[0,-1,0]]']='C34+'
JonesCub['[[0,1,0],[0,0,1],[1,0,0]]']='C31-'
JonesCub['[[0,1,0],[0,0,-1],[-1,0,0]]']='C32-'
JonesCub['[[0,-1,0],[0,0,1],[-1,0,0]]']='C33-'
JonesCub['[[0,-1,0],[0,0,-1],[1,0,0]]']='C34-'
JonesCub['[[1,0,0],[0,0,-1],[0,1,0]]']='C4x+'
JonesCub['[[0,0,1],[0,1,0],[-1,0,0]]']='C4y+'
JonesCub['[[0,-1,0],[1,0,0],[0,0,1]]']='C4z+'
JonesCub['[[1,0,0],[0,0,1],[0,-1,0]]']='C4x-'
JonesCub['[[0,0,-1],[0,1,0],[1,0,0]]']='C4y-'
JonesCub['[[0,1,0],[-1,0,0],[0,0,1]]']='C4z-'
JonesCub['[[0,1,0],[1,0,0],[0,0,-1]]']='C2a'
JonesCub['[[0,-1,0],[-1,0,0],[0,0,-1]]']='C2b'
JonesCub['[[0,0,1],[0,-1,0],[1,0,0]]']='C2c'
JonesCub['[[-1,0,0],[0,0,1],[0,1,0]]']='C2d'
JonesCub['[[0,0,-1],[0,-1,0],[-1,0,0]]']='C2e'
JonesCub['[[-1,0,0],[0,0,-1],[0,-1,0]]']='C2f'
JonesCub['[[-1,0,0],[0,-1,0],[0,0,-1]]']='I'
JonesCub['[[-1,0,0],[0,1,0],[0,0,1]]']='mx'
JonesCub['[[1,0,0],[0,-1,0],[0,0,1]]']='my'
JonesCub['[[1,0,0],[0,1,0],[0,0,-1]]']='mz'
JonesCub['[[0,0,-1],[-1,0,0],[0,-1,0]]']='S61-'
JonesCub['[[0,0,1],[-1,0,0],[0,1,0]]']='S62-'
JonesCub['[[0,0,1],[1,0,0],[0,-1,0]]']='S63-'
JonesCub['[[0,0,-1],[1,0,0],[0,1,0]]']='S64-'
JonesCub['[[0,-1,0],[0,0,-1],[-1,0,0]]']='S61+'
JonesCub['[[0,-1,0],[0,0,1],[1,0,0]]']='S62+'
JonesCub['[[0,1,0],[0,0,-1],[1,0,0]]']='S63+'
JonesCub['[[0,1,0],[0,0,1],[-1,0,0]]']='S64+'
JonesCub['[[-1,0,0],[0,0,1],[0,-1,0]]']='S4x-'
JonesCub['[[0,0,-1],[0,-1,0],[1,0,0]]']='S4y-'
JonesCub['[[0,1,0],[-1,0,0],[0,0,-1]]']='S4z-'
JonesCub['[[-1,0,0],[0,0,-1],[0,1,0]]']='S4x+'
JonesCub['[[0,0,1],[0,-1,0],[-1,0,0]]']='S4y+'
JonesCub['[[0,-1,0],[1,0,0],[0,0,-1]]']='S4z+'
JonesCub['[[0,-1,0],[-1,0,0],[0,0,1]]']='mda'
JonesCub['[[0,1,0],[1,0,0],[0,0,1]]']='mdb'
JonesCub['[[0,0,-1],[0,1,0],[-1,0,0]]']='mdc'
JonesCub['[[1,0,0],[0,0,-1],[0,-1,0]]']='mdd'
JonesCub['[[0,0,1],[0,1,0],[1,0,0]]']='mde'
JonesCub['[[1,0,0],[0,0,1],[0,1,0]]']='mdf'
JonesHex['[[1,0,0],[0,1,0],[0,0,1]]']='E'
JonesHex['[[1,-1,0],[1,0,0],[0,0,1]]']='C6+'
JonesHex['[[0,-1,0],[1,-1,0],[0,0,1]]']='C3+'
JonesHex['[[-1,0,0],[0,-1,0],[0,0,1]]']='C2'
JonesHex['[[-1,1,0],[-1,0,0],[0,0,1]]']='C3-'
JonesHex['[[0,1,0],[-1,1,0],[0,0,1]]']='C6-'
JonesHex['[[-1,1,0],[0,1,0],[0,0,-1]]']='C21p'
JonesHex['[[1,0,0],[1,-1,0],[0,0,-1]]']='C22p'
JonesHex['[[0,-1,0],[-1,0,0],[0,0,-1]]']='C23p'
JonesHex['[[1,-1,0],[0,-1,0],[0,0,-1]]']='C21pp'
JonesHex['[[-1,0,0],[-1,1,0],[0,0,-1]]']='C22pp'
JonesHex['[[0,1,0],[1,0,0],[0,0,-1]]']='C23pp'
JonesHex['[[-1,0,0],[0,-1,0],[0,0,-1]]']='I'
JonesHex['[[-1,1,0],[-1,0,0],[0,0,-1]]']='S3-'
JonesHex['[[0,1,0],[-1,1,0],[0,0,-1]]']='S6-'
JonesHex['[[1,0,0],[0,1,0],[0,0,-1]]']='mh'
JonesHex['[[1,-1,0],[1,0,0],[0,0,-1]]']='S6+'
JonesHex['[[0,-1,0],[1,-1,0],[0,0,-1]]']='S3+'
JonesHex['[[1,-1,0],[0,-1,0],[0,0,1]]']='md1'
JonesHex['[[-1,0,0],[-1,1,0],[0,0,1]]']='md2'
JonesHex['[[0,1,0],[1,0,0],[0,0,1]]']='md3'
JonesHex['[[-1,1,0],[0,1,0],[0,0,1]]']='mv1'
JonesHex['[[1,0,0],[1,-1,0],[0,0,1]]']='mv2'
JonesHex['[[0,-1,0],[-1,0,0],[0,0,1]]']='mv3'
def getJonesOper(Rmat,spg_num):
if(143<=int(spg_num)<=194): Jones=JonesHex
else: Jones=JonesCub
mat_str=str(np.round(Rmat).astype(int).tolist()).replace(' ','')
if mat_str not in Jones: return 'N/A'
else: return Jones[mat_str]
brav_latt=("TricPrim","MonoPrim","MonoBase","OrthPrim","OrthBase","OrthBody","OrthFace",
"TetrPrim","TetrBody","TrigPrim","HexaPrim","CubiPrim","CubiFace","CubiBody")
def getSGlatt(SGNo):
if(SGNo>230 or SGNo<1): print("Warning: getSGlatt(SGNo) ",SGNo," out of range."); return
BLNo={}
BLNo["TricPrim"]=(1,2)
BLNo["MonoPrim"]=(3,4,6,7,10,11,13,14)
BLNo["MonoBase"]=(5,8,9,12,15)
BLNo["OrthPrim"]=(16,17,18,19,25,26,27,28,29,30,31,32,33,34,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62)
BLNo["OrthBase"]=(20,21,35,36,37,38,39,40,41,63,64,65,66,67,68)
BLNo["OrthBody"]=(23,24,44,45,46,71,72,73,74)
BLNo["OrthFace"]=(22,42,43,69,70)
BLNo["TetrPrim"]=(75,76,77,78,81,83,84,85,86,89,90,91,92,93,94,95,96,99,100,101,102,103,104,105,106,111,112,113,114,\
115,116,117,118,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138)
BLNo["TetrBody"]=(79,80,82,87,88,97,98,107,108,109,110,119,120,121,122,139,140,141,142)
BLNo["TrigPrim"]=(146,148,155,160,161,166,167)
BLNo["HexaPrim"]=(143,144,145,147,149,150,151,152,153,154,156,157,158,159,162,163,164,165,168,169,170,171,172,173,174,\
175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194)
BLNo["CubiPrim"]=(195,198,200,201,205,207,208,212,213,215,218,221,222,223,224)
BLNo["CubiFace"]=(196,202,203,209,210,216,219,225,226,227,228)
BLNo["CubiBody"]=(197,199,204,206,211,214,217,220,229,230)
for brav in BLNo:
if(SGNo in BLNo[brav]): return brav
OrthBase_C2A=np.mat([[0.5,1,-0.5],[-0.5,1,0.5],[0.5,0,0.5]])
'''OrthBase_C2A is the bases transformation matrix from the C-base-centered orthorhombic lattice in Tab.3.1 to the
A-base-centered orthorhombic lattice in the note(v) of Tab.3.1 in the BC book.'''
def Q_and_S_from_spg_to_BC(spgnum, latt=[[]]):
'''The lattice basic vectors which can generate the operations defined in the BC (means Bradley
and Cracknell) Tab.3.7 are named (t1_BC1,t2_BC1,t3_BC1) and (t1_BC2,t2_BC2,t3_BC2) which
corresond to the first line and second line in Tab.3.7 respectively. These BC1 and BC2 basic vectors
are compitable with the ones defined in BC Tab.3.1 but additional rotations may be needed to
give the same form in Tab.3.1.
Transformation matrix (Q) transforms the idealized standard lattice (as',bs',cs') from spglib (also the
same with ITA) to BC2 by (t1_BC2,t2_BC2,t3_BC2)=(as',bs',cs').Q. To result in the same form
in Tab.3.1, say (t1'_BC2,t2'_BC2,t3'_BC2), a rotation S1 is needed, that is
(t1_BC2', t2_BC2', t3_BC2')=S1.(t1_BC2,t2_BC2,t3_BC2)=S1.(as',bs',cs').Q
However, Tab.3.7 uses different orientations in the first line (i.e. BC1) for some spacegroups,
a transformation matrix U is needed to convert BC2 to BC1,
(t1_BC1,t2_BC1,t3_BC1)=(t1_BC2,t2_BC2,t3_BC2).U.
The BC1 basic vectors also maybe need a rotation S to convert it to the Tab.3.1 form
(t1_BC1', t2_BC1', t3_BC1')=S.(t1_BC1,t2_BC1,t3_BC1)=S.(as',bs',cs').Q.U.
If we start with BC2', then (t1_BC2', t2_BC2', t3_BC2').U also need a rotation to the BC1' form
(t1_BC1', t2_BC1', t3_BC1')=S2.(t1_BC2', t2_BC2', t3_BC2').U=S2.S1.(as',bs',cs').Q.U
Then we can combine the to rotations S1 and S2 to form S=S2.S1.
Thus, the rotation matrix S has two origins, S1 and S2. S1 originates from the different lattice
directions between the idealized standard lattice in spglib (the same as ITA) and the one in BC Tab.3.1,
and S2 originates from the different orientions used in Tab.3.7 for some space groups.
In fact, it turns out that if S1!=I3 then S2==I3 and if S2!=I3 then S1==I3, which means either
S1 or S2 takes effect.
This function only gives Q and S. U is given by SG_gen_elem.
Note that all basic vectors in the above equations are COLUMN vectors.
For as',bs',cs' see https://atztogo.github.io/spglib/definition.html#def-idealize-cell
The relations between the basic vectors here and the lattice in get_all_cells are:
(as',bs',cs')=Lsi^T (t1_BC2,t2_BC2,t3_BC2)=LBC2^T (t1_BC1,t2_BC1,t3_BC1)=LBC1^T (t1,t2,t3)=LBC^T
Parameter latt is not used for brav other than "MonoPrim" and "MonoBase", otherwise it should be the idealized
standard lattice from spglib to calculate the angle between as' and cs', which is also the angle gamma between t1 and t2.
'''
cg=sg=0
t=sqrt(3)/2
brav=getSGlatt(spgnum)
if brav in ("MonoPrim","MonoBase"):
# latt is only used in monoclinic system to get the sin and cos of gamma angle
if len(latt)!=3: print("\nError: Parameter latt is needed for monoclinic crystal system!\n"); exit(1)
cg=np.dot(latt[0],latt[2])/sqrt(np.dot(latt[0],latt[0])*np.dot(latt[2],latt[2]))
sg=sqrt(1-cg**2)
QS1={"TricPrim" : ([[1,0,0],[0,1,0],[0,0,1]],[[1,0,0],[0,1,0],[0,0,1]]),
"MonoPrim" : ([[0,1,0],[0,0,1],[1,0,0]],[[sg,0,-cg],[-cg,0,-sg],[0,1,0]]),
"MonoBase" : ([[0,0.5,0.5],[0,-0.5,0.5],[1,0,0]],[[sg,0,-cg],[-cg,0,-sg],[0,1,0]]),
"OrthPrim" : ([[0,1,0],[-1,0,0],[0,0,1]],[[1,0,0],[0,1,0],[0,0,1]]),
"OrthBase" : ([[0.5,0.5,0],[-0.5,0.5,0],[0,0,1]],[[1,0,0],[0,1,0],[0,0,1]]),
"OrthBody" : ([[0.5,-0.5,0.5],[0.5,-0.5,-0.5],[0.5,0.5,-0.5]],[[1,0,0],[0,1,0],[0,0,1]]),
"OrthFace" : ([[0.5,0,0.5],[0,-0.5,-0.5],[0.5,0.5,0]],[[1,0,0],[0,1,0],[0,0,1]]),
"TetrPrim" : ([[1,0,0],[0,1,0],[0,0,1]],[[1,0,0],[0,1,0],[0,0,1]]),
"TetrBody" : ([[-0.5,0.5,0.5],[0.5,-0.5,0.5],[0.5,0.5,-0.5]],[[1,0,0],[0,1,0],[0,0,1]]),
"TrigPrim" : ([[2./3,-1./3,-1./3],[1./3,1./3,-2./3],[1./3,1./3,1./3]],[[-0.5,t,0],[-t,-0.5,0],[0,0,1]]),
"HexaPrim" : ([[1,0,0],[0,1,0],[0,0,1]],[[0,1,0],[-1,0,0],[0,0,1]]),
"CubiPrim" : ([[1,0,0],[0,1,0],[0,0,1]],[[1,0,0],[0,1,0],[0,0,1]]),
"CubiFace" : ([[0,0.5,0.5],[0.5,0,0.5],[0.5,0.5,0]],[[1,0,0],[0,1,0],[0,0,1]]),
"CubiBody" : ([[-0.5,0.5,0.5],[0.5,-0.5,0.5],[0.5,0.5,-0.5]],[[1,0,0],[0,1,0],[0,0,1]]) }
if 38<=spgnum<=41: # These 4 space groups use different basic vectors, refer to BC book Tab.3.1 note (v).
(Q_C, S1)= QS1[brav]
Q_A=np.array(Q_C@OrthBase_C2A).tolist()
Q=Q_A
else: (Q,S1)=QS1[brav]
S2_bAc=[[0,1,0],[-1,0,0],[0,0,1]] # C4z- # bAc means the orientation "b -a c" in the ITA
S2_bca=[[0,1,0],[0,0,1],[1,0,0]] # C3(111)-
S2_Cba=[[0,0,-1],[0,1,0],[1,0,0]] # C4y-
S2_aCb=[[1,0,0],[0,0,-1],[0,1,0]] # C4x+
S2=np.eye(3)
if spgnum in [17,19,28,29,31,33,36,46,53,61,70,122]: S2=S2_bAc
if spgnum in [38,39,40,41,57]: S2=S2_bca
if spgnum in [51,54]: S2=S2_Cba
if spgnum in [52,60]: S2=S2_aCb
S=(np.array(S2)@S1).tolist()
return (Q,S)
BC_rot_name={
'TricPrim': ['E','I'],'MonoPrim':['E','C2z','I','mz'], 'MonoBase':['E','C2z','I','mz'],
'OrthPrim': ['E','C2x','C2y','C2z','I','mx','my','mz'],'OrthBase':['E','C2x','C2y','C2z','I','mx','my','mz'],
'OrthBody': ['E','C2x','C2y','C2z','I','mx','my','mz'],'OrthFace':['E','C2x','C2y','C2z','I','mx','my','mz'],
'TetrPrim': ['E','C4z+','C2z','C4z-','C2x','C2y','C2a','C2b','I','S4z-','mz','S4z+','mx','my','mda','mdb'],
'TetrBody': ['E','C4z+','C2z','C4z-','C2x','C2y','C2a','C2b','I','S4z-','mz','S4z+','mx','my','mda','mdb'],
'TrigPrim': ['E','C3+','C3-','C21p','C22p','C23p','I','S6-','S6+','md1','md2','md3'],
'HexaPrim': ['E','C6+','C3+','C2','C3-','C6-','C21p','C22p','C23p','C21pp','C22pp','C23pp',
'I','S3-','S6-','mh','S6+','S3+','md1','md2','md3','mv1','mv2','mv3'],
'CubiPrim': ['E','C2x','C2y','C2z','C31+','C32+','C33+','C34+','C31-','C32-','C33-','C34-',
'C4x+','C4y+','C4z+','C4x-','C4y-','C4z-','C2a','C2b','C2c','C2d','C2e','C2f',
'I','mx','my','mz','S61-','S62-','S63-','S64-','S61+','S62+','S63+','S64+',
'S4x-','S4y-','S4z-','S4x+','S4y+','S4z+','mda','mdb','mdc','mdd','mde','mdf'],
'CubiBody': ['E','C2x','C2y','C2z','C31+','C32+','C33+','C34+','C31-','C32-','C33-','C34-',
'C4x+','C4y+','C4z+','C4x-','C4y-','C4z-','C2a','C2b','C2c','C2d','C2e','C2f',
'I','mx','my','mz','S61-','S62-','S63-','S64-','S61+','S62+','S63+','S64+',
'S4x-','S4y-','S4z-','S4x+','S4y+','S4z+','mda','mdb','mdc','mdd','mde','mdf'],
'CubiFace': ['E','C2x','C2y','C2z','C31+','C32+','C33+','C34+','C31-','C32-','C33-','C34-',
'C4x+','C4y+','C4z+','C4x-','C4y-','C4z-','C2a','C2b','C2c','C2d','C2e','C2f',
'I','mx','my','mz','S61-','S62-','S63-','S64-','S61+','S62+','S63+','S64+',
'S4x-','S4y-','S4z-','S4x+','S4y+','S4z+','mda','mdb','mdc','mdd','mde','mdf'],
}
BC_rot_mat={
'TricPrim': [[[1,0,0],[0,1,0],[0,0,1]], [[-1,0,0],[0,-1,0],[0,0,-1]]],
'MonoPrim': [[[1,0,0],[0,1,0],[0,0,1]], [[-1,0,0],[0,-1,0],[0,0,1]], [[-1,0,0],[0,-1,0],[0,0,-1]], [[1,0,0],[0,1,0],[0,0,-1]]],
'MonoBase': [[[1,0,0],[0,1,0],[0,0,1]], [[-1,0,0],[0,0,-1],[0,-1,0]], [[-1,0,0],[0,-1,0],[0,0,-1]], [[1,0,0],[0,0,1],[0,1,0]]],
'OrthPrim': [[[1,0,0],[0,1,0],[0,0,1]], [[-1,0,0],[0,1,0],[0,0,-1]], [[1,0,0],[0,-1,0],[0,0,-1]], [[-1,0,0],[0,-1,0],[0,0,1]],
[[-1,0,0],[0,-1,0],[0,0,-1]], [[1,0,0],[0,-1,0],[0,0,1]], [[-1,0,0],[0,1,0],[0,0,1]], [[1,0,0],[0,1,0],[0,0,-1]]],
'OrthBase': [[[1,0,0],[0,1,0],[0,0,1]], [[0,1,0],[1,0,0],[0,0,-1]], [[0,-1,0],[-1,0,0],[0,0,-1]], [[-1,0,0],[0,-1,0],[0,0,1]],
[[-1,0,0],[0,-1,0],[0,0,-1]], [[0,-1,0],[-1,0,0],[0,0,1]], [[0,1,0],[1,0,0],[0,0,1]], [[1,0,0],[0,1,0],[0,0,-1]]],
'OrthBody': [[[1,0,0],[0,1,0],[0,0,1]], [[0,-1,1],[0,-1,0],[1,-1,0]], [[-1,0,0],[-1,0,1],[-1,1,0]], [[0,1,-1],[1,0,-1],[0,0,-1]],
[[-1,0,0],[0,-1,0],[0,0,-1]], [[0,1,-1],[0,1,0],[-1,1,0]], [[1,0,0],[1,0,-1],[1,-1,0]], [[0,-1,1],[-1,0,1],[0,0,1]]],
'OrthFace': [[[1,0,0],[0,1,0],[0,0,1]], [[0,0,1],[-1,-1,-1],[1,0,0]], [[-1,-1,-1],[0,0,1],[0,1,0]], [[0,1,0],[1,0,0],[-1,-1,-1]],
[[-1,0,0],[0,-1,0],[0,0,-1]], [[0,0,-1],[1,1,1],[-1,0,0]], [[1,1,1],[0,0,-1],[0,-1,0]], [[0,-1,0],[-1,0,0],[1,1,1]]],
'TetrPrim': [[[1,0,0],[0,1,0],[0,0,1]], [[0,-1,0],[1,0,0],[0,0,1]], [[-1,0,0],[0,-1,0],[0,0,1]], [[0,1,0],[-1,0,0],[0,0,1]],
[[1,0,0],[0,-1,0],[0,0,-1]], [[-1,0,0],[0,1,0],[0,0,-1]], [[0,1,0],[1,0,0],[0,0,-1]], [[0,-1,0],[-1,0,0],[0,0,-1]],
[[-1,0,0],[0,-1,0],[0,0,-1]], [[0,1,0],[-1,0,0],[0,0,-1]], [[1,0,0],[0,1,0],[0,0,-1]], [[0,-1,0],[1,0,0],[0,0,-1]],
[[-1,0,0],[0,1,0],[0,0,1]], [[1,0,0],[0,-1,0],[0,0,1]], [[0,-1,0],[-1,0,0],[0,0,1]], [[0,1,0],[1,0,0],[0,0,1]]],
'TetrBody': [[[1,0,0],[0,1,0],[0,0,1]], [[0,1,0],[0,1,-1],[-1,1,0]], [[0,1,-1],[1,0,-1],[0,0,-1]], [[1,0,-1],[1,0,0],[1,-1,0]],
[[-1,0,0],[-1,0,1],[-1,1,0]], [[0,-1,1],[0,-1,0],[1,-1,0]], [[-1,0,1],[0,-1,1],[0,0,1]], [[0,-1,0],[-1,0,0],[0,0,-1]],
[[-1,0,0],[0,-1,0],[0,0,-1]], [[0,-1,0],[0,-1,1],[1,-1,0]], [[0,-1,1],[-1,0,1],[0,0,1]], [[-1,0,1],[-1,0,0],[-1,1,0]],
[[1,0,0],[1,0,-1],[1,-1,0]], [[0,1,-1],[0,1,0],[-1,1,0]], [[1,0,-1],[0,1,-1],[0,0,-1]], [[0,1,0],[1,0,0],[0,0,1]]],
'TrigPrim': [[[1,0,0],[0,1,0],[0,0,1]], [[0,0,1],[1,0,0],[0,1,0]], [[0,1,0],[0,0,1],[1,0,0]], [[-1,0,0],[0,0,-1],[0,-1,0]],
[[0,0,-1],[0,-1,0],[-1,0,0]], [[0,-1,0],[-1,0,0],[0,0,-1]], [[-1,0,0],[0,-1,0], [0,0,-1]], [[0,0,-1],[-1,0,0],[0,-1,0]],
[[0,-1,0],[0,0,-1],[-1,0,0]], [[1,0,0],[0,0,1],[0,1,0]], [[0,0,1],[0,1,0],[1,0,0]], [[0,1,0],[1,0,0],[0,0,1]]],
'HexaPrim': [[[1,0,0],[0,1,0],[0,0,1]], [[1,-1,0],[1,0,0],[0,0,1]], [[0,-1,0],[1,-1,0],[0,0,1]], [[-1,0,0],[0,-1,0],[0,0,1]],
[[-1,1,0],[-1,0,0],[0,0,1]], [[0,1,0],[-1,1,0],[0,0,1]], [[-1,1,0],[0,1,0],[0,0,-1]], [[1,0,0],[1,-1,0],[0,0,-1]],
[[0,-1,0],[-1,0,0],[0,0,-1]], [[1,-1,0], [0,-1,0],[0,0,-1]], [[-1,0,0],[-1,1,0],[0,0,-1]], [[0,1,0],[1,0,0],[0,0,-1]],
[[-1,0,0],[0,-1,0],[0,0,-1]], [[-1,1,0],[-1,0,0],[0,0,-1]], [[0,1,0],[-1,1,0],[0,0,-1]], [[1,0,0],[0,1,0],[0,0,-1]],
[[1,-1,0],[1,0,0],[0,0,-1]], [[0,-1,0],[1,-1,0],[0,0,-1]], [[1,-1,0],[0,-1,0],[0,0,1]], [[-1,0,0],[-1,1,0],[0,0,1]],
[[0,1,0],[1,0,0],[0,0,1]], [[-1,1,0],[0,1,0],[0,0,1]], [[1,0,0],[1,-1,0],[0,0,1]], [[0,-1,0],[-1,0,0],[0,0,1]]],
'CubiPrim': [[[1,0,0],[0,1,0],[0,0,1]], [[1,0,0],[0,-1,0],[0,0,-1]], [[-1,0,0],[0,1,0],[0,0,-1]], [[-1,0,0],[0,-1,0],[0,0,1]],
[[0,0,1],[1,0,0],[0,1,0]], [[0,0,-1],[1,0,0],[0,-1,0]], [[0,0,-1],[-1,0,0],[0,1,0]], [[0,0,1],[-1,0,0],[0,-1,0]],
[[0,1,0],[0,0,1],[1,0,0]], [[0,1,0],[0,0,-1],[-1,0,0]], [[0,-1,0],[0,0,1],[-1,0,0]], [[0,-1,0],[0,0,-1],[1,0,0]],
[[1,0,0],[0,0,-1],[0,1,0]], [[0,0,1],[0,1,0],[-1,0,0]], [[0,-1,0],[1,0,0],[0,0,1]], [[1,0,0],[0,0,1],[0,-1,0]],
[[0,0,-1],[0,1,0],[1,0,0]], [[0,1,0],[-1,0,0],[0,0,1]], [[0,1,0],[1,0,0],[0,0,-1]], [[0,-1,0],[-1,0,0],[0,0,-1]],
[[0,0,1],[0,-1,0],[1,0,0]], [[-1,0,0],[0,0,1],[0,1,0]], [[0,0,-1],[0,-1,0],[-1,0,0]], [[-1,0,0],[0,0,-1],[0,-1,0]],
[[-1,0,0],[0,-1,0],[0,0,-1]], [[-1,0,0],[0,1,0],[0,0,1]], [[1,0,0],[0,-1,0],[0,0,1]], [[1,0,0],[0,1,0],[0,0,-1]],
[[0,0,-1],[-1,0,0],[0,-1,0]], [[0,0,1],[-1,0,0],[0,1,0]], [[0,0,1],[1,0,0],[0,-1,0]], [[0,0,-1],[1,0,0],[0,1,0]],
[[0,-1,0],[0,0,-1],[-1,0,0]], [[0,-1,0],[0,0,1],[1,0,0]], [[0,1,0],[0,0,-1],[1,0,0]], [[0,1,0],[0,0,1],[-1,0,0]],
[[-1,0,0],[0,0,1],[0,-1,0]], [[0,0,-1],[0,-1,0],[1,0,0]], [[0,1,0],[-1,0,0],[0,0,-1]], [[-1,0,0],[0,0,-1],[0,1,0]],
[[0,0,1],[0,-1,0],[-1,0,0]], [[0,-1,0],[1,0,0],[0,0,-1]], [[0,-1,0],[-1,0,0],[0,0,1]], [[0,1,0],[1,0,0],[0,0,1]],
[[0,0,-1],[0,1,0],[-1,0,0]], [[1,0,0],[0,0,-1],[0,-1,0]], [[0,0,1],[0,1,0],[1,0,0]], [[1,0,0],[0,0,1],[0,1,0]]],
'CubiFace': [[[1,0,0],[0,1,0],[0,0,1]], [[-1,-1,-1],[0,0,1],[0,1,0]], [[0,0,1],[-1,-1,-1],[1,0,0]], [[0,1,0],[1,0,0],[-1,-1,-1]],
[[0,0,1],[1,0,0],[0,1,0]], [[0,1,0],[-1,-1,-1],[0,0,1]], [[1,0,0],[0,0,1],[-1,-1,-1]], [[-1,-1,-1],[0,1,0],[1,0,0]],
[[0,1,0],[0,0,1],[1,0,0]], [[-1,-1,-1],[1,0,0],[0,0,1]], [[1,0,0],[-1,-1,-1],[0,1,0]], [[0,0,1],[0,1,0],[-1,-1,-1]],
[[0,-1,0],[1,1,1],[-1,0,0]], [[0,-1,0],[0,0,-1],[1,1,1]], [[1,1,1],[0,0,-1],[-1,0,0]], [[0,0,-1],[-1,0,0],[1,1,1]],
[[1,1,1],[-1,0,0],[0,-1,0]], [[0,0,-1],[1,1,1],[0,-1,0]], [[-1,0,0],[0,-1,0],[1,1,1]], [[0,-1,0],[-1,0,0],[0,0,-1]],
[[-1,0,0],[1,1,1],[0,0,-1]], [[1,1,1],[0,-1,0],[0,0,-1]], [[0,0,-1],[0,-1,0],[-1,0,0]], [[-1,0,0],[0,0,-1],[0,-1,0]],
[[-1,0,0],[0,-1,0],[0,0,-1]], [[1,1,1],[0,0,-1],[0,-1,0]], [[0,0,-1],[1,1,1],[-1,0,0]], [[0,-1,0],[-1,0,0],[1,1,1]],
[[0,0,-1],[-1,0,0],[0,-1,0]], [[0,-1,0],[1,1,1],[0,0,-1]], [[-1,0,0],[0,0,-1],[1,1,1]], [[1,1,1], [0,-1,0],[-1,0,0]],
[[0,-1,0],[0,0,-1],[-1,0,0]], [[1,1,1],[-1,0,0],[0,0,-1]], [[-1,0,0],[1,1,1],[0,-1,0]], [[0,0,-1],[0,-1,0],[1,1,1]],
[[0,1,0],[-1,-1,-1],[1,0,0]], [[0,1,0],[0,0,1],[-1,-1,-1]], [[-1,-1,-1],[0,0,1],[1,0,0]], [[0,0,1],[1,0,0],[-1,-1,-1]],
[[-1,-1,-1],[1,0,0],[0,1,0]], [[0,0,1],[-1,-1,-1],[0,1,0]], [[1,0,0],[0,1,0],[-1,-1,-1]], [[0,1,0],[1,0,0],[0,0,1]],
[[1,0,0],[-1,-1,-1],[0,0,1]], [[-1,-1,-1],[0,1,0],[0,0,1]], [[0,0,1],[0,1,0],[1,0,0]], [[1,0,0],[0,0,1],[0,1,0]]],
'CubiBody': [[[1,0,0],[0,1,0],[0,0,1]], [[-1,0,0],[-1,0,1],[-1,1,0]], [[0,-1,1],[0,-1,0],[1,-1,0]], [[0,1,-1],[1,0,-1],[0,0,-1]],
[[0,0,1],[1,0,0],[0,1,0]], [[-1,1,0],[-1,0,0],[-1,0,1]], [[1,-1,0],[0,-1,1],[0,-1,0]], [[0,0,-1],[0,1,-1],[1,0,-1]],
[[0,1,0],[0,0,1],[1,0,0]], [[0,-1,0],[1,-1,0],[0,-1,1]], [[1,0,-1],[0,0,-1],[0,1,-1]], [[-1,0,1],[-1,1,0],[-1,0,0]],
[[0,-1,1],[0,0,1],[-1,0,1]], [[1,-1,0],[1,0,-1],[1,0,0]], [[0,1,0],[0,1,-1],[-1,1,0]], [[0,1,-1],[-1,1,0],[0,1,0]],
[[0,0,1],[-1,0,1],[0,-1,1]], [[1,0,-1],[1,0,0],[1,-1,0]], [[-1,0,1],[0,-1,1],[0,0,1]], [[0,-1,0],[-1,0,0],[0,0,-1]],
[[-1,1,0],[0,1,0],[0,1,-1]], [[1,0,0],[1,-1,0],[1,0,-1]], [[0,0,-1], [0,-1,0],[-1,0,0]], [[-1,0,0],[0,0,-1],[0,-1,0]],
[[-1,0,0],[0,-1,0],[0,0,-1]], [[1,0,0],[1,0,-1],[1,-1,0]], [[0,1,-1],[0,1,0],[-1,1,0]], [[0,-1,1],[-1,0,1],[0,0,1]],
[[0,0,-1],[-1,0,0],[0,-1,0]], [[1,-1,0],[1,0,0],[1,0,-1]], [[-1,1,0],[0,1,-1],[0,1,0]], [[0,0,1],[0,-1,1],[-1,0,1]],
[[0,-1,0],[0,0,-1],[-1,0,0]], [[0,1,0],[-1,1,0],[0,1,-1]], [[-1,0,1],[0,0,1], [0,-1,1]], [[1,0,-1],[1,-1,0],[1,0,0]],
[[0,1,-1],[0,0,-1],[1,0,-1]], [[-1,1,0],[-1,0,1],[-1,0,0]], [[0,-1,0],[0,-1,1],[1,-1,0]], [[0,-1,1],[1,-1,0],[0,-1,0]],
[[0,0,-1],[1,0,-1],[0,1,-1]], [[-1,0,1],[-1,0,0],[-1,1,0]], [[1,0,-1],[0,1,-1],[0,0,-1]], [[0,1,0],[1,0,0],[0,0,1]],
[[1,-1,0],[0,-1,0],[0,-1,1]], [[-1,0,0],[-1,1,0],[-1,0,1]], [[0,0,1],[0,1,0],[1,0,0]], [[1,0,0],[0,0,1],[0,1,0]]]
}
BC_mat_to_name={}
for brav in brav_latt:
toBCname={}
for name,mat in zip(BC_rot_name[brav],BC_rot_mat[brav]):
mat_str=str(np.round(mat).astype(int).tolist()).replace(' ','')
toBCname[mat_str]=name
BC_mat_to_name[brav]=toBCname
BC_name_to_mat={}
for brav in brav_latt:
toBCmat={}
for name,mat in zip(BC_rot_name[brav],BC_rot_mat[brav]):
toBCmat[name]=mat
BC_name_to_mat[brav]=toBCmat
def get_BC_rot_name(spgnum, BC_Rmat, latt_type='C'):
brav=getSGlatt(spgnum)
# 对于38-41这四个底心正交格子的空间群，ITA（包括spglib）中用的是A底心，而BC书中用的是C底心
# BC书中的Tab3.1中的基矢也是按C底心给的。BC书中Tab.3.7中的38-41号空间群的第二行生成元是
# 按A底心格子算的，为了得到这个结果，必须使用不同的基矢定义（见Tab3.1的note(v)），因而旋转
# 矩阵也会变化。但是BC_mat_to_name中存储的旋转名称对应的是C底心的，所以A底心的矩阵要转成
# C底心的矩阵才能得到正确的旋转名称。
# latt_type is either 'A' or 'C', and it's only effective when 38<=spgnum<=41
if 38<=spgnum<=41 and latt_type=='A':
Rmat=np.array(OrthBase_C2A@BC_Rmat@OrthBase_C2A.I)
else: Rmat=BC_Rmat
mat_str=str(np.round(Rmat).astype(int).tolist()).replace(' ','')
if mat_str not in BC_mat_to_name[brav]: return 'N/A'
else: return BC_mat_to_name[brav][mat_str]
def get_BC_rot_mat(spgnum, rotname, latt_type='C'):
brav=getSGlatt(spgnum)
if rotname not in BC_name_to_mat[brav]: print('Error: Wrong rot name for lattice',brav+'!'); return []
mat=BC_name_to_mat[brav][rotname]
if 38<=spgnum<=41 and latt_type=='A': mat=np.array(OrthBase_C2A.I@mat@OrthBase_C2A)
return np.array(mat)
def init_SG_gen_elem():
global SG_gen_elem
I3=[[1,0,0],[0,1,0],[0,0,1]]; o=[0,0,0]
h1=[0.5,0,0]; h2=[0,0.5,0]; h3=[0,0,0.5]
h12=[0.5,0.5,0]; h23=[0,0.5,0.5]; h13=[0.5,0,0.5]; h123=[0.5,0.5,0.5]
# tbd=[[-1,0,0],[0,-1,0],[0,0,-1]]
U38to41=[[-1,0,0],[0,0,1],[0,1,0]] # bca
UorthP_bAc=[[0,-1,0],[1,0,0],[0,0,1]]
UorthB_bAc=[[0,1,0],[0,1,-1],[-1,1,0]]
UorthP_Cba=[[1,0,0],[0,0,1],[0,-1,0]]
UorthP_aCb=[[0,0,-1],[0,1,0],[1,0,0]]
UorthP_bca=[[0,-1,0],[0,0,1],[-1,0,0]]
UorthF_bAc=[[1,1,1],[0,0,-1],[-1,0,0]]
UtetrB_bAc=[[0,1,0],[0,1,-1],[-1,1,0]]
SG_gen_elem={
1:[[['E',o]],o,I3,[]],
2:[[['I',o]],o,I3,[]],
3:[[['C2z',o]],o,I3,[]],
4:[[['C2z',h3]],o,I3,[]],
5:[[['C2z',o]],o,I3,[]],
6:[[['mz',o]],o,I3,[]],
7:[[['mz',h1]],o,I3,[]],
8:[[['mz',o]],o,I3,[]],
9:[[['mz',h1]],o,I3,[]],
10:[[['C2z',o],['I',o]],o,I3,[]],
11:[[['C2z',h3],['I',h3]],[0,0,0.25],I3,[['C2z',h3],['I',o]]],
12:[[['C2z',o],['I',o]],o,I3,[]],
13:[[['C2z',o],['I',h1]],[0.25,0,0],I3,[['C2z',h1],['I',o]]],
14:[[['C2z',h3],['I',h13]],[-0.25,0,0.25],I3,[['C2z',h13],['I',o]]],
15:[[['C2z',o],['I',h1]],[0.25,0,0],I3,[['C2z',h1],['I',o]]],
16:[[['C2x',o],['C2y',o]],o,I3,[]],
17:[[['C2x',h3],['C2y',o]],o,UorthP_bAc,[['C2x',o],['C2y',h3]]],
18:[[['C2x',h12],['C2y',h12]],o,I3,[]],
19:[[['C2x',h23],['C2y',h12]],o,UorthP_bAc,[['C2x',h12],['C2y',h13]]],
20:[[['C2x',o],['C2y',h3]],o,I3,[]],
21:[[['C2x',o],['C2y',o]],o,I3,[]],
22:[[['C2x',o],['C2y',o]],o,I3,[]],
23:[[['C2x',o],['C2y',o]],o,I3,[]],
24:[[['C2x',h23],['C2y',h12]],h1,I3,[['C2x',h12],['C2y',h13]]],
25:[[['mx',o],['my',o]],o,I3,[]],
26:[[['mx',o],['my',h3]],o,I3,[]],
27:[[['mx',h3],['my',h3]],o,I3,[]],
28:[[['mx',h1],['my',o]],[-0.25,0,0],UorthP_bAc,[['mx',h2],['my',h2]]],
29:[[['mx',h1],['my',h3]],[-0.25,0,0],UorthP_bAc,[['mx',h23],['my',h2]]],
30:[[['mx',h13],['my',h3]],[-0.25,0,0],I3,[['mx',h13],['my',h13]]],
31:[[['mx',h13],['my',o]],o,UorthP_bAc,[['mx',o],['my',h23]]],
32:[[['mx',h1],['my',h2]],[-0.25,0.25,0],I3,[['mx',h12],['my',h12]]],
33:[[['mx',h1],['my',h23]],[-0.25,0.25,0],UorthP_bAc,[['mx',h123],['my',h12]]],
34:[[['mx',h13],['my',h23]],[-0.25,0.25,0],I3,[['mx',h123],['my',h123]]],
35:[[['mx',o],['my',o]],o,I3,[]],
36:[[['mx',h3],['my',o]],o,UorthP_bAc,[['mx',o],['my',h3]]],
37:[[['mx',h3],['my',h3]],o,I3,[]],
38:[[['mz',o],['mx',o]],o,U38to41,[['mx',o],['my',o]]],
39:[[['mz',h12],['mx',h12]],o,U38to41,[['mx',h13],['my',h13]]],
40:[[['mz',h3],['mx',h3]],o,U38to41,[['mx',h2],['my',h2]]],
41:[[['mz',h123],['mx',h123]],o,U38to41,[['mx',h123],['my',h123]]],
42:[[['mx',o],['my',o]],o,I3,[]],
43:[[['mx',h2],['my',h1]],[0,0,0.25],I3,[['mx',[0.75,0.75,0.75]],['my',[0.75,0.75,0.75]]]],
44:[[['mx',o],['my',o]],o,I3,[]],
45:[[['mx',h12],['my',h12]],o,I3,[]],
46:[[['mx',h23],['my',h23]],o,UorthB_bAc,[['mx',h13],['my',h13]]],
47:[[['C2x',o],['C2y',o],['I',o]],o,I3,[]],
48:[[['C2x',o],['C2y',o],['I',h123]],o,I3,[]],
49:[[['C2x',o],['C2y',o],['I',h3]],[0,0,0.25],I3,[['C2x',h3],['C2y',h3],['I',o]]],
50:[[['C2x',o],['C2y',o],['I',h12]],o,I3,[]],
51:[[['C2x',h3],['C2y',o],['I',o]],o,UorthP_Cba,[['C2x',h2],['C2y',o],['I',o]]],
52:[[['C2x',h3],['C2y',o],['I',h12]],[0.25,0.25,0],UorthP_aCb,[['C2x',h13],['C2y',h123],['I',o]]],
53:[[['C2x',h3],['C2y',o],['I',h1]],[-0.25,0,0],UorthP_bAc,[['C2x',o],['C2y',h23],['I',o]]],
54:[[['C2x',h3],['C2y',o],['I',h2]],[0,0.25,0],UorthP_Cba,[['C2x',h23],['C2y',h3],['I',o]]],
55:[[['C2x',h12],['C2y',h12],['I',o]],o,I3,[]],
56:[[['C2x',h12],['C2y',h12],['I',h123]],[-0.25,-0.25,-0.25],I3,[['C2x',h23],['C2y',h13],['I',o]]],
57:[[['C2x',h12],['C2y',h12],['I',h2]],[0,0.25,0],UorthP_bca,[['C2x',h1],['C2y',h13],['I',o]]],
58:[[['C2x',h12],['C2y',h12],['I',h3]],[0,0,-0.25],I3,[['C2x',h123],['C2y',h123],['I',o]]],
59:[[['C2x',h12],['C2y',h12],['I',h12]],o,I3,[]],
60:[[['C2x',h12],['C2y',h12],['I',h13]],[-0.25,0,0.25],UorthP_aCb,[['C2x',h12],['C2y',h3],['I',o]]],
61:[[['C2x',h23],['C2y',h12],['I',o]],o,UorthP_bAc,[['C2x',h12],['C2y',h13],['I',o]]],
62:[[['C2x',h23],['C2y',h12],['I',h12]],[0.25,0.25,0],I3,[['C2x',h123],['C2y',h1],['I',o]]],
63:[[['C2x',o],['C2y',h3],['I',o]],o,I3,[]],
64:[[['C2x',o],['C2y',h3],['I',h12]],[0.25,0.25,0],I3,[['C2x',o],['C2y',h123],['I',o]]],
65:[[['C2x',o],['C2y',o],['I',o]],o,I3,[]],
66:[[['C2x',o],['C2y',o],['I',h3]],[0,0,0.25],I3,[['C2x',h3],['C2y',h3],['I',o]]],
67:[[['C2x',o],['C2y',o],['I',h12]],[0.25,0.25,0],I3,[['C2x',o],['C2y',h12],['I',o]]],
#68:[[['C2x',o],['C2y',o],['I',h123]],[-0.25,0.25,0.25],I3,[['C2x',h123],['C2y',h3],['I',o]]], # original data in the BC book
68:[[['C2x',o],['C2y',o],['I',h123]],o,I3,[]], #revised
69:[[['C2x',o],['C2y',o],['I',o]],o,I3,[]],
70:[[['C2x',o],['C2y',o],['I',[0.25,0.25,0.25]]],o,UorthF_bAc,[['C2x',o],['C2y',o],['I',[0.75,0.75,0.75]]]],
71:[[['C2x',o],['C2y',o],['I',o]],o,I3,[]],
72:[[['C2x',o],['C2y',o],['I',h12]],[0.25,0.25,0],I3,[['C2x',h12],['C2y',h12],['I',o]]],
73:[[['C2x',h23],['C2y',h12],['I',o]],h1,I3,[['C2x',h12],['C2y',h13],['I',o]]],
74:[[['C2x',h23],['C2y',h12],['I',h12]],[0.75,0.25,0],I3,[['C2x',o],['C2y',h23],['I',o]]],
75:[[['C4z+',o]],o,I3,[]],
76:[[['C4z+',[0,0,0.25]]],o,I3,[]],
77:[[['C4z+',h3]],o,I3,[]],
78:[[['C4z+',[0,0,0.75]]],o,I3,[]],
79:[[['C4z+',o]],o,I3,[]],
80:[[['C4z+',[0.75,0.25,0.5]]],o,I3,[]],
81:[[['S4z+',o]],o,I3,[]],
82:[[['S4z+',o]],o,I3,[]],
83:[[['C4z+',o],['I',o]],o,I3,[]],
84:[[['C4z+',h3],['I',h3]],[0,0,0.25],I3,[['C4z+',h3],['I',o]]],
85:[[['C4z+',h12],['I',h12]],o,I3,[]],
86:[[['C4z+',h123],['I',h123]],o,I3,[]],
87:[[['C4z+',o],['I',o]],o,I3,[]],
88:[[['C4z+',[0.75,0.25,0.5]],['I',[0.75,0.25,0.5]]],o,I3,[]],
89:[[['C4z+',o],['C2x',o]],o,I3,[]],
90:[[['C4z+',o],['C2x',h12]],h1,I3,[['C4z+',h12],['C2x',h12]]],
91:[[['C4z+',[0,0,0.25]],['C2x',o]],[0,0,0.25],I3,[['C4z+',[0,0,0.25]],['C2x',h3]]],
92:[[['C4z+',[0,0,0.25]],['C2x',h12]],[0.5,0,-0.375],I3,[['C4z+',[0.5,0.5,0.25]],['C2x',[0.5,0.5,0.75]]]],
93:[[['C4z+',h3],['C2x',o]],o,I3,[]],
94:[[['C4z+',h3],['C2x',h12]],[0.5,0,0.25],I3,[['C4z+',h123],['C2x',h123]]],
95:[[['C4z+',[0,0,0.75]],['C2x',o]],[0,0,0.25],I3,[['C4z+',[0,0,0.75]],['C2x',h3]]],
96:[[['C4z+',[0,0,0.75]],['C2x',h12]],[0.5,0,-0.125],I3,[['C4z+',[0.5,0.5,0.75]],['C2x',[0.5,0.5,0.25]]]],
97:[[['C4z+',o],['C2x',o]],o,I3,[]],
98:[[['C4z+',[0.75,0.25,0.5]],['C2x',h23]],[0.125,0.125,0],I3,[['C4z+',[0.75,0.25,0.5]],['C2x',[0.75,0.25,0.5]]]],
99:[[['C4z+',o],['mx',o]],o,I3,[]],
100:[[['C4z+',o],['mx',h12]],o,I3,[]],
101:[[['C4z+',h3],['mx',h3]],o,I3,[]],
102:[[['C4z+',h3],['mx',h123]],h1,I3,[['C4z+',h123],['mx',h123]]],
103:[[['C4z+',o],['mx',h3]],o,I3,[]],
104:[[['C4z+',o],['mx',h123]],o,I3,[]],
105:[[['C4z+',h3],['mx',o]],o,I3,[]],
106:[[['C4z+',h3],['mx',h12]],o,I3,[]],
107:[[['C4z+',o],['mx',o]],o,I3,[]],
108:[[['C4z+',o],['mx',h12]],o,I3,[]],
109:[[['C4z+',[0.75,0.25,0.5]],['mx',o]],o,I3,[]],
110:[[['C4z+',[0.75,0.25,0.5]],['mx',h12]],o,I3,[]],
111:[[['S4z+',o],['C2x',o]],o,I3,[]],
112:[[['S4z+',o],['C2x',h3]],o,I3,[]],
113:[[['S4z+',o],['C2x',h12]],o,I3,[]],
114:[[['S4z+',o],['C2x',h123]],o,I3,[]],
115:[[['S4z+',o],['C2a',o]],o,I3,[]],
116:[[['S4z+',o],['C2a',h3]],o,I3,[]],
117:[[['S4z+',o],['C2a',h12]],o,I3,[]],
118:[[['S4z+',o],['C2a',h123]],o,I3,[]],
119:[[['S4z+',o],['C2a',o]],o,I3,[]],
120:[[['S4z+',o],['C2a',h12]],o,I3,[]],
121:[[['S4z+',o],['C2x',o]],o,I3,[]],
122:[[['S4z+',o],['C2x',[0.25,0.75,0.5]]],o,UtetrB_bAc,[['S4z+',o],['C2x',[0.75,0.25,0.5]]]],
123:[[['C4z+',o],['C2x',o],['I',o]],o,I3,[]],
124:[[['C4z+',o],['C2x',o],['I',h3]],[0,0,0.25],I3,[['C4z+',o],['C2x',h3],['I',o]]],
#125:[[['C4z+',h12],['C2x',o],['I',h12]],[0.25,-0.25,0],I3,[['C4z+',h1],['C2x',h2],['I',o]]], # original data in the BC book
125:[[['C4z+',h12],['C2x',o],['I',h12]],[0.5,0,0],I3,[['C4z+',o],['C2x',o],['I',h12]]], # revised
126:[[['C4z+',h12],['C2x',o],['I',h123]],h1,I3,[['C4z+',o],['C2x',o],['I',h123]]],
127:[[['C4z+',h12],['C2x',h12],['I',o]],h1,I3,[['C4z+',o],['C2x',h12],['I',o]]],
128:[[['C4z+',h12],['C2x',h12],['I',h3]],[0.5,0,0.25],I3,[['C4z+',o],['C2x',h123],['I',o]]],
129:[[['C4z+',o],['C2x',h12],['I',h12]],h1,I3,[['C4z+',h12],['C2x',h12],['I',h12]]],
130:[[['C4z+',o],['C2x',h12],['I',h123]],[0.5,0,0.25],I3,[['C4z+',h12],['C2x',h123],['I',h12]]],
131:[[['C4z+',h3],['C2x',o],['I',o]],o,I3,[]],
132:[[['C4z+',h3],['C2x',o],['I',h3]],[0,0,0.25],I3,[['C4z+',h3],['C2x',h3],['I',o]]],
133:[[['C4z+',h123],['C2x',o],['I',h12]],[0,0,0.25],I3,[['C4z+',h123],['C2x',h3],['I',h123]]],
134:[[['C4z+',h123],['C2x',o],['I',h123]],o,I3,[]],
135:[[['C4z+',h123],['C2x',h12],['I',o]],h1,I3,[['C4z+',h3],['C2x',h12],['I',o]]],
136:[[['C4z+',h123],['C2x',h12],['I',h3]],[0,0,0.25],I3,[['C4z+',h123],['C2x',h123],['I',o]]],
137:[[['C4z+',h3],['C2x',h12],['I',h12]],[0.5,0,0.25],I3,[['C4z+',h123],['C2x',h123],['I',h123]]],
138:[[['C4z+',h3],['C2x',h12],['I',h123]],h1,I3,[['C4z+',h123],['C2x',h12],['I',h123]]],
139:[[['C4z+',o],['C2x',o],['I',o]],o,I3,[]],
140:[[['C4z+',h12],['C2x',o],['I',h12]],[0.75,0.25,0.5],I3,[['C4z+',o],['C2x',h12],['I',o]]],
#141:[[['C4z+',h2],['C2x',h12],['I',h12]],[0.25,0.25,0],I3,[['C4z+',h2],['C2x',o],['I',o]]], # original data in the BC book
141:[[['C4z+',h2],['C2x',h12],['I',h12]],[3/8,1/8,1/4],I3,[['C4z+',[3/4,1/4,1/2]],['C2x',[3/4,1/4,1/2]],['I',[3/4,1/4,1/2]]]], # revised
#142:[[['C4z+',h1],['C2x',h12],['I',o]],o,tbd,[['C4z+',h2],['C2x',h12],['I',o]]], # original data in the BC book
142:[[['C4z+',h1],['C2x',h12],['I',o]],[1/8,3/8,-1/4],I3,[['C4z+',[3/4,1/4,1/2]],['C2x',[1/4,3/4,1/2]],['I',[3/4,1/4,1/2]]]], # revised
143:[[['C3+',o]],o,I3,[]],
144:[[['C3+',[0,0,1/3]]],o,I3,[]],
145:[[['C3+',[0,0,2/3]]],o,I3,[]],
146:[[['C3+',o]],o,I3,[]],
147:[[['S6+',o]],o,I3,[]],
148:[[['S6+',o]],o,I3,[]],
149:[[['C3+',o],['C21p',o]],o,I3,[]],
150:[[['C3+',o],['C21pp',o]],o,I3,[]],
151:[[['C3+',[0,0,1/3]],['C21p',[0,0,2/3]]],[0,0,1/6],I3,[['C3+',[0,0,1/3]],['C21p',[0,0,1/3]]]],
152:[[['C3+',[0,0,1/3]],['C21pp',[0,0,2/3]]],o,I3,[]],
153:[[['C3+',[0,0,2/3]],['C21p',[0,0,1/3]]],[0,0,-1/6],I3,[['C3+',[0,0,2/3]],['C21p',[0,0,2/3]]]],
154:[[['C3+',[0,0,2/3]],['C21pp',[0,0,1/3]]],o,I3,[]],
#155:[[['C3+',o],['C21p',o]],o,tbd,[['C3+',o],['C21pp',o]]], # original data in the BC book
155:[[['C3+',o],['C21p',o]],o,I3,[]], # revised
156:[[['C3+',o],['mv1',o]],o,I3,[]],
157:[[['C3+',o],['md1',o]],o,I3,[]],
158:[[['C3+',o],['mv1',h3]],o,I3,[]],
159:[[['C3+',o],['md1',h3]],o,I3,[]],
#160:[[['C3+',o],['md1',o]],o,tbd,[['C3+',o],['mv1',o]]], # original data in the BC book
160:[[['C3+',o],['md1',o]],o,I3,[]], # revised
#161:[[['C3+',o],['md1',h123]],o,tbd,[['C3+',o],['mv1',h123]]], # original data in the BC book
161:[[['C3+',o],['md1',h123]],o,I3,[]], # revised
162:[[['S6+',o],['md1',o]],o,I3,[]],
163:[[['S6+',o],['md1',h3]],o,I3,[]],
164:[[['S6+',o],['mv1',o]],o,I3,[]],
165:[[['S6+',o],['mv1',h3]],o,I3,[]],
#166:[[['S6+',o],['md1',o]],o,tbd,[['S6+',o],['mv1',o]]], # original data in the BC book
166:[[['S6+',o],['md1',o]],o,I3,[]], # revised
#167:[[['S6+',o],['md1',h123]],o,tbd,[['S6+',o],['mv1',h123]]], # original data in the BC book
167:[[['S6+',o],['md1',h123]],o,I3,[]], # revised
168:[[['C6+',o]],o,I3,[]],
169:[[['C6+',[0,0,1/6]]],o,I3,[]],
170:[[['C6+',[0,0,5/6]]],o,I3,[]],
171:[[['C6+',[0,0,1/3]]],o,I3,[]],
172:[[['C6+',[0,0,2/3]]],o,I3,[]],
173:[[['C6+',h3]],o,I3,[]],
174:[[['S3+',o]],o,I3,[]],
175:[[['C6+',o],['mh',o]],o,I3,[]],
176:[[['C6+',h3],['mh',o]],[0,0,0.25],I3,[['C6+',h3],['mh',h3]]],
177:[[['C6+',o],['C21p',o]],o,I3,[]],
#178:[[['C6+',[0,0,1/6]],['C21p',o]],o,tbd,[['C6+',[0,0,1/6]],['C21pp',o]]], # original data in the BC book
178:[[['C6+',[0,0,1/6]],['C21p',o]],[0,0,1/4],I3,[['C6+',[0,0,1/6]],['C21pp',o]]], # revised
#179:[[['C6+',[0,0,5/6]],['C21p',o]],o,tbd,[['C6+',[0,0,5/6]],['C21pp',o]]], # original data in the BC book
179:[[['C6+',[0,0,5/6]],['C21p',o]],[0,0,1/4],I3,[['C6+',[0,0,5/6]],['C21pp',o]]], # revised
180:[[['C6+',[0,0,1/3]],['C21p',o]],o,I3,[]],
181:[[['C6+',[0,0,2/3]],['C21p',o]],o,I3,[]],
#182:[[['C6+',h3],['C21p',o]],o,tbd,[['C6+',h3],['C21pp',o]]], # original data in the BC book
182:[[['C6+',h3],['C21p',o]],[0,0,1/4],I3,[['C6+',h3],['C21pp',o]]], # revised
183:[[['C6+',o],['mv1',o]],o,I3,[]],
184:[[['C6+',o],['mv1',h3]],o,I3,[]],
185:[[['C6+',h3],['mv1',h3]],o,I3,[]],
186:[[['C6+',h3],['mv1',o]],o,I3,[]],
187:[[['S3+',o],['mv1',o]],o,I3,[]],
188:[[['S3+',o],['mv1',h3]],[0,0,0.25],I3,[['S3+',h3],['mv1',h3]]],
189:[[['S3+',o],['md1',o]],o,I3,[]],
190:[[['S3+',o],['md1',h3]],[0,0,0.25],I3,[['S3+',h3],['md1',h3]]],
191:[[['C6+',o],['C21p',o],['I',o]],o,I3,[]],
192:[[['C6+',o],['C21p',h3],['I',o]],o,I3,[]],
193:[[['C6+',h3],['C21p',o],['I',o]],o,I3,[]],
194:[[['C6+',h3],['C21p',h3],['I',o]],o,I3,[]],
195:[[['C2z',o],['C2x',o],['C31+',o]],o,I3,[]],
196:[[['C2z',o],['C2x',o],['C31+',o]],o,I3,[]],
197:[[['C2z',o],['C2x',o],['C31+',o]],o,I3,[]],
198:[[['C2z',h13],['C2x',h12],['C31+',o]],o,I3,[]],
199:[[['C2z',h13],['C2x',h12],['C31+',o]],o,I3,[]],
200:[[['C2z',o],['C2x',o],['C31+',o],['I',o]],o,I3,[]],
201:[[['C2z',o],['C2x',o],['C31+',o],['I',h123]],o,I3,[]],
202:[[['C2z',o],['C2x',o],['C31+',o],['I',o]],o,I3,[]],
203:[[['C2z',o],['C2x',o],['C31+',o],['I',[0.25,0.25,0.25]]],o,I3,[]],
204:[[['C2z',o],['C2x',o],['C31+',o],['I',o]],o,I3,[]],
205:[[['C2z',h13],['C2x',h12],['C31+',o],['I',o]],o,I3,[]],
206:[[['C2z',h13],['C2x',h12],['C31+',o],['I',o]],o,I3,[]],
207:[[['C2z',o],['C2x',o],['C2a',o],['C31+',o]],o,I3,[]],
208:[[['C2z',o],['C2x',o],['C2a',h123],['C31+',o]],o,I3,[]],
209:[[['C2z',o],['C2x',o],['C2a',o],['C31+',o]],o,I3,[]],
210:[[['C2z',o],['C2x',o],['C2a',[0.25,0.25,0.25]],['C31+',o]],o,I3,[]],
211:[[['C2z',o],['C2x',o],['C2a',o],['C31+',o]],o,I3,[]],
212:[[['C2z',h13],['C2x',h12],['C2a',[0.25,0.75,0.75]],['C31+',o]],o,I3,[]],
213:[[['C2z',h13],['C2x',h12],['C2a',[0.75,0.25,0.25]],['C31+',o]],o,I3,[]],
214:[[['C2z',h13],['C2x',h12],['C2a',h1],['C31+',o]],o,I3,[]],
215:[[['C2z',o],['C2x',o],['mda',o],['C31+',o]],o,I3,[]],
216:[[['C2z',o],['C2x',o],['mda',o],['C31+',o]],o,I3,[]],
217:[[['C2z',o],['C2x',o],['mda',o],['C31+',o]],o,I3,[]],
218:[[['C2z',o],['C2x',o],['mda',h123],['C31+',o]],o,I3,[]],
219:[[['C2z',o],['C2x',o],['mda',h123],['C31+',o]],o,I3,[]],
220:[[['C2z',h13],['C2x',h12],['mda',h1],['C31+',o]],o,I3,[]],
221:[[['C2z',o],['C2x',o],['C2a',o],['C31+',o],['I',o]],o,I3,[]],
222:[[['C2z',o],['C2x',o],['C2a',o],['C31+',o],['I',h123]],o,I3,[]],
223:[[['C2z',o],['C2x',o],['C2a',h123],['C31+',o],['I',o]],o,I3,[]],
224:[[['C2z',o],['C2x',o],['C2a',h123],['C31+',o],['I',h123]],o,I3,[]],
225:[[['C2z',o],['C2x',o],['C2a',o],['C31+',o],['I',o]],o,I3,[]],
226:[[['C2z',o],['C2x',o],['C2a',o],['C31+',o],['I',h123]],[0.25,0.25,0.25],I3,[['C2z',o],['C2x',o],['C2a',h123],['C31+',o],['I',o]]],
227:[[['C2z',o],['C2x',o],['C2a',[0.25,0.25,0.25]],['C31+',o],['I',[0.25,0.25,0.25]]],o,I3,[]],
228:[[['C2z',o],['C2x',o],['C2a',[0.25,0.25,0.25]],['C31+',o],['I',[0.75,0.75,0.75]]],o,I3,[]],
229:[[['C2z',o],['C2x',o],['C2a',o],['C31+',o],['I',o]],o,I3,[]],
230:[[['C2z',h13],['C2x',h12],['C2a',h1],['C31+',o],['I',o]],o,I3,[]]}
#------------------ end of init_SG_gen_elem() ----------------------
init_SG_gen_elem()
def read_poscar(file):
poscar=open(file,'r')
nl=0
# global alat, atom_pos, atom_types, type_nums, natom, atom_numbers
alat=np.empty((3,3))
while True:
line=poscar.readline(); ss=line.split(); nl+=1
if not line: break
# print(nl,ss) # for debug
if(nl==2): scale=float(ss[0])
if(3<=nl<=5): alat[nl-3]=np.array(list(map(float,ss)))*scale
if nl==6:
noatomtypes=False
if ss[0].isnumeric(): noatomtypes=True; nl+=1 # for old POSCAR format without atom types
else: atom_types=np.array(ss)
if(nl==7): type_nums=np.array(list(map(int,ss))); natom=np.sum(type_nums); atom_pos=np.empty((natom,3))
if(nl==8):
if ss[0][0]=='s' or ss[0][0]=='S': nl-=1; continue
elif ss[0][0]=='d' or ss[0][0]=='D': Direct=True
else: Direct=False
if(9<=nl<=8+natom): atom_pos[nl-9]=np.array(list(map(float,ss[0:3])))
if noatomtypes: atom_types=["N/A"]*type_nums.size
if(not Direct):
atom_pos=list(map(lambda p: np.array(np.dot(np.mat(alat).T.I, p*scale))[0], atom_pos))
atom_numbers=[]
for (i,j) in zip(atom_types,type_nums): atom_numbers+=[atom_label2number[i]]*j
return (alat,atom_pos,atom_numbers)
def write_poscar(cell, filename):
(latt,atom_pos,atom_number)=map(np.array,cell)
(uan,idx,inv)=np.unique(atom_number, return_index=True,return_inverse=True)
idx=np.sort(idx)
uatm=atom_number[idx]
newidx=[]; natm=[0]*len(uatm)
for i,an in enumerate(uatm):
condlist=[atom_number==an]
choicelist=[list(range(len(atom_number)))]
tmp=np.sort(np.unique(np.select(condlist,choicelist,-1))).tolist() # -1 for False
if(-1 in tmp): tmp.remove(-1)
natm[i]=len(tmp)
newidx+=tmp
file=open(filename,"w")
file.write(re.sub(".vasp$","",filename)+": generated by getBCsymmetry.py\n")
file.write(" 1\n")
for i in latt:
file.write("%20.15f %20.15f %20.15f\n"%tuple(i))
file.write(("%4s "*len(uatm))%tuple(list(map(lambda i:atom_number2label[i],uatm)))+"\n")
file.write(("%4d "*len(natm))%tuple(natm)+"\n")
file.write("Direct\n")
for i in atom_pos[newidx]:
file.write("%20.15f %20.15f %20.15f"%tuple(i)+"\n")
file.close()
'''Note that we can use ase.io to read file, it's very easy.
import ase.io
def ase_read_file(filename):
s=ase.io.read(filename)
return (s.cell, s.get_scaled_positions(), s.get_atomic_numbers())
'''
def get_all_cells(dataset, prec=1e-5):
''' Get all the cells in the cell-changing process. There are six cells in total.
1. The input cell
2. The spglib standardlized cell before idealization.
3. The spglib standardlized cell after idealization, with origin and orientation of the
crystal the same as in ITA (first setting).
4. The cell using the BC basic vectors in Tab.3.1 assuming the vectors a,b,c are the basic
vectors of the previous step 3. This corresponds to the second line of the revised Tab.3.7.
5. The cell generating the BC operations, i.e. the ones in the first line of Tab.3.7.
6. The final cell obtained by rotating the crystal to make the basic vectors literally
the same as in Tab.3.1.
'''
ndig=15
spgnum=dataset['number']
p0=np.around(dataset['origin_shift'],ndig)
P=np.around(dataset["transformation_matrix"],ndig)
(Q,S)=Q_and_S_from_spg_to_BC(spgnum,dataset['std_lattice'])
(gen1,t0,U,gen2)=SG_gen_elem[spgnum]
Lsi =std_lat_after_idl=chop(dataset["std_lattice"])
Ls =std_lat_before_idl=chop([email protected](dataset['std_rotation_matrix']).I.T)
L0 =input_lat=chop(np.mat(dataset['transformation_matrix']).T@std_lat_before_idl)
LBC2=(np.array(Lsi).T@Q).T
LBC1=(np.array(LBC2).T@U).T
LBC=([email protected](LBC1).T).T
atom_numbers=dataset['std_types']
pos_s=np.round(dataset['std_positions'],ndig)
pos_0=mymod(np.round(list(map(lambda v: np.dot(np.mat(P).I,v-p0).tolist()[0], pos_s)),ndig),1)
pos_BC2=mymod(np.round(list(map(lambda v: np.dot(np.mat(Q).I,v).tolist()[0], pos_s)),ndig),1)
pos_BC1=mymod(np.round(list(map(lambda v: np.dot(np.mat(U).I,v).tolist()[0], pos_BC2)),ndig)+t0,1)
pos_0=np.array(pos_0); pos_BC1=np.array(pos_BC1); pos_BC2=np.array(pos_BC2)
atom_numbers0=atom_numbers.copy()
atom_numbers1=atom_numbers.copy()
if np.round(det(P),2)<1: # remove duplicate atom positions
nn=int(np.round(-np.log10(prec)))
tmp=np.round(pos_0,nn)
(tmp,idx)=np.unique(tmp,axis=0,return_index=True)
idx=np.sort(idx)
pos_0=pos_0[idx]
atom_numbers0=atom_numbers[idx]
if np.round(det(Q),2)<1: # remove duplicate atom positions
nn=int(np.round(-np.log10(prec)))
tmp=np.round(pos_BC2,nn)
(tmp,idx)=np.unique(tmp,axis=0,return_index=True)
idx=np.sort(idx)
pos_BC2=pos_BC2[idx]
pos_BC1=pos_BC1[idx]
atom_numbers1=atom_numbers[idx]
cells={}
cells[1]=(np.around(L0,ndig), pos_0, atom_numbers0)
cells[2]=(np.around(Ls,ndig), pos_s, atom_numbers)
cells[3]=(np.around(Lsi,ndig), pos_s, atom_numbers)
cells[4]=(np.around(LBC2,ndig), pos_BC2, atom_numbers1)
cells[5]=(np.around(LBC1,ndig), pos_BC1, atom_numbers1)
cells[6]=(np.around(LBC,ndig), pos_BC1, atom_numbers1)
return cells
def output_poscar(dataset, filename, arg_select, prec=1e-5):
bn=os.path.basename(filename); bns=bn.split('.')
if len(bns)>1: bn='.'.join(bns[:-1])
#print(bn)
cells=get_all_cells(dataset, prec)
if arg_select=='a': ss=[1,2,3,4,5,6]
else:
ss=[]
for c in list(arg_select):
if c.isnumeric() and 1<=int(c)<=6: ss+=[int(c)]
for s in ss:
fn=bn+"_"+str(s)+".vasp"
print("File "+fn+" is output.")
write_poscar(cells[s], fn)
def chop(x, eps=1e-14):
if(isinstance(x,str)): return x
if(np.array([x]).ndim==1):
if(abs(x)<eps): return 0
else: return x
else: return list(map(chop,np.array(x)))
def mymod(x,y):
eps=1e-14
if(np.array([x]).ndim==1):
m=x%y
if(abs(m-y)<eps): return 0
else: return m
else: return list(map(lambda L:mymod(L,y),np.array(x)))
def list2tuple(L):
if type(L)==list or type(L)==np.ndarray:
return tuple(map(list2tuple,L))
else: return L
def myreadcif(filename, symprec=1e-5):
def rmprs(numstr): # remove (2) in the number string like 3.45(2)
if(type(numstr)!=list):
return float(re.sub(r"\(.*\)","",numstr))
else:
return list(map(rmprs,numstr))
def poseq(p1,p2,eps): # judge if the positions p1 and p2 equal within tolerance eps
(x1,y1,z1)=p1; (x2,y2,z2)=p2; (s1,s2,s3)=[0]*3
(d1,d2,d3)=abs(np.array(p2)-p1)
(t1,t2,t3)=[False]*3
if(d1<eps): t1=True; s1=0
elif(1-d1<eps): t1=True; s1=-1 if x2>x1 else 1; d1=1-d1
if(d2<eps): t2=True; s2=0
elif(1-d2<eps): t2=True; s2=-1 if y2>y1 else 1; d2=1-d2
if(d3<eps): t3=True; s3=0
elif(1-d3<eps): t3=True; s3=-1 if z2>z1 else 1; d3=1-d3
return t1 and t2 and t3, max(d1,d2,d3), [s1,s2,s3]
cf=ReadCif(filename)
data=cf[cf.keys()[0]]
#-------------construct the basic lattice vectors--------------
a=rmprs(data['_cell_length_a'])
b=rmprs(data['_cell_length_b'])
c=rmprs(data['_cell_length_c'])
alpha=rmprs(data['_cell_angle_alpha'])*np.pi/180
beta=rmprs(data['_cell_angle_beta'])*np.pi/180
gamma=rmprs(data['_cell_angle_gamma'])*np.pi/180
latt=[[0]*3]*3
latt[0]=[a,0,0]
latt[1]=[b*cos(gamma),b*sin(gamma),0]
tmp1=c*cos(beta)
tmp2=c*(cos(alpha)/sin(gamma)-cos(beta)/tan(gamma))
latt[2]=[tmp1,tmp2,sqrt(c**2-tmp1**2-tmp2**2)]
latt=chop(latt)
#----------------------------------------------------------------
xs1=rmprs(data['_atom_site_fract_x'])
ys1=rmprs(data['_atom_site_fract_y'])
zs1=rmprs(data['_atom_site_fract_z'])
pos1=np.array([xs1,ys1,zs1]).T
atmL1=data['_atom_site_label']
atmL1=list(map(lambda s:re.sub('[0-9]','',s),atmL1))
occ=rmprs(data['_atom_site_occupancy'])
if(np.array(occ)<1).any(): print("Warning: fractional occupations exist!")
if('_atom_site_symmetry_multiplicity' in data.keys()):
multi=list(map(int,data['_atom_site_symmetry_multiplicity']))
has_multi=True
else: has_multi=False
for k in data.keys():
if k.find('_xyz')>-1: symkey=k
# the key for xyz symmetry operations may be '_symmetry_equiv_pos_as_xyz'
# or '_space_group_symop_operation_xyz'
symxyz=data[symkey]
# pos1[i] is the position of each inequivalent atom under symmetry
# pos2[i] is a list of all positions equivalent to pos1[i] under the transformation
# symxyz. pos2[i] has duplicate positions.
# pos[i] is the list of equivalent positions of pos1[i] with all duplicate
# ones removed. len(pos[i]) should equal to multi[i] if the latter exists.
#----------------generate pos2 according to symxyz----------------------
pos2=[]
for p in pos1:
tmp=[]
for xyz in symxyz:
(x,y,z)=p; x1,y1,z1=eval(xyz)
tmp.append([x1,y1,z1])
pos2.append(tmp)
pos2=mymod(pos2,1)
#---------------generate pos by removing duplication--------------------
pos=[]; mindiff=[1e8]*len(pos2)
for k,p in enumerate(pos2):
idx=list(range(len(p)))
for i,pi in enumerate(p):
if idx[i]==-1: continue
for j in range(i+1,len(p)):
pj=p[j]
eq,diff,s=poseq(pi,pj,symprec)
if(eq): idx[j]=-1
if(symprec < diff < mindiff[k]): mindiff[k]=diff
# print('mindiff=',mindiff[k])
idx=np.unique(idx).tolist()
if -1 in idx: idx.remove(-1)
# print("idx: ",idx)
pos.append(np.array(p)[idx])
mymul=list(map(len,pos))
allpos=[]; alllabels=[]
for i,j in enumerate(mymul):
allpos+=pos[i].tolist(); alllabels+=[atmL1[i]]*j
atom_numbers=list(map(lambda L:atom_label2number[L],alllabels))
#-----------------------------------------------------------------------
if not has_multi: return (latt,allpos,atom_numbers)
tmp=(np.array(mymul)==multi)
# print(tmp)
if(tmp.all()): return (latt,allpos,atom_numbers)
#-----------the following is for mymul!=multi --------------------------
# If len(pos[i])>multi[i], then not all duplications are removed in pos[i].
# In this case, we use a larger tolerance mindiff[k]*2 to redo the
# duplication-removing procedure.
for k in (i for i in range(len(tmp)) if tmp[i]==False):
# print("pos2:\n",np.array(pos2[k]))
# print("pos:\n",pos[k].tolist())
p=pos[k]
idx=list(range(len(p)))
for i,pi in enumerate(p):
if idx[i]==-1: continue
for j in range(i+1,len(p)):
pj=p[j]
eq,diff,s=poseq(pi,pj,mindiff[k]*2)
if(eq): idx[j]=-1
idx=np.unique(idx).tolist()
if -1 in idx: idx.remove(-1)
# print("idx: ",idx)
pos[k]=np.array(p)[idx]
# print("pos(new):\n",pos[k].tolist())
# print(" # ", len(pos[k])==multi[k])
#-----------------------------------------------------------------------
allpos=[]; alllabels=[]
mymul=list(map(len,pos))
for i,j in enumerate(mymul):
allpos+=pos[i].tolist(); alllabels+=[atmL1[i]]*j
atom_numbers=list(map(lambda L:atom_label2number[L],alllabels))
return (latt,allpos,atom_numbers)
def getSGoperations(dataset):
spgnum=dataset['number']
p0=dataset['origin_shift']
Ri=dataset["rotations"]; vi=dataset["translations"] # input operations
P=dataset["transformation_matrix"]
(Q,S)=Q_and_S_from_spg_to_BC(spgnum,dataset['std_lattice'])
Rs=[0]*len(Ri); vs=[0]*len(Ri) # spglib standard operations, the same as ITA
RBC2=[0]*len(Ri); vBC2=[0]*len(Ri) # operatioons for the 2nd line in BC Tab.3.7, ITA setting, BC basic vectors
RBC1=[0]*len(Ri); vBC1=[0]*len(Ri) # operatioons for the 1st line in BC Tab.3.7
(gen1,t0,U,gen2)=SG_gen_elem[spgnum]
for j in range(len(Ri)):
Rs[j]=np.array(np.round(P@Ri[j]@np.mat(P).I).astype(int))
vs[j]=np.dot(P,vi[j])+p0-np.dot(Rs[j],p0)
RBC2[j]=np.array(np.mat(Q).I@Rs[j]@Q)
vBC2[j]=np.array(np.dot(np.mat(Q).I, vs[j]))[0]
RBC1[j]=np.array(np.mat(U).I@RBC2[j]@U)
vBC1[j]=np.array(np.dot(np.mat(U).I, vBC2[j]))[0]
vBC1[j]=vBC1[j]+t0-np.dot(RBC1[j],t0)
#--------------check if gen1 is corresponding to gen2 one by one----------
if gen2!=[]:
gen1_from2=[0]*len(gen1)
for i in range(len(gen1)):
R2=get_BC_rot_mat(spgnum,gen2[i][0],'A')
v2=gen2[i][1]
R1_from2=np.array(np.mat(U).I@R2@U)
v1_from2=np.array(np.dot(np.mat(U).I, v2))[0]
v1_from2=v1_from2+t0-np.dot(R1_from2,t0)
gen1_from2[i]=[get_BC_rot_name(spgnum,R1_from2), v1_from2]
gen1_from2=list(map(lambda g: [g[0],np.round(np.round(g[1],4)%1,4).tolist()], gen1_from2))
gen1_round=list(map(lambda g: [g[0],np.round(g[1],4).tolist()], gen1))
# print('#No. %3d gen1_round==gen1_from2: '%spgnum,(gen1_round==gen1_from2))
# print('gen1_round: ',gen1_round)
# print('gen1_from2: ',gen1_from2)
#--------------begin check BC Tab.3.7-------------------
ndig=4
gen1=list(map(lambda g: [g[0],np.round(g[1],ndig)], gen1))
gen2=list(map(lambda g: [g[0],np.round(g[1],ndig)], gen2))
set_gen1=set(list2tuple(gen1))
set_gen2=set(list2tuple(gen2))
set_BC1=[0]*len(Ri); set_BC2=[0]*len(Ri)
for j in range(len(Ri)):
set_BC1[j]=[get_BC_rot_name(spgnum,RBC1[j]),np.round(np.round(vBC1[j],ndig)%1,ndig)]
set_BC2[j]=[get_BC_rot_name(spgnum,RBC2[j],'A' if 38<=spgnum<=41 else 'C'),np.round(np.round(vBC2[j],ndig)%1,ndig)]
set_BC1=set(list2tuple(set_BC1))
set_BC2=set(list2tuple(set_BC2))
if (U==np.eye(3)).all(): star=""
elif (U==-np.eye(3)).all(): star="(tbd)"
else: star="(*)"
if not (t0==np.zeros(3)).all(): star+=" (t)"
# print(("#No. %3d "+star)%spgnum, "gen1 in BC1 and gen2 in BC2:",set_gen1.issubset(set_BC1), set_gen2.issubset(set_BC2))
# print('gen1:',set_gen1); print('gen2:',set_gen2); print('BC1:',set_BC1); print('BC2:',set_BC2); print()
#--------------end check BC Tab.3.7-------------------
return { 'input_rot': np.array(Ri), 'input_trans': np.array(vi),
'spg_std_rot': np.array(Rs), 'spg_std_trans': np.array(vs),
'BC_ITA_rot': np.array(RBC2), 'BC_ITA_trans': np.array(vBC2),
'BC_rot': np.array(RBC1), 'BC_trans': np.array(vBC1) }
def get_BZ_type(sgno, LBC):
brav=getSGlatt(sgno)
if brav in ("TricPrim","MonoPrim","MonoBase","OrthPrim","TetrPrim","HexaPrim",
"CubiPrim","CubiBody","CubiFace"): return brav
if brav=="OrthBase":
a=2*LBC[0,0]; b=-2*LBC[0,1]
BZtype=("a" if a>b else "b")
if brav=="OrthBody":
a,b,c=2*LBC[0]
if a==max(a,b,c): BZtype="a"
elif b==max(a,b,c): BZtype="b"
elif c==max(a,b,c): BZtype="c"
if brav=="OrthFace":
a=2*LBC[0,0]; b=-2*LBC[1,1]; c=2*LBC[0,2]
BZtype="a"
if 1/c**2>1/a**2+1/b**2: BZtype="b"
if 1/b**2>1/a**2+1/c**2: BZtype="c"
if 1/a**2>1/c**2+1/b**2: BZtype="d"
if brav=="TetrBody":
a=2*LBC[0,1]; c=2*LBC[0,2]
BZtype=("a" if a>c else "b")
if brav=="TrigPrim":
a=-LBC[0,1]; c=LBC[0,2]
BZtype=("a" if a>sqrt(2)*c else "b")
return brav+"("+BZtype+")"
def print_dataset(dataset, prec=1e-5):
spgnum=dataset['number']
p0=dataset['origin_shift']
print("# Space group: %s %3d"%(dataset['international'],spgnum),'\n')
Ri=dataset["rotations"]; vi=dataset["translations"]
P=dataset["transformation_matrix"]
ops=getSGoperations(dataset)
Rs=ops['spg_std_rot']; vs=ops['spg_std_trans']
RBC2=ops['BC_ITA_rot']; vBC2=ops['BC_ITA_trans']
RBC1=ops['BC_rot']; vBC1=ops['BC_trans']
print('# Symmetry operations:')
print('# (R0,v0): Operations on the input structure.')
print('# (Rs,vs): Standard operations in spglib, the same as ITA, using conventional basic vectors.')
print('# (RBC2,vBC2): The operations in the 2nd line of my revised BC Tab.3.7, transformed from the standard ITA\n#'+' '*14,
'operations by Q matrix, using the BC basic vectors in Tab.3.1 [note(v) for space group 38-41].')
print('# (RBC1,vBC1): The operations using by BC, i.e. the 1st line of BC Tab.3.7.\n')
print('# (R0,v0)',' '*23,'(Rs,vs)',' '*21,'(RBC2,vBC2)',' '*21,'(RBC1,vBC1)')
for j in range(len(Ri)):
print("# %-4d:"%(j+1), "%-5s"%getJonesOper(Ri[j],spgnum)," "*25,"%-5s"%getJonesOper(Rs[j],spgnum), " "*25,
"%-5s"%get_BC_rot_name(spgnum,RBC2[j],'A' if 38<=spgnum<=41 else 'C')," "*25,
"%-5s"%get_BC_rot_name(spgnum,RBC1[j]))
for k in (0,1,2):
print("%4d%4d%4d "%tuple(Ri[j,k]), "%- 12.8f"%chop(vi[j,k]), " "*4, end="")
print("%4d%4d%4d "%tuple(Rs[j,k]), "%- 12.8f"%chop(vs[j,k]), " "*4, end="")
print("%4g%4g%4g "%tuple(RBC2[j,k]), "%- 12.8f"%chop(vBC2[j,k])," "*4, end="")
print("%4g%4g%4g "%tuple(RBC1[j,k]), "%- 12.8f"%chop(vBC1[j,k]))
print()
(Q,S)=Q_and_S_from_spg_to_BC(spgnum,dataset['std_lattice'])
(gen1,t0,U,gen2)=SG_gen_elem[spgnum]
cells=get_all_cells(dataset, prec)
L0 =cells[1][0]; Ls =cells[2][0]; Lsi =cells[3][0]
LBC2=cells[4][0]; LBC1=cells[5][0]; LBC =cells[6][0]
print('# transformation_matrix [P]: (a0,b0,c0)=(as,bs,cs).P, and origin_shift p0 = O - Os:')
for i,j in zip(P,p0):
print(" %- 16.11g %- 16.11g %- 16.11g" % tuple(chop(i)), "% 28.10f"%chop(j))
print("# std_rotation_matrix (R): (as',bs',cs')=(R.as,R.bs,R.cs)")
for i in dataset['std_rotation_matrix']: print(" %- 16.11g %- 16.11g %- 16.11g" % tuple(chop(i)))
print("# transformation matrix [Q]: (t1BC2,t2BC2,t3BC2)=(as',bs',cs').Q")
for i in Q: print(" %- 16.11g %- 16.11g %- 16.11g" % tuple(chop(i)))
print("# transformation matrix [U]: and origin shift t0 = OBC2-OBC1: (t1BC1,t2BC1,t3BC1)=(t1BC2,t2BC2,t3BC2).U")
for i,j in zip(U,t0):