pyxtal.symmetry module
- Module for storing & accessing symmetry group information, including
Group class
Wyckoff_Position class.
Hall class
- class pyxtal.symmetry.Group(group, dim=3, use_hall=False, style='pyxtal', quick=False)[source]
Bases:
object
Class for storing a set of Wyckoff positions for a symmetry group. See the documentation for details about settings.
Examples
>>> from pyxtal.symmetry import Group >>> g = Group(64) >>> g -- Spacegroup --# 64 (Cmce)-- 16g site symm: 1 8f site symm: m.. 8e site symm: .2. 8d site symm: 2.. 8c site symm: -1 4b site symm: 2/m.. 4a site symm: 2/m..
one can access data such as symbol, number and Wyckoff_positions
>>> g.symbol 'Cmce' >>> g.number 64 >>> g.Wyckoff_positions[0] Wyckoff position 16g in space group 64 with site symmetry 1 x, y, z -x, -y+1/2, z+1/2 -x, y+1/2, -z+1/2 x, -y, -z -x, -y, -z x, y+1/2, -z+1/2 x, -y+1/2, z+1/2 -x, y, z x+1/2, y+1/2, z -x+1/2, -y+1, z+1/2 -x+1/2, y+1, -z+1/2 x+1/2, -y+1/2, -z -x+1/2, -y+1/2, -z x+1/2, y+1, -z+1/2 x+1/2, -y+1, z+1/2 -x+1/2, y+1/2, z
We also provide several utilities functions, e.g., one can search the possible wyckoff_combinations by a formula
>>> g.list_wyckoff_combinations([4, 2]) ([], [], []) >>> g.list_wyckoff_combinations([4, 8]) ([[['4a'], ['8c']], [['4a'], ['8d']], [['4a'], ['8e']], [['4a'], ['8f']], [['4b'], ['8c']], [['4b'], ['8d']], [['4b'], ['8e']], [['4b'], ['8f']]], [False, True, True, True, False, True, True, True], [[[6], [4]], [[6], [3]], [[6], [2]], [[6], [1]], [[5], [4]], [[5], [3]], [[5], [2]], [[5], [1]]] )
or search the subgroup information
>>> g.get_max_t_subgroup()['subgroup'] [12, 14, 15, 20, 36, 39, 41]
or check if a given composition is compatible with Wyckoff positions
>>> g = Group(225) >>> g.check_compatible([64, 28, 24]) (True, True)
or check the possible transition paths to a given supergroup
>>> g = Group(59) >>> g.search_supergroup_paths(139, 2) [[71, 139], [129, 139], [137, 139]]
- Parameters:
group – the group symbol or international number
(defult (dim) – 3): the periodic dimension of the group
(default (style) – False): whether or not use the hall number
(default – pyxtal): the choice of hall number (‘pyxtal’/’spglib’)
(defaut (quick) – False): whether or not ignore the wyckoff information
- add_k_transitions(path, n=1)[source]
Adds additional k transitions to a subgroup path. ONLY n = 1 is supported for now. It will return viable additions in front of each group in the path.
- Parameters:
path – a single result of search_subgroup_paths function
n – number of extra k transitions to add to the given path
- Returns:
a list of maximal subgroup chains with extra k type transitions
- cellsize()[source]
Returns the number of duplicate atoms in the conventional lattice (in contrast to the primitive cell). Based on the type of cell centering (P, A, C, I, R, or F)
- check_compatible(numIons, valid_orientations=None)[source]
Checks if the number of atoms is compatible with the Wyckoff positions. Considers the number of degrees of freedom for each Wyckoff position, and makes sure at least one valid combination of WP’s exists.
- Parameters:
numIons – list of integers
valid_orientations – list of possible orientations (molecule only)
- Returns:
True/False has_freedom: True/False
- Return type:
Compatible
- get_lists(numIon, used_indices)[source]
Compute the lists of possible mult/maxn/freedom/i_wp
- Parameters:
numIon – integer number of atoms
used_indices – a list of integer numbers
- get_lists_mol(numIon, used_indices, orientations)[source]
Compute the lists of possible mult/maxn/freedom/i_wp
- Parameters:
numIon – integer number of atoms
used_indices – a list of integer numbers
orientations – list of orientations
- get_max_subgroup(H)[source]
Returns the dicts for both t and k subgroup, H is just track the type QZ: the function name is not instructive, need to revise later
- get_site_dof(sites)[source]
compute the degree of freedom for each site :param sites: list, e.g. [‘4a’, ‘8b’] or [‘a’, ‘b’]
- Returns:
True or False
- get_splitters_from_relation(struc, relation)[source]
Get the valid symmetry relations for a structure to its supergroup e.g.,
- Parameters:
struc (-) – pyxtal structure
group_type (-) – t or k
- Returns:
list of valid transitions
- get_splitters_from_structure(struc, group_type='t')[source]
Get the valid symmetry relations for a structure to its supergroup e.g.,
- Parameters:
struc (-) – pyxtal structure
group_type (-) – t or k
- Returns:
list of valid transitions [(id, ([‘4a’], [‘4b’], [[‘4a’], [‘4c’]])]
- get_symmetry_directions()[source]
Table 2.1.3.1 from International Tables for Crystallography (2016). Vol. A, Chapter 2.1, pp. 142–174. including Primary, secondary and Tertiary
- get_valid_solutions(solutions)[source]
check if the solutions are valid a special WP such as (0,0,0) cannot be occupied twice
- Parameters:
solutions – list of solutions about the distibution of WP sites
- Returns:
the filtered solutions that are vaild
- get_wyckoff_position(index)[source]
Returns a single Wyckoff_position object.
- Parameters:
index – the index of the Wyckoff position within the group.
Returns: a Wyckoff_position object
- get_wyckoff_position_from_xyz(xyz, decimals=4)[source]
Returns a single Wyckoff_position object.
- Parameters:
xyz – a trial [x, y, z] coordinate
Returns: a Wyckoff_position object
- is_valid_combination(sites)[source]
check if the solutions are valid. A special WP with zero freedom (0,0,0) cannot be occupied twice.
- Parameters:
sites – list, e.g. [‘4a’, ‘8b’] or [‘a’, ‘b’]
- Returns:
True or False
- classmethod list_groups(dim=3)[source]
Function for quick print of groups and symbols.
- Parameters:
group – the group symbol or international number
dim – the periodic dimension of the group
- list_wyckoff_combinations(numIons, quick=False, numWp=(None, None), Nmax=10000000)[source]
List all possible wyckoff combinations for the given formula. Note this is really designed for a light weight calculation. If the solution space is big, set quick as True.
- Parameters:
numIons (list) – [12, 8]
quick ()Boolean) – quickly generate some solutions
numWp (tuple) – (min_wp, max_wp)
Nmax – maximumly allowed combinations
- Returns:
list of possible sites has_freedom: list of boolean numbers indices: list of wp indices
- Return type:
Combinations
- path_to_general_wp(index=1, max_steps=1)[source]
Find the path to transform the special wp into general site
- Parameters:
group – Group object
index – the index of starting wp
max_steps – the number of steps to search
- Returns:
a list of (g_types, subgroup_id, spg_number, wp_list (optional))
- path_to_subgroup(H)[source]
- For a given a path, extract the
a list of (g_types, subgroup_id, spg_number, wp_list (optional))
- search_subgroup_paths(G, max_layer=5)[source]
Search paths to transit to subgroup H. if - path1 is a>>e - path2 is a>>b>>c>>e path 2 will not be counted since path 1 exists
- Parameters:
G – final subgroup number
max_layer – the number of supergroup calculations needed.
- Returns:
list of possible paths ordered from H to G
- search_supergroup_paths(H, max_layer=5)[source]
Search paths to transit to super group H. if - path1 is a>>e - path2 is a>>b>>c>>e path 2 will not be counted since path 1 exists
- Parameters:
H – final supergroup number
max_layer – the number of supergroup calculations needed.
- Returns:
list of possible paths ordered from G to H
- class pyxtal.symmetry.Hall(spgnum, style='pyxtal', permutation=False)[source]
Bases:
object
Class for conversion between Hall and standard spacegroups http://cci.lbl.gov/sginfo/itvb_2001_table_a1427_hall_symbols.html
- Parameters:
spg_num – interger number between 1 and 230
style – spglib or pyxtal
permutation – allow permutation or not
- class pyxtal.symmetry.Wyckoff_position[source]
Bases:
object
Class for a single Wyckoff position within a symmetry group
Examples
>>> from pyxtal.symmetry import Wyckoff_position as wp >>> wp.from_group_and_index(19, 0) Wyckoff position 4a in space group 19 with site symmetry 1 x, y, z -x+1/2, -y, z+1/2 -x, y+1/2, -z+1/2 x+1/2, -y+1/2, -z
- are_equivalent_pts(pt1, pt2, cell=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]), tol=0.05)[source]
Check if two pts are equivalent
- distance_check(pt, lattice, tol)[source]
Given a list of fractional coordinates, merges them within a given tolerance, and checks if the merged coordinates satisfy a Wyckoff position.
- Parameters:
pt – the originl point (3-vector)
lattice – a 3x3 matrix representing the unit cell
tol – the cutoff distance for merging coordinates
- Returns:
True or False
- equivalent_set(index)[source]
Transform the wp to another equivalent set. Needs to update both wp and positions
- Parameters:
transformation – index
- from_group_and_index(index, dim=3, use_hall=False, style='pyxtal', wyckoffs=None)[source]
Creates a Wyckoff_position using the space group number and index
- Parameters:
group – the international number of the symmetry group
index – the index of the Wyckoff position within the group.
dim – the periodic dimension of the crystal
(default (style) – False): whether or not use the hall number
(default – pyxtal): ‘pyxtal’ or ‘spglib’ for hall number
- from_group_and_letter(letter, dim=3, style='pyxtal', hn=None)[source]
Creates a Wyckoff_position using the space group number and index
- Parameters:
group – the international number of the symmetry group
letter – e.g. 4a
dim – the periodic dimension of the crystal
style – ‘pyxtal’ or spglib, differing in the choice of origin
hn – hall_number
- from_index_quick(wyckoffs, index, P=None, P1=None)[source]
A short cut to create the WP object from a given index ignore the site symmetry and generators Mainly used for the update function
- Parameters:
wyckoffs – wyckoff position
index – index of wp
P – transformation matrix (rot + trans)
- from_symops(G)[source]
search Wyckoff Position by symmetry operations
- Parameters:
ops – a list of symmetry operations
G – the Group object
- Returns:
Wyckoff_position
- from_symops_wo_group()[source]
search Wyckoff Position by symmetry operations Now only supports space group symmetry Assuming general position only
- Parameters:
ops – a list of symmetry operations
- Returns:
Wyckoff_position
- get_all_positions(pos)[source]
return the list of position from any single coordinate from wp. The position does not have to be the 1st number in the wp list
>>> from pyxtal.symmetry import Group >>> wp2 = Group(62)[-1] >>> wp2 Wyckoff position 4a in space group 62 with site symmetry -1 0, 0, 0 1/2, 0, 1/2 0, 1/2, 0 1/2, 1/2, 1/2 >>> wp2.get_all_positions([1/2, 1/2, 1/2]) array([[0. , 0. , 0. ], [0.5, 0. , 0.5], [0. , 0.5, 0. ], [0.5, 0.5, 0.5]])
- get_euclidean_generator(cell, idx=0)[source]
return the symmetry operation object at the Euclidean space
- Parameters:
cell – 3*3 cell matrix
idx – the index of wp generator
- Returns:
pymatgen SymmOp object
- get_euclidean_symmetries()[source]
return the symmetry operation object at the Euclidean space
- Returns:
list of pymatgen SymmOp object
- has_equivalent_ops(wp2, tol=0.001)[source]
check if two wps are equivalent
- Parameters:
wp2 – wp object or list of operations
- merge(pt, lattice, tol, orientations=None, group=None)[source]
Given a list of fractional coordinates, merges them within a given tolerance, and checks if the merged coordinates satisfy a Wyckoff position.
- Parameters:
pt – the originl point (3-vector)
lattice – a 3x3 matrix representing the unit cell
tol – the cutoff distance for merging coordinates
orientations – the valid orientations for a given molecule.
- Returns:
3-vector after merge wp: a Wyckoff_position object, If no match, returns False. valid_ori: the valid orientations after merge
- Return type:
pt
- process_ops()[source]
handle some annoying cases e.g., in I2, [‘1/2, y, 1/2’, ‘0, y+1/2, 0’] can be transfered to [‘0, y, 0’, ‘1/2, y+1/2, 1/2’]
- project(point, cell=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]), PBC=[1, 1, 1], id=0)[source]
Given a 3-vector and a Wyckoff position operator, returns the projection onto the axis, plane, or point.
>>> wp.project_point([0,0.3,0.1], array([0. , 0.3, 0.1])
- Parameters:
point – a 3-vector (numeric list, tuple, or array)
cell – 3x3 matrix describing the unit cell vectors
PBC – A periodic boundary condition list, where 1 means periodic, 0 means not periodic. Ex: [1,1,1] -> full 3d periodicity, [0,0,1] -> 1d periodicity along the z axis
- Returns:
a transformed 3-vector (numpy array)
- search_all_generators(pos, ops=None, tol=0.01)[source]
search generator for a special Wyckoff position
- Parameters:
pos – initial xyz position
ops – list of symops
tol – tolerance
- Returns:
the position that matchs the standard setting
- Return type:
pos1
- search_generator(pos, ops=None, tol=0.01)[source]
search generator for a special Wyckoff position
- Parameters:
pos – initial xyz position
ops – list of symops
tol – tolerance
- Returns:
the position that matchs the standard setting
- Return type:
pos1
- search_generator_dist(pt, lattice=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]), group=None)[source]
For a given special wp, (e.g., [(x, 0, 1/4), (0, x, 1/4)]), return the first position and distance
- Parameters:
pt – 1*3 vector
lattice – 3*3 matrix
- Returns:
the best matched pt diff: numerical difference
- Return type:
pt
- short_distances(pt, lattice, tol)[source]
Given a list of fractional coordinates, merges them within a given tolerance, and checks if the merged coordinates satisfy a Wyckoff position.
- Parameters:
pt – the originl point (3-vector)
lattice – a 3x3 matrix representing the unit cell
tol – the cutoff distance for merging coordinates
- Returns:
a list of short distances
- transform_from_matrix(trans=None, reset=True, update=False)[source]
Transform the symmetry operation according to cell transformation Mostly needed when optimizing the lattice
- pyxtal.symmetry.abc2matrix(abc)[source]
convert the abc string representation to matrix :param abc: string like ‘a, b, c’ or ‘a+c, b, c’ or ‘a+1/4, b+1/4, c’
- Returns:
4*4 affine matrix
- pyxtal.symmetry.are_equivalent_ops(op1, op2, tol=0.01)[source]
check if two ops are equivalent, assuming the same ordering
- pyxtal.symmetry.check_symmetry_and_dim(number, dim=3)[source]
check if it is a valid number for the given symmetry
- Parameters:
number – int
dim – 0, 1, 2, 3
- pyxtal.symmetry.check_wyckoff_position(points, group, tol=0.001)[source]
Given a list of points, returns a single index of a matching Wyckoff position in the space group. Checks the site symmetry of each supplied point against the site symmetry for each point in the Wyckoff position. Also returns a point which can be used to generate the rest using the Wyckoff position operators.
- Parameters:
points – a list of 3d coordinates or SymmOps to check
group – a Group object
tol – the max distance between equivalent points
- Returns:
index is a single index for the Wyckoff position within the sg. If no matching WP is found, returns False. point is a coordinate taken from the list points. When plugged into the Wyckoff position, it will generate all the other points.
- Return type:
index, p
- pyxtal.symmetry.choose_wyckoff(G, number=None, site=None, dim=3)[source]
Choose a Wyckoff position to fill based on the current number of atoms needed to be placed within a unit cell Rules:
use the pre-assigned list if this is provided
The new position’s multiplicity is equal/less than (number).
We prefer positions with large multiplicity.
- Parameters:
G – a pyxtal.symmetry.Group object
number – the number of atoms still needed in the unit cell
site – the pre-assigned Wyckoff sites (e.g., 4a)
- Returns:
Wyckoff position. If no position is found, returns False
- pyxtal.symmetry.choose_wyckoff_mol(G, number, site, orientations, gen_site=True, dim=3)[source]
Choose a Wyckoff position to fill based on the current number of molecules needed to be placed within a unit cell
Rules:
The new position’s multiplicity is equal/less than (number).
We prefer positions with large multiplicity.
The site must admit valid orientations for the desired molecule.
- Parameters:
G – a pyxtal.symmetry.Group object
number – the number of molecules still needed in the unit cell
orientations – the valid orientations for a given molecule.
gen_site – general WP only
- Returns:
Wyckoff position. If no position is found, returns False
- pyxtal.symmetry.get_close_packed_groups(pg)[source]
List the close packed groups based on the molcular symmetry Compiled from AIK Book, Table 2 P34
- Parameters:
pg – point group symbol
- Returns:
list of space group numbers
- pyxtal.symmetry.get_generators(num, dim=3)[source]
Returns a list of Wyckoff generators for a given group. 1st index: index of WP in sg (0 is the WP with largest multiplicity) 2nd index: a generator for the WP This function is useful for rotating molecules based on Wyckoff position, since special Wyckoff positions only encode positional information, but not information about the orientation. The generators for each Wyckoff position form a subset of the spacegroup’s general Wyckoff position.
- Parameters:
num – the international spacegroup number
dim – dimension
- Returns:
a 2d list of symmop objects [[wp0], [wp1], … ]
- pyxtal.symmetry.get_point_group(number)[source]
Parse the point group symmetry info from space group. According to http://img.chem.ucl.ac.uk/sgp/misc/pointgrp.htm, among 32(230) point(space) groups, there are
10(68) polar groups,
11(92) centrosymmetric groups,
11(65) enantiomorphic groups
- Parameters:
number – space group number
- Returns:
point group symbol polar: 1, 2, m, mm2, 3, 3m, 4, 4mm, 6, 6mm centrosymmetry: -1, 2/m, mmm, 4/m, 4/mmm, -3, -3m, 6/m, 6/mmm, m-3, m-3m enantiomorphic: 1, 2, 222, 4, 422, 3, 32, 6, 622, 23, 432
- pyxtal.symmetry.get_symbol_and_number(input_group, dim=3)[source]
Function for quick conversion between symbols and numbers.
- Parameters:
input_group – the group symbol or international number
dim – the periodic dimension of the group
- pyxtal.symmetry.get_symmetry_directions(lattice_type, symbol='P', unique_axis='b')[source]
Get the symmetry directions
- pyxtal.symmetry.get_symmetry_from_ops(ops, tol=1e-05)[source]
get the hall number from symmetry operations.
- Parameters:
ops – tuple of (rotation, translation) or list of strings
tol – tolerance
- pyxtal.symmetry.get_wyckoff_symmetry(num, dim=3)[source]
Returns a list of site symmetry for a given group. 1st index: index of WP in sg (0 is the WP with largest multiplicity) 2nd index: a point within the WP 3rd index: a site symmetry SymmOp of the point
- Parameters:
sg – the international spacegroup number
dim – 0, 1, 2, 3
- Returns:
a 3d list of SymmOp objects representing the site symmetry of each point in each Wyckoff position
- pyxtal.symmetry.get_wyckoffs(num, organized=False, dim=3)[source]
Returns a list of Wyckoff positions for a given group. Has option to organize the list based on multiplicity (this is used for random_crystal.wyckoffs)
For an unorganized list:
1st index: index of WP in sg (0 is the WP with largest multiplicity)
2nd index: a SymmOp object in the WP
For an organized list:
1st index: specifies multiplicity (0 is the largest multiplicity)
2nd index: a WP within the group of equal multiplicity.
3nd index: a SymmOp object within the Wyckoff position
You may switch between organized and unorganized lists using the methods i_from_jk and jk_from_i. For example, if a Wyckoff position is the [i] entry in an unorganized list, it will be the [j][k] entry in an organized list.
- Parameters:
num – the international group number
dim – dimension [0, 1, 2, 3]
organized – whether or not to organize the list based on multiplicity
- Returns:
a list of Wyckoff positions, each of which is a list of SymmOp’s
- pyxtal.symmetry.index_from_letter(letter, group, dim=3)[source]
Given the Wyckoff letter, returns the index of a Wyckoff position.
- Parameters:
letter – The wyckoff letter
group – an unorganized Wyckoff position array or Group object (preferred)
dim – the periodicity dimension of the symmetry group.
- Returns:
a single index specifying the location of the Wyckoff position.
- pyxtal.symmetry.jk_from_i(i, olist)[source]
Given an organized list (Wyckoff positions or orientations), determine the two indices which correspond to a single index for an unorganized list. Used mainly for organized Wyckoff position lists, but can be used for other lists organized in a similar way
- Parameters:
i – a single index corresponding to the item’s location in the unorganized list
olist – the organized list
- Returns:
- two indices corresponding to the item’s location in the
organized list
- Return type:
[j, k]
- pyxtal.symmetry.letter_from_index(index, group, dim=3)[source]
Given a Wyckoff position’s index within a spacegroup, return its number and letter e.g. ‘4a’
- Parameters:
index – WP’s index (0 is the general position)
group – an unorganized Wyckoff position array or Group object (preferred)
dim – the periodicity dimension of the symmetry group.
- Returns:
the Wyckoff letter corresponding to the Wyckoff position (for example, for position 4a, the function would return ‘a’)
- pyxtal.symmetry.op_transform(ops, affine_matrix)[source]
x, y, z -> x+1/2, y+1/2, z 0, 1/2, z -> 1/2, 0, z
- Parameters:
ops – SymmOp object
permutation – list, e.g. [0, 1, 2]
- Returns:
the new SymmOp object
- pyxtal.symmetry.organized_wyckoffs(group)[source]
Takes a Group object or unorganized list of Wyckoff positions and returns a 2D list of Wyckoff positions organized by multiplicity.
- Parameters:
group – a pyxtal.symmetry.Group object
- Returns:
a 2D list of Wyckoff_position objects if group is a Group object. a 3D list of SymmOp objects if group is a 2D list of SymmOps
- pyxtal.symmetry.para2ferro(pg)[source]
88 potential paraelectric-to-ferroelectric phase transitions https://journals.aps.org/prb/abstract/10.1103/PhysRevB.2.754 https://pubs.rsc.org/en/content/articlelanding/2016/cs/c5cs00308c
- Parameters:
group (paraelectric point)
- Returns:
list of ferroelectric point groups
- pyxtal.symmetry.search_cloest_wp(G, wp, op, pos)[source]
For a given position, search for the cloest wp which satisfies the desired symmetry relation, e.g., for pos (0.1, 0.12, 0.2) and op (x, x, z) the closest match is (0.11, 0.11, 0.2)
- Parameters:
G – space group number
wp – Wyckoff object
op – symmetry operation belonging to wp
pos – initial xyz position
- Returns:
the position that matchs symmetry operation
- Return type:
pos1
- pyxtal.symmetry.site_symm(point, gen_pos, tol=0.001, lattice=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]), PBC=None)[source]
Given a point and a general Wyckoff position, return the list of symmetry operations leaving the point (coordinate or SymmOp) invariant. The returned SymmOps are a subset of the general position. The site symmetry can be used for determining the Wyckoff position for a set of points, or for determining the valid orientations of a molecule within a given Wyckoff position.
- Parameters:
point – a 1x3 coordinate or SymmOp object to find the symmetry of. If a SymmOp is given, the returned symmetries must also preserve the point’s orientaion
gen_pos – the general position of the spacegroup. Can be a Wyckoff_position object or list of SymmOp objects.
tol – the numberical tolerance for determining equivalent positions and orientations.
lattice – a 3x3 matrix representing the lattice vectors of the unit cell
PBC – A periodic boundary condition list, 1 means periodic, 0 means not periodic. Ex: [1,1,1] -> full 3d periodicity, [0,0,1] -> periodicity along the z axis. Need not be defined here if gen_pos is a Wyckoff_position object.
- Returns:
a list of SymmOp objects which leave the given point invariant
- class pyxtal.symmetry.site_symmetry(ops, lattice_type, hm_symbol)[source]
Bases:
object
Derive the site symmetry group from symmetry operations site-symmetry group is indicated by an oriented symbol, which is a variation of the Hermann–Mauguin point-group symbol that provides information about the orientation of the symmetry elements. The constituents of the oriented symbol are ordered according to the symmetry directions of the corresponding crystal lattice (primary, secondary and tertiary)
- Parameters:
ops – a list of SymmOp objects representing the site symmetry
lattice_type (str) – e.g., ‘cubic’
hm_symbol (str) – hm_symbol for lattice ‘P’, ‘R’
- Returns:
a string representing the site symmetry (e.g., 2mm)
- set_full_hm_symbols(tables)[source]
Set the full hm symbols for each axis
- Parameters:
tables – sorted table with (list of symmetry elements, symbols, order)
- Returns:
a list of symmetry elements on {primary, secondary, tertiery} directions
- to_beautiful_matrix_representation(skip=True)[source]
A shortcut to check the representation
- Parameters:
skip (bool) – whether or not skip 1 or -1 symmetry
- to_matrix_representation()[source]
To create a 15 * 14 binary matrix to represent the symmetry elements on each axes #[1, -1, 2, m, 3, 2/m, 4, -3, 6, 4/m, -6, 6/m] [1, -1, 2, m, 3, 4, -3, 6, -6]
- pyxtal.symmetry.swap_xyz_ops(ops, permutation)[source]
change the symmetry operation by swaping the axes
- Parameters:
ops – SymmOp object
permutation – list, e.g. [0, 1, 2]
- Returns:
the new xyz string after transformation
- pyxtal.symmetry.swap_xyz_string(xyzs, permutation)[source]
Permutate the xyz string operation
- Parameters:
xyzs – e.g. [‘x’, ‘y+1/2’, ‘-z’]
permuation – list, e.g., [0, 2, 1]
- Returns:
the new xyz string after transformation
- pyxtal.symmetry.symmetry_element_from_axis(axis)[source]
Given an axis, returns a SymmOp representing a symmetry element on the axis. For example, the symmetry element for the vector (0,0,2) would be (0,0,z).
- Parameters:
axis – a 3-vector representing the symmetry element
- Returns:
a SymmOp object of form (ax, bx, cx), (ay, by, cy), or (az, bz, cz)