"""
Module for storing and accessing symmetry group information, including a Group class and
a Wyckoff_Position class. These classes are used for generation of random structures.
"""
#Imports
#------------------------------
#Standard Libraries
from pkg_resources import resource_filename
#External Libraries
from pymatgen.symmetry.analyzer import generate_full_symmops
from pandas import read_csv
from monty.serialization import loadfn
#PyXtal imports
from pyxtal.operations import *
#Constants
#------------------------------
letters = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
wyckoff_df = read_csv(resource_filename("pyxtal", "database/wyckoff_list.csv"))
wyckoff_symmetry_df = read_csv(resource_filename("pyxtal", "database/wyckoff_symmetry.csv"))
wyckoff_generators_df = read_csv(resource_filename("pyxtal", "database/wyckoff_generators.csv"))
layer_df = read_csv(resource_filename("pyxtal", "database/layer.csv"))
layer_symmetry_df = read_csv(resource_filename("pyxtal", "database/layer_symmetry.csv"))
layer_generators_df = read_csv(resource_filename("pyxtal", "database/layer_generators.csv"))
rod_df = read_csv(resource_filename("pyxtal", "database/rod.csv"))
rod_symmetry_df = read_csv(resource_filename("pyxtal", "database/rod_symmetry.csv"))
rod_generators_df = read_csv(resource_filename("pyxtal", "database/rod_generators.csv"))
point_df = read_csv(resource_filename("pyxtal", "database/point.csv"))
point_symmetry_df = read_csv(resource_filename("pyxtal", "database/point_symmetry.csv"))
point_generators_df = read_csv(resource_filename("pyxtal", "database/point_generators.csv"))
symbols = loadfn(resource_filename("pyxtal", "database/symbols.json"))
Identity = SymmOp.from_xyz_string('x,y,z')
Inversion = SymmOp.from_xyz_string('-x,-y,-z')
op_o = SymmOp.from_xyz_string('0,0,0')
op_x = SymmOp.from_xyz_string('x,0,0')
op_y = SymmOp.from_xyz_string('0,y,0')
op_z = SymmOp.from_xyz_string('0,0,z')
pglist = ['C1','Ci','C2','Cs','C2h','D2','C2v','D2h',
'C4','S4','C4h','D4','C4v','D2d','D4h','C3',
'C3i','D3','C3v','D3d','C6','C3h','C6h','D6',
'C6v','D3h','D6h','T','Th','O','Td','Oh',
'C5', 'C7', 'C8',
'D5', 'D7', 'D8',
'C5v', 'C7v', 'C8v',
'C5h',
'D5h', 'D7h', 'D8h',
'D4d', 'D5d', 'D6d', 'D7d', 'D8d',
'S6', 'S8', 'S10', 'S12',
'I', 'Ih',
'C*', 'C*h']
#TODO: Add space, layer, and Rod group symbol lists
#Define functions
#------------------------------
def list_point_groups():
"""
Prints out the numbers and symbols of the crystallographic point groups
"""
print("-- Point group numbers and symbols --")
for i, sym in enumerate(pglist):
print(" " + str(i+1) + ": " + sym)
def symmetry_element_from_axis(axis):
"""
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).
Args:
axis: a 3-vector representing the symmetry element
Returns:
a SymmOp object of form (ax, bx, cx), (ay, by, cy), or (az, bz, cz)
"""
if len(axis) != 3:
return
#Vector must be non-zero
if dsquared(axis) < 1e-6:
return
v = np.array(axis) / np.linalg.norm(axis)
#Find largest component (x, y, or z)
abs_vals = [abs(a) for a in v]
f1 = max(abs_vals)
index1 = list(abs_vals).index(f1)
#Initialize an affine matrix
m = np.eye(4)
m[:3] = [0.,0.,0.,0.]
#Set values for affine matrix
m[:3,index1] = v
return SymmOp(m)
def get_wyckoffs(sg, organized=False, PBC=[1,1,1]):
"""
Returns a list of Wyckoff positions for a given space 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: corresponds to a Wyckoff position within the group of equal
multiplicity.
3nd index: corresponds to 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.
Args:
sg: the international spacegroup number
organized: whether or not to organize the list based on multiplicity
PBC: A periodic boundary condition list, where 1 means periodic, 0 means not periodic.
Ex: [1,1,1] -> full 3d periodicity, [0,0,1] -> periodicity along the z axis
Returns:
a list of Wyckoff positions, each of which is a list of SymmOp's
"""
if PBC != [1,1,1]:
coor = [0,0,0]
for i, a in enumerate(PBC):
if not a:
coor[i] = 0.5
coor = np.array(coor)
wyckoff_strings = eval(wyckoff_df["0"][sg])
wyckoffs = []
for x in wyckoff_strings:
if PBC != [1,1,1]:
op = SymmOp.from_xyz_string(x[0])
coor1 = op.operate(coor)
invalid = False
for i, a in enumerate(PBC):
if not a:
if not abs(coor1[i]-0.5) < 1e-2:
#invalid wyckoffs for layer group
invalid = True
if invalid is False:
wyckoffs.append([])
for y in x:
wyckoffs[-1].append(SymmOp.from_xyz_string(y))
else:
wyckoffs.append([])
for y in x:
wyckoffs[-1].append(SymmOp.from_xyz_string(y))
if organized:
wyckoffs_organized = [[]] #2D Array of WP's organized by multiplicity
old = len(wyckoffs[0])
for wp in wyckoffs:
mult = len(wp)
if mult != old:
wyckoffs_organized.append([])
old = mult
wyckoffs_organized[-1].append(wp)
return wyckoffs_organized
else:
return wyckoffs
def get_layer(num, organized=False):
"""
Returns a list of Wyckoff positions for a given 2D layer group. Has
option to organize the list based on multiplicity (this is used for
random_crystal_2D.wyckoffs) For an unorganized list:
1st index: index of WP in layer group (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: corresponds to a Wyckoff position within the group of equal
multiplicity.
3nd index: corresponds to 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.
For layer groups with more than one possible origin, origin choice 2 is
used.
Args:
num: the international layer group number
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
"""
wyckoff_strings = eval(layer_df["0"][num])
wyckoffs = []
for x in wyckoff_strings:
wyckoffs.append([])
for y in x:
wyckoffs[-1].append(SymmOp.from_xyz_string(y))
if organized:
wyckoffs_organized = [[]] #2D Array of WP's organized by multiplicity
old = len(wyckoffs[0])
for wp in wyckoffs:
mult = len(wp)
if mult != old:
wyckoffs_organized.append([])
old = mult
wyckoffs_organized[-1].append(wp)
return wyckoffs_organized
else:
return wyckoffs
def get_rod(num, organized=False):
"""
Returns a list of Wyckoff positions for a given 1D Rod group. Has option to
organize the list based on multiplicity (this is used for
random_crystal_1D.wyckoffs) For an unorganized list:
1st index: index of WP in layer group (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: corresponds to a Wyckoff position within the group of equal
multiplicity.
3nd index: corresponds to 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.
For Rod groups with more than one possible setting, setting choice 1
is used.
Args:
num: the international Rod group number
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
"""
wyckoff_strings = eval(rod_df["0"][num])
wyckoffs = []
for x in wyckoff_strings:
wyckoffs.append([])
for y in x:
wyckoffs[-1].append(SymmOp.from_xyz_string(y))
if organized:
wyckoffs_organized = [[]] #2D Array of WP's organized by multiplicity
old = len(wyckoffs[0])
for wp in wyckoffs:
mult = len(wp)
if mult != old:
wyckoffs_organized.append([])
old = mult
wyckoffs_organized[-1].append(wp)
return wyckoffs_organized
else:
return wyckoffs
def get_point(num, organized=False):
"""
Returns a list of Wyckoff positions for a given crystallographic point group.
Has option to organize the list based on multiplicity.
1st index: index of WP in layer group (0 is the WP with largest multiplicity)
2nd index: a SymmOp object in the WP
For point groups except T, Th, O, Td, and Oh, unique axis z is used.
Args:
num: the point group number (see bottom of source code for a list)
organized: whether or not to organize the list based on multiplicity
molecular: whether or not to convert to Euclidean reference frame
(for hexagonal lattices: point groups 16-27)
Returns:
a list of Wyckoff positions, each of which is a list of SymmOp's
"""
wyckoff_strings = eval(point_df["0"][num])
wyckoffs = []
for x in wyckoff_strings:
wyckoffs.append([])
for y in x:
op = SymmOp(y)
wyckoffs[-1].append(op)
if organized:
wyckoffs_organized = [[]] #2D Array of WP's organized by multiplicity
old = len(wyckoffs[0])
for wp in wyckoffs:
mult = len(wp)
if mult != old:
wyckoffs_organized.append([])
old = mult
wyckoffs_organized[-1].append(wp)
return wyckoffs_organized
else:
return wyckoffs
def get_wyckoff_symmetry(sg, PBC=[1,1,1], molecular=False):
"""
Returns a list of Wyckoff position site symmetry for a given space 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
Args:
sg: the international spacegroup number
PBC: A periodic boundary condition list, where 1 means periodic, 0 means not periodic.
Ex: [1,1,1] -> full 3d periodicity, [0,0,1] -> periodicity along the z axis
molecular: whether or not to return the Euclidean point symmetry
operations. If True, cuts off translational part of operation, and
converts non-orthogonal operations (3-fold and 6-fold rotations)
to (orthogonal) pure rotations. Should be used when dealing with
molecular crystals
Returns:
a 3d list of SymmOp objects representing the site symmetry of each
point in each Wyckoff position
"""
if PBC != [1,1,1]:
coor = [0,0,0]
for i, a in enumerate(PBC):
if not a:
coor[i] = 0.5
coor = np.array(coor)
wyckoffs = get_wyckoffs(sg, PBC=PBC)
P = SymmOp.from_rotation_and_translation([[1,-.5,0],[0,math.sqrt(3)/2,0],[0,0,1]], [0,0,0])
symmetry_strings = eval(wyckoff_symmetry_df["0"][sg])
symmetry = []
convert = False
if molecular is True:
if sg >= 143 and sg <= 194:
convert = True
#Loop over Wyckoff positions
for x, w in zip(symmetry_strings, wyckoffs):
if PBC != [1,1,1]:
op = w[0]
coor1 = op.operate(coor)
invalid = False
for i, a in enumerate(PBC):
if not a:
if not abs(coor1[i]-0.5) < 1e-2:
invalid = True
if invalid == False:
symmetry.append([])
#Loop over points in WP
for y in x:
symmetry[-1].append([])
#Loop over ops
for z in y:
op = SymmOp.from_xyz_string(z)
if convert is True:
#Convert non-orthogonal trigonal/hexagonal operations
op = P*op*P.inverse
if molecular is False:
symmetry[-1][-1].append(op)
elif molecular is True:
op = SymmOp.from_rotation_and_translation(op.rotation_matrix,[0,0,0])
symmetry[-1][-1].append(op)
else:
symmetry.append([])
#Loop over points in WP
for y in x:
symmetry[-1].append([])
#Loop over ops
for z in y:
op = SymmOp.from_xyz_string(z)
if convert is True:
#Convert non-orthogonal trigonal/hexagonal operations
op = P*op*P.inverse
if molecular is False:
symmetry[-1][-1].append(op)
elif molecular is True:
op = SymmOp.from_rotation_and_translation(op.rotation_matrix,[0,0,0])
symmetry[-1][-1].append(op)
return symmetry
def get_layer_symmetry(num, molecular=False):
"""
Returns a list of Wyckoff position site symmetry for a given space group.
1st index: index of WP in group (0 is the WP with largest multiplicity)
2nd index: a point within the WP
3rd index: a site symmetry SymmOp of the point
Args:
num: the layer group number
molecular: whether or not to return the Euclidean point symmetry
operations. If True, cuts off translational part of operation, and
converts non-orthogonal operations (3-fold and 6-fold rotations)
to (orthogonal) pure rotations. Should be used when dealing with
molecular crystals
Returns:
a 3d list of SymmOp objects representing the site symmetry of each
point in each Wyckoff position
"""
P = SymmOp.from_rotation_and_translation([[1,-.5,0],[0,math.sqrt(3)/2,0],[0,0,1]], [0,0,0])
symmetry_strings = eval(layer_symmetry_df["0"][num])
symmetry = []
convert = False
if molecular is True:
if num >= 65:
convert = True
#Loop over Wyckoff positions
for x in symmetry_strings:
symmetry.append([])
#Loop over points in WP
for y in x:
symmetry[-1].append([])
#Loop over ops
for z in y:
op = SymmOp.from_xyz_string(z)
if convert is True:
#Convert non-orthogonal trigonal/hexagonal operations
op = P*op*P.inverse
if molecular is False:
symmetry[-1][-1].append(op)
elif molecular is True:
op = SymmOp.from_rotation_and_translation(op.rotation_matrix,[0,0,0])
symmetry[-1][-1].append(op)
return symmetry
def get_rod_symmetry(num, molecular=False):
"""
Returns a list of Wyckoff position site symmetry for a given Rod group.
1st index: index of WP in group (0 is the WP with largest multiplicity)
2nd index: a point within the WP
3rd index: a site symmetry SymmOp of the point
Args:
num: the Rod group number
molecular: whether or not to return the Euclidean point symmetry
operations. If True, cuts off translational part of operation, and
converts non-orthogonal operations (3-fold and 6-fold rotations)
to (orthogonal) pure rotations. Should be used when dealing with
molecular crystals
Returns:
a 3d list of SymmOp objects representing the site symmetry of each
point in each Wyckoff position
"""
P = SymmOp.from_rotation_and_translation([[1,-.5,0],[0,math.sqrt(3)/2,0],[0,0,1]], [0,0,0])
symmetry_strings = eval(rod_symmetry_df["0"][num])
symmetry = []
convert = False
if molecular is True:
if num >= 42:
convert = True
#Loop over Wyckoff positions
for x in symmetry_strings:
symmetry.append([])
#Loop over points in WP
for y in x:
symmetry[-1].append([])
#Loop over ops
for z in y:
op = SymmOp.from_xyz_string(z)
if convert is True:
#Convert non-orthogonal trigonal/hexagonal operations
op = P*op*P.inverse
if molecular is False:
symmetry[-1][-1].append(op)
elif molecular is True:
op = SymmOp.from_rotation_and_translation(op.rotation_matrix,[0,0,0])
symmetry[-1][-1].append(op)
return symmetry
def get_point_symmetry(num):
"""
Returns a list of Wyckoff position site symmetry for a given point group.
1st index: index of WP in group (0 is the WP with largest multiplicity)
2nd index: a point within the WP
3rd index: a site symmetry SymmOp of the point
Args:
num: the point group number
molecular: whether or not to convert to Euclidean reference frame
(for hexagonal lattices: point groups 16-27)
Returns:
a 3d list of SymmOp objects representing the site symmetry of each
point in each Wyckoff position
"""
symmetry_strings = eval(point_symmetry_df["0"][num])
symmetry = []
#Loop over Wyckoff positions
for wp in symmetry_strings:
symmetry.append([])
#Loop over points in WP
for point in wp:
symmetry[-1].append([])
#Loop over ops
for m in point:
op = SymmOp(m)
symmetry[-1][-1].append(op)
return symmetry
def get_wyckoff_generators(sg, PBC=[1,1,1], molecular=False):
"""
Returns a list of Wyckoff generators for a given space 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.
Args:
sg: the international spacegroup number
PBC: A periodic boundary condition list, where 1 means periodic, 0 means not periodic.
Ex: [1,1,1] -> full 3d periodicity, [0,0,1] -> periodicity along the z axis
molecular: whether or not to return the Euclidean point symmetry
operations. If True, cuts off translational part of operation, and
converts non-orthogonal operations (3-fold and 6-fold rotations)
to (orthogonal) pure rotations. Should be used when dealing with
molecular crystals
Returns:
a 2d list of SymmOp objects which can be used to generate a Wyckoff position given a
single fractional (x,y,z) coordinate
"""
if PBC != [1,1,1]:
coor = [0,0,0]
for i, a in enumerate(PBC):
if not a:
coor[i] = 0.5
coor = np.array(coor)
wyckoffs = get_wyckoffs(sg, PBC=PBC)
P = SymmOp.from_rotation_and_translation([[1,-.5,0],[0,math.sqrt(3)/2,0],[0,0,1]], [0,0,0])
generator_strings = eval(wyckoff_generators_df["0"][sg])
generators = []
convert = False
if molecular is True:
if sg >= 143 and sg <= 194:
convert = True
#Loop over Wyckoff positions
for x, w in zip(generator_strings, wyckoffs):
if PBC != [1,1,1]:
op = w[0]
coor1 = op.operate(coor)
invalid = False
for i, a in enumerate(PBC):
if not a:
if not abs(coor1[i]-0.5) < 1e-2:
invalid = True
if invalid == False:
generators.append([])
#Loop over ops
for y in x:
op = SymmOp.from_xyz_string(y)
if convert is True:
#Convert non-orthogonal trigonal/hexagonal operations
op = P*op*P.inverse
if molecular is False:
generators[-1].append(op)
elif molecular is True:
op = SymmOp.from_rotation_and_translation(op.rotation_matrix,[0,0,0])
generators[-1].append(op)
else:
generators.append([])
for y in x:
op = SymmOp.from_xyz_string(y)
if convert is True:
#Convert non-orthogonal trigonal/hexagonal operations
op = P*op*P.inverse
if molecular is False:
generators[-1].append(op)
elif molecular is True:
op = SymmOp.from_rotation_and_translation(op.rotation_matrix,[0,0,0])
generators[-1].append(op)
return generators
def get_layer_generators(num, molecular=False):
"""
Returns a list of Wyckoff generators for a given layer group.
1st index: index of WP in group (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 group's general Wyckoff position.
Args:
num: the layer group number
molecular: whether or not to return the Euclidean point symmetry
operations. If True, cuts off translational part of operation, and
converts non-orthogonal operations (3-fold and 6-fold rotations)
to (orthogonal) pure rotations. Should be used when dealing with
molecular crystals
Returns:
a 2d list of SymmOp objects which can be used to generate a Wyckoff position given a
single fractional (x,y,z) coordinate
"""
P = SymmOp.from_rotation_and_translation([[1,-.5,0],[0,math.sqrt(3)/2,0],[0,0,1]], [0,0,0])
generator_strings = eval(layer_generators_df["0"][num])
generators = []
convert = False
if molecular is True:
if num >= 65:
convert = True
#Loop over Wyckoff positions
for x in generator_strings:
generators.append([])
#Loop over ops
for y in x:
op = SymmOp.from_xyz_string(y)
if convert is True:
#Convert non-orthogonal trigonal/hexagonal operations
op = P*op*P.inverse
if molecular is False:
generators[-1].append(op)
elif molecular is True:
op = SymmOp.from_rotation_and_translation(op.rotation_matrix,[0,0,0])
generators[-1].append(op)
return generators
def get_rod_generators(num, molecular=False):
"""
Returns a list of Wyckoff generators for a given Rod group.
1st index: index of WP in group (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 group's general Wyckoff position.
Args:
num: the Rod group number
molecular: whether or not to return the Euclidean point symmetry
operations. If True, cuts off translational part of operation, and
converts non-orthogonal operations (3-fold and 6-fold rotations)
to (orthogonal) pure rotations. Should be used when dealing with
molecular crystals
Returns:
a 2d list of SymmOp objects which can be used to generate a Wyckoff position given a
single fractional (x,y,z) coordinate
"""
P = SymmOp.from_rotation_and_translation([[1,-.5,0],[0,math.sqrt(3)/2,0],[0,0,1]], [0,0,0])
generator_strings = eval(rod_generators_df["0"][num])
generators = []
convert = False
if molecular is True:
if num >= 42:
convert = True
#Loop over Wyckoff positions
for x in generator_strings:
generators.append([])
#Loop over ops
for y in x:
op = SymmOp.from_xyz_string(y)
if convert is True:
#Convert non-orthogonal trigonal/hexagonal operations
op = P*op*P.inverse
if molecular is False:
generators[-1].append(op)
elif molecular is True:
op = SymmOp.from_rotation_and_translation(op.rotation_matrix,[0,0,0])
generators[-1].append(op)
return generators
def get_point_generators(num):
"""
Returns a list of Wyckoff generators for a given point group.
1st index: index of WP in group (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 group's general Wyckoff position.
Args:
num: the Rod group number
molecular: whether or not to convert to Euclidean reference frame
(for hexagonal lattices: point groups 16-27)
Returns:
a 2d list of SymmOp objects which can be used to generate a Wyckoff position given a
single fractional (x,y,z) coordinate
"""
generator_strings = eval(point_generators_df["0"][num])
generators = []
#Loop over Wyckoff positions
for x in generator_strings:
generators.append([])
#Loop over ops
for y in x:
op = SymmOp(y)
generators[-1].append(op)
return generators
def general_position(number, dim=3):
"""
Returns a Wyckoff_position object for the general Wyckoff position of the given
group.
Args:
number: the international number of the group
dim: the dimension of the group 3: space group, 2: layer group, 1: Rod group
Returns:
a Wyckoff_position object for the general position
"""
return Wyckoff_position.from_group_and_index(number, 0, dim=dim)
def site_symm(point, gen_pos, tol=1e-3, lattice=Euclidean_lattice, PBC=None):
"""
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.
Args:
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.
Can be obtained using general_position()
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, where 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
"""
if PBC == None:
if type(gen_pos) == Wyckoff_position:
PBC = gen_pos.PBC
else:
PBC=[1,1,1]
#Convert point into a SymmOp
if type(point) != SymmOp:
point = SymmOp.from_rotation_and_translation([[0,0,0],[0,0,0],[0,0,0]], np.array(point))
symmetry = []
for op in gen_pos:
is_symmetry = True
#Calculate the effect of applying op to point
difference = SymmOp((op*point).affine_matrix - point.affine_matrix)
#Check that the rotation matrix is unaltered by op
if not np.allclose(difference.rotation_matrix, np.zeros((3,3)), rtol = 1e-3, atol = 1e-3):
is_symmetry = False
#Check that the displacement is less than tol
displacement = difference.translation_vector
if distance(displacement, lattice, PBC=PBC) > tol:
is_symmetry = False
if is_symmetry:
"""The actual site symmetry's translation vector may vary from op by
a factor of +1 or -1 (especially when op contains +-1/2).
We record this to distinguish between special Wyckoff positions.
As an example, consider the point (-x+1/2,-x,x+1/2) in position 16c
of space group Ia-3(206). The site symmetry includes the operations
(-z+1,x-1/2,-y+1/2) and (y+1/2,-z+1/2,-x+1). These operations are
not listed in the general position, but correspond to the operations
(-z,x+1/2,-y+1/2) and (y+1/2,-z+1/2,-x), respectively, just shifted
by (+1,-1,0) and (0,0,+1), respectively.
"""
el = SymmOp.from_rotation_and_translation(op.rotation_matrix, op.translation_vector - np.round(displacement))
symmetry.append(el)
return symmetry
def check_wyckoff_position(points, group, tol=1e-3):
"""
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
Args:
points: a list of 3d coordinates or SymmOps to check
group: a Group object
tol: the max distance between equivalent points
Returns:
index, p: 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.
"""
points = np.array(points)
wyckoffs = group.wyckoffs
w_symm_all = group.w_symm
PBC = group.PBC
#new method
#Store the squared distance tolerance
t = tol**2
#Loop over Wyckoff positions
for i, wp in enumerate(wyckoffs):
#Check that length of points and wp are equal
if len(wp) != len(points): continue
failed = False
#Search for a generating point
for p in points:
failed = False
#Check that point works as x,y,z value for wp
xyz = filtered_coords_euclidean(wp[0].operate(p) - p, PBC=PBC)
if dsquared(xyz) > t: continue
#Calculate distances between original and generated points
pw = np.array([op.operate(p) for op in wp])
dw = distance_matrix(points, pw, None, PBC=PBC, metric="sqeuclidean")
#Check each row for a zero
for row in dw:
num = (row < t).sum()
if num < 1:
failed = True
break
if failed is True: continue
#Check each column for a zero
for column in dw.T:
num = (column < t).sum()
if num < 1:
failed = True
break
#Calculate distance between original and generated points
ps = np.array([op.operate(p) for op in w_symm_all[i][0]])
ds = distance_matrix([p], ps, None, PBC=PBC, metric="sqeuclidean")
#Check whether any generated points are too far away
num = (ds > t).sum()
if num > 0:
failed = True
if failed is True: continue
return i, p
return False, None
#TODO: Use Group object instead of organized array
def letter_from_index(index, group, dim=3):
"""
Given a Wyckoff position's index within a spacegroup, return its number
and letter e.g. '4a'
Args:
index: a single integer describing the WP's index within the
spacegroup (0 is the general position)
group: an unorganized Wyckoff position array or Group object (preferred)
dim: the periodicity dimension of the symmetry group. Used for consideration
of "o" Wyckoff positions in point groups. Not used if group is a Group
Returns:
the Wyckoff letter corresponding to the Wyckoff position (for example,
for position 4a, the function would return 'a')
"""
letters1 = letters
#See whether the group has an "o" Wyckoff position
checko = False
if type(group) == Group and group.dim == 0:
checko = True
elif dim == 0:
checko = True
if checko is True:
if len(group[-1]) == 1 and group[-1][0] == SymmOp.from_xyz_string('0,0,0'):
#o comes before a
letters1 = "o" + letters
length = len(group)
return letters1[length - 1 - index]
def index_from_letter(letter, group, dim=3):
"""
Given the Wyckoff letter, returns the index of a Wyckoff position within
the spacegroup
Args:
letter: The wyckoff letter
group: an unorganized Wyckoff position array or Group object (preferred)
dim: the periodicity dimension of the symmetry group. Used for consideration
of "o" Wyckoff positions in point groups. Not used if group is a Group
Returns:
a single index specifying the location of the Wyckoff position within
the spacegroup (0 is the general position)
"""
letters1 = letters
#See whether the group has an "o" Wyckoff position
checko = False
if type(group) == Group and group.dim == 0:
checko = True
elif dim == 0:
checko = True
if checko is True:
if len(group[-1]) == 1 and group[-1][0] == SymmOp.from_xyz_string('0,0,0'):
#o comes before a
letters1 = "o" + letters
length = len(group)
return length - 1 - letters1.index(letter)
def jk_from_i(i, olist):
"""
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
Args:
i: a single index corresponding to the item's location in the
unorganized list
olist: the organized list
Returns:
[j, k]: two indices corresponding to the item's location in the
organized list
"""
num = -1
found = False
for j , a in enumerate(olist):
for k , b in enumerate(a):
num += 1
if num == i:
return [j, k]
printx("Error: Incorrect Wyckoff position list or index passed to jk_from_i", priority=1)
return None
def i_from_jk(j, k, olist):
"""
Inverse operation of jk_from_i: gives one list index from 2
Args:
j, k: indices corresponding to the location of an element in the
organized list
olist: the organized list of Wyckoff positions or molecular orientations
Returns:
i: one index corresponding to the item's location in the
unorganized list
"""
num = -1
for x, a in enumerate(olist):
for y, b in enumerate(a):
num += 1
if x == j and y == k:
return num
printx("Error: Incorrect Wyckoff position list or index passed to jk_from_i", priority=1)
return None
def ss_string_from_ops(ops, number, dim=3, complete=True):
"""
Print the Hermann-Mauguin symbol for a site symmetry group, using a list of
SymmOps as input. Note that the symbol does not necessarily refer to the
x,y,z axes. For information on reading these symbols, see:
http://en.wikipedia.org/wiki/Hermann-Mauguin_notation#Point_groups
Args:
ops: a list of SymmOp objects representing the site symmetry
number: International number of the symmetry group. Used to determine which
axes to show. For example, a 3-fold rotation in a cubic system is
written as ".3.", whereas a 3-fold rotation in a trigonal system is
written as "3.."
dim: the dimension of the crystal. Also used to determine notation type
complete: whether or not all symmetry operations in the group
are present. If False, we generate the rest
Returns:
a string representing the site symmetry. Ex: "2mm"
"""
#TODO: Automatically detect which symm_type to use based on ops
#Determine which notation to use
symm_type = "high"
if dim == 3:
if number >= 1 and number <= 74:
#Triclinic, monoclinic, orthorhombic
symm_type = "low"
elif number >= 75 and number <= 194:
#Trigonal, Hexagonal, Tetragonal
symm_type = "medium"
elif number >= 195 and number <= 230:
#cubic
symm_type = "high"
if dim == 2:
if number >= 1 and number <= 48:
#Triclinic, monoclinic, orthorhombic
symm_type = "low"
elif number >= 49 and number <= 80:
#Trigonal, Hexagonal, Tetragonal
symm_type = "medium"
if dim == 1:
if number >= 1 and number <= 22:
#Triclinic, monoclinic, orthorhombic
symm_type = "low"
elif number >= 23 and number <= 75:
#Trigonal, Hexagonal, Tetragonal
symm_type = "medium"
#TODO: replace sg with number, add dim variable
#Return the symbol for a single axis
#Will be called later in the function
def get_symbol(opas, order, has_reflection):
#ops: a list of Symmetry operations about the axis
#order: highest order of any symmetry operation about the axis
#has_reflection: whether or not the axis has mirror symmetry
if has_reflection is True:
#rotations have priority
for opa in opas:
if opa.order == order and opa.type == "rotation":
return str(opa.rotation_order)+"/m"
for opa in opas:
if (opa.order == order and opa.type == "rotoinversion"
and opa.order != 2):
return "-"+str(opa.rotation_order)
return "m"
elif has_reflection is False:
#rotoinversion has priority
for opa in opas:
if opa.order == order and opa.type == "rotoinversion":
return "-"+str(opa.rotation_order)
for opa in opas:
if opa.order == order and opa.type == "rotation":
return str(opa.rotation_order)
return "."
#Given a list of single-axis symbols, return the one with highest symmetry
#Will be called later in the function
def get_highest_symbol(symbols):
symbol_list = ['.','2','m','-2','2/m','3','4','-4','4/m','-3','6','-6','6/m']
max_index = 0
use_list = True
for j, symbol in enumerate(symbols):
if symbol in symbol_list:
i = symbol_list.index(symbol)
else:
use_list = False
num_str = ''.join(c for c in symbol if c.isdigit())
i1 = int(num_str)
if 'm' in symbol or '-' in symbol:
if i1 % 2 == 0:
i = i1
elif i1 % 2 == 1:
i = i1 * 2
else:
i = i1
if i > max_index:
max_j = j
max_index = i
if use_list is True:
return symbol_list[max_index]
else:
return symbols[max_j]
#Return whether or not two axes are symmetrically equivalent
#It is assumed that both axes possess the same symbol
#Will be called within combine_axes
def are_symmetrically_equivalent(index1, index2):
axis1 = axes[index1]
axis2 = axes[index2]
condition1 = False
condition2 = False
#Check for an operation mapping one axis onto the other
for op in ops:
if condition1 is False or condition2 is False:
new1 = op.operate(axis1)
new2 = op.operate(axis2)
if np.isclose(abs(np.dot(new1, axis2)), 1):
condition1 = True
if np.isclose(abs(np.dot(new2, axis1)), 1):
condition2 = True
if condition1 is True and condition2 is True:
return True
else:
return False
#Given a list of axis indices, return the combined symbol
#Axes may or may not be symmetrically equivalent, but must be of the same
#type (x/y/z, face-diagonal, body-diagonal)
#Will be called for mid- and high-symmetry crystallographic point groups
def combine_axes(indices):
symbols = {}
for index in deepcopy(indices):
symbol = get_symbol(params[index],orders[index],reflections[index])
if symbol == ".":
indices.remove(index)
else:
symbols[index] = symbol
if indices == []:
return "."
#Remove redundant axes
for i in deepcopy(indices):
for j in deepcopy(indices):
if j > i:
if symbols[i] == symbols[j]:
if are_symmetrically_equivalent(i, j):
if j in indices:
indices.remove(j)
#Combine symbols for non-equivalent axes
new_symbols = []
for i in indices:
new_symbols.append(symbols[i])
symbol = ""
while new_symbols != []:
highest = get_highest_symbol(new_symbols)
symbol += highest
new_symbols.remove(highest)
if symbol == "":
printx("Error: could not combine site symmetry axes.", priority=1)
return
else:
return symbol
#Generate needed ops
if complete is False:
ops = generate_full_symmops(ops, 1e-3)
#Get OperationAnalyzer object for all ops
opas = []
for op in ops:
opas.append(OperationAnalyzer(op))
#Store the symmetry of each axis
params = [[],[],[],[],[],[],[],[],[],[],[],[],[]]
has_inversion = False
#Store possible symmetry axes for crystallographic point groups
axes = [[1,0,0],[0,1,0],[0,0,1],
[1,1,0],[0,1,1],[1,0,1],[1,-1,0],[0,1,-1],[1,0,-1],
[1,1,1],[-1,1,1],[1,-1,1],[1,1,-1]]
for i, axis in enumerate(axes):
axes[i] = axis/np.linalg.norm(axis)
for opa in opas:
if opa.type != "identity" and opa.type != "inversion":
found = False
for i, axis in enumerate(axes):
if np.isclose(abs(np.dot(opa.axis, axis)), 1):
found = True
params[i].append(opa)
#Store uncommon axes for trigonal and hexagonal lattices
if found is False:
axes.append(opa.axis)
#Check that new axis is not symmetrically equivalent to others
unique = True
for i, axis in enumerate(axes):
if i != len(axes)-1:
if are_symmetrically_equivalent(i, len(axes)-1):
unique = False
if unique is True:
params.append([opa])
elif unique is False:
axes.pop()
elif opa.type == "inversion":
has_inversion = True
#Determine how many high-symmetry axes are present
n_axes = 0
#Store the order of each axis
orders = []
#Store whether or not each axis has reflection symmetry
reflections = []
for axis in params:
order = 1
high_symm = False
has_reflection = False
for opa in axis:
if opa.order >= 3:
high_symm = True
if opa.order > order:
order = opa.order
if opa.order == 2 and opa.type == "rotoinversion":
has_reflection = True
orders.append(order)
if high_symm == True:
n_axes += 1
reflections.append(has_reflection)
#Triclinic, monoclinic, orthorhombic
#Positions in symbol refer to x,y,z axes respectively
if symm_type == "low":
symbol = (get_symbol(params[0], orders[0], reflections[0])+
get_symbol(params[1], orders[1], reflections[1])+
get_symbol(params[2], orders[2], reflections[2]))
if symbol != "...":
return symbol
elif symbol == "...":
if has_inversion is True:
return "-1"
else:
return "1"
#Trigonal, Hexagonal, Tetragonal
elif symm_type == "medium":
#1st symbol: z axis
s1 = get_symbol(params[2], orders[2], reflections[2])
#2nd symbol: x or y axes (whichever have higher symmetry)
s2 = combine_axes([0,1])
#3rd symbol: face-diagonal axes (whichever have highest symmetry)
s3 = combine_axes(list(range(3, len(axes))))
symbol = s1+" "+s2+" "+s3
if symbol != ". . .":
return symbol
elif symbol == ". . .":
if has_inversion is True:
return "-1"
else:
return "1"
#Cubic
elif symm_type == "high":
pass
#1st symbol: x, y, and/or z axes (whichever have highest symmetry)
s1 = combine_axes([0,1,2])
#2nd symbol: body-diagonal axes (whichever has highest symmetry)
s2 = combine_axes([9,10,11,12])
#3rd symbol: face-diagonal axes (whichever have highest symmetry)
s3 = combine_axes([3,4,5,6,7,8])
symbol = s1+" "+s2+" "+s3
if symbol != ". . .":
return symbol
elif symbol == ". . .":
if has_inversion is True:
return "-1"
else:
return "1"
else:
printx("Error: invalid spacegroup number", priority=1)
return
def symbol_from_number(number, symbol):
"""
Returns the H-M symbol for a given international group number
"""
#TODO: Create database/lists of symbols for groups
pass
def organized_wyckoffs(group):
"""
Takes a Group object or unorganized list of Wyckoff positions and returns
a 2D list of Wyckoff positions organized by multiplicity.
Args:
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
"""
if type(group) == Group:
wyckoffs = group.Wyckoff_positions
else:
wyckoffs = group
wyckoffs_organized = [[]] #2D Array of WP's organized by multiplicity
old = len(wyckoffs[0])
for wp in wyckoffs:
mult = len(wp)
if mult != old:
wyckoffs_organized.append([])
old = mult
wyckoffs_organized[-1].append(wp)
return wyckoffs_organized
def calculate_generators(wp, gen_pos, PBC=[1,1,1]):
"""
Calculate the generating operations for a WP given the general position
and the site symmetry ops for the WP
Args:
gen_pos: a list of SymmOp objects for the general position
ss: a list of symmetry operations for each point in the WP
"""
gens = []
for point in wp:
for op in gen_pos:
if op not in gens:
transformed_matrix = np.dot(op.affine_matrix, wp[0].affine_matrix)
if np.allclose(transformed_matrix, point.affine_matrix,atol=.01,rtol=.001):
gens.append(op)
break
return gens
class Wyckoff_position():
"""
Class for a single Wyckoff position within a symmetry group
"""
def from_dict(dictionary):
"""
Constructs a Wyckoff_position object using a dictionary. Used mainly by the
Wyckoff class for constructing a list of Wyckoff_position objects at once
"""
wp = Wyckoff_position()
for key in dictionary:
setattr(wp, key, dictionary[key])
return wp
def __str__(self):
try:
return self.string
except:
if self.dim not in list(range(4)):
return "Error: invalid crystal dimension. Must be a number between 0 and 3."
s = "Wyckoff position "+str(self.multiplicity)+self.letter+" in "
if self.dim == 3:
s += "space "
elif self.dim == 2:
s += "layer "
elif self.dim == 1:
s += "Rod "
elif self.dim == 0:
s += "Point group " + self.symbol
if self.dim != 0:
s += "group " + str(self.number)
s += " with site symmetry "+ss_string_from_ops(self.symmetry_m[0], self.number, dim=self.dim)
for op in self.ops:
s += "\n" + op.as_xyz_string()
self.string = s
return self.string
def __repr__(self):
return str(self)
def from_group_and_index(group, index, dim=3, PBC=None):
"""
Creates a Wyckoff_position using the space group number and index
Args:
group: the international number of the symmetry group
index: the index or letter of the Wyckoff position within the group.
0 is always the general position, and larger indeces represent positions
with lower multiplicity. Alternatively, index can be the Wyckoff letter
("4a6" or "f")
dim: the periodic dimension of the crystal
PBC: the periodic boundary conditions
"""
wp = Wyckoff_position()
wp.dim = dim
if type(group) == int:
wp.number = group
number = group
else:
#TODO: add symbol interpretation
printx("Error: must use an integer group number.", priority=1)
return
use_letter = False
if type(index) == int:
wp.index = index
elif type(index) == str:
use_letter = True
#Extract letter from number-letter combinations ("4d"->"d")
for c in index:
if c.isalpha():
index = c
break
if dim == 3:
if number not in range(1, 231):
printx("Error: invalid symmetry group "+str(group)+" for dimension "+str(self.dim), priority=1)
return
if PBC == None:
wp.PBC = [1,1,1]
else:
wp.PBC = PBC
ops_all = get_wyckoffs(wp.number)
if use_letter is True:
wp.index = index_from_letter(index, ops_all, dim=dim)
wp.letter = index
else:
wp.letter = letter_from_index(wp.index, ops_all, dim=dim)
if wp.index >= len(ops_all) or wp.index < 0:
printx("Error while generating Wyckoff_position: index out of range for specified group", priority=1)
return
wp.ops = ops_all[wp.index]
"""The Wyckoff positions for the crystal's spacegroup."""
wp.multiplicity = len(wp.ops)
wp.symmetry = get_wyckoff_symmetry(wp.number)[wp.index]
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=False)"""
wp.symmetry_m = get_wyckoff_symmetry(wp.number, molecular=True)[wp.index]
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=False)"""
wp.generators = get_wyckoff_generators(wp.number)[wp.index]
"""A list of Wyckoff generators (molecular=False)"""
wp.generators_m = get_wyckoff_generators(wp.number, molecular=True)[wp.index]
"""A list of Wyckoff generators (molecular=True)"""
wp.inverse_generators = get_inverse_ops(wp.generators)
"""A list of inverses of the generators (molecular=False)"""
wp.inverse_generators_m = get_inverse_ops(wp.generators_m)
"""A list of inverses of the generators (molecular=True)"""
elif dim == 2:
if number not in range(1, 81):
printx("Error: invalid symmetry group "+str(group)+" for dimension "+str(self.dim), priority=1)
return
if PBC == None:
wp.PBC = [1,1,0]
else:
wp.PBC = PBC
ops_all = get_layer(wp.number)
if use_letter is True:
wp.index = index_from_letter(index, ops_all, dim=dim)
wp.letter = index
else:
wp.letter = letter_from_index(wp.index, ops_all, dim=dim)
if wp.index >= len(ops_all) or wp.index < 0:
printx("Error while generating Wyckoff_position: index out of range for specified group", priority=1)
return
wp.ops = ops_all[wp.index]
"""The Wyckoff positions for the crystal's spacegroup."""
wp.multiplicity = len(wp.ops)
wp.symmetry = get_layer_symmetry(wp.number)[wp.index]
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=False)"""
wp.symmetry_m = get_layer_symmetry(wp.number, molecular=True)[wp.index]
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=False)"""
wp.generators = get_layer_generators(wp.number)[wp.index]
"""A list of Wyckoff generators (molecular=False)"""
wp.generators_m = get_layer_generators(wp.number, molecular=True)[wp.index]
"""A list of Wyckoff generators (molecular=True)"""
wp.inverse_generators = get_inverse_ops(wp.generators)
"""A list of inverses of the generators (molecular=False)"""
wp.inverse_generators_m = get_inverse_ops(wp.generators_m)
"""A list of inverses of the generators (molecular=True)"""
elif dim == 1:
if number not in range(1, 76):
printx("Error: invalid symmetry group "+str(group)+" for dimension "+str(self.dim), priority=1)
return
if PBC == None:
wp.PBC = [0,0,1]
else:
wp.PBC = PBC
ops_all = get_rod(wp.number)
if use_letter is True:
wp.index = index_from_letter(index, ops_all, dim=dim)
wp.letter = index
else:
wp.letter = letter_from_index(wp.index, ops_all, dim=dim)
if wp.index >= len(ops_all) or wp.index < 0:
printx("Error while generating Wyckoff_position: index out of range for specified group", priority=1)
return
wp.ops = ops_all[wp.index]
"""The Wyckoff positions for the crystal's spacegroup."""
wp.multiplicity = len(wp.ops)
wp.symmetry = get_rod_symmetry(wp.number)[wp.index]
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=False)"""
wp.symmetry_m = get_rod_symmetry(wp.number, molecular=True)[wp.index]
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=False)"""
wp.generators = get_rod_generators(wp.number)[wp.index]
"""A list of Wyckoff generators (molecular=False)"""
wp.generators_m = get_rod_generators(wp.number, molecular=True)[wp.index]
"""A list of Wyckoff generators (molecular=True)"""
wp.inverse_generators = get_inverse_ops(wp.generators)
"""A list of inverses of the generators (molecular=False)"""
wp.inverse_generators_m = get_inverse_ops(wp.generators_m)
"""A list of inverses of the generators (molecular=True)"""
elif dim == 0:
if number not in range(1, 57):
printx("Error: invalid symmetry group "+str(group)+" for dimension "+str(self.dim), priority=1)
return
#Generate a Group and retrieve Wyckoff position from it
g = Group(group, dim=0)
try:
wp = g[index]
except:
printx("Error while generating Wyckoff_position: index out of range for specified group", priority=1)
return wp
def wyckoff_from_generating_op(gen_op, gen_pos):
"""
Given a general position and generating operation (ex: "x,0,0"), returns a
Wyckoff_position object.
Args:
gen_op: a SymmOp into which the generating coordinate will be plugged
gen_pos: a list of SymmOps representing the general position
Returns:
a list of SymmOps
"""
def is_valid_generator(op):
m = op.affine_matrix
#Check for x,y+ax,z+bx+cy format
#Make sure y, z are not referred to before second and third slots, respectively
if (np.array([m[0][1], m[0][2], m[1][2]]) != 0.0).any():
if (np.array([m[2][0], m[2][1], m[1][0]]) != 0.0).any():
return False
for i in range(0, 3):
#Check for translation
if m[i][i] != 0 and m[i][3] != 0:
return False
#Check that x, y, z are present in desired spot and positive
if np.linalg.norm(m[:,i]) > 0:
if m[i][i] == 0:
return False
return True
def filter_zeroes(op):
m = op.affine_matrix
m2 = m
for i, x in enumerate(m):
for j, y in enumerate(x):
if np.isclose(y, 0, atol=1e-3):
m2[i][j] = 0
return SymmOp(m2)
#new_ops = [filter_zeroes(op*gen_op) for op in gen_pos]
new_ops = [filter_zeroes(SymmOp(np.dot(op.affine_matrix, gen_op.affine_matrix))) for op in gen_pos]
#Remove redundant ops
op_list = []
for op1 in new_ops:
passed = True
for op2 in op_list:
if np.allclose(op1.affine_matrix, op2.affine_matrix):
passed = False
break
if passed is True:
op_list.append(op1)
#Check for identity op
if Identity in op_list:
index = op_list.index(Identity)
op2 = op_list[0]
op_list[index] = op2
op_list[0] = Identity
return op_list
#Check for generating op
found = False
for op in op_list:
if is_valid_generator(op):
#Place generating op at beginning of list
index = op_list.index(op)
op2 = op_list[0]
op_list[index] = op2
op_list[0] = op
found = True
break
if found is False:
printx("Error: Could not find generating op.", priority=0)
printx("gen_op: ")
printx(str(gen_op))
printx("gen_pos: ")
printx(str(gen_pos))
return op_list
#Make sure first op is normalized
m = op_list[0].affine_matrix
x_factor = 1
y_factor = 1
z_factor = 1
if m[0][0] != 0:
if m[0][0] != 1: x_factor = m[0][0]
if m[1][1] != 0:
if m[1][1] != 1: y_factor = m[1][1]
if m[2][2] != 0:
if m[2][2] != 1: z_factor = m[2][2]
new_list = []
for op in op_list:
m = op.affine_matrix
m2 = m
m2[:,0] = m2[:,0] / x_factor
m2[:,1] = m2[:,1] / y_factor
m2[:,2] = m2[:,2] / z_factor
new_list.append(SymmOp(m2))
return new_list
def symmetry_from_wyckoff(wp, gen_pos):
symm = []
for op in wp:
symm.append(site_symm(op, gen_pos))
return symm
def __iter__(self):
yield from self.ops
def __getitem__(self, index):
return self.ops[index]
def __len__(self):
return self.multiplicity
def get_site_symmetry(self):
return ss_string_from_ops(self.symmetry_m[0], self.number, dim=self.dim)
class Group():
"""
Class for storing a set of Wyckoff positions for a symmetry group. See the documentation
for details about settings.
Args:
group: the group symbol or international number
dim: the periodic dimension of the group
"""
pglist_crystallographic = ['C1','Ci','C2','Cs','C2h','D2','C2v','D2h',
'C4','S4','C4h','D4','C4v','D2d','D4h','C3',
'C3i','D3','C3v','D3d','C6','C3h','C6h','D6',
'C6v','D3h','D6h','T','Th','O','Td','Oh']
"""List of crystallographic point groups"""
pglist = ['C1','Ci','C2','Cs','C2h','D2','C2v','D2h',
'C4','S4','C4h','D4','C4v','D2d','D4h','C3',
'C3i','D3','C3v','D3d','C6','C3h','C6h','D6',
'C6v','D3h','D6h','T','Th','O','Td','Oh',
'C5', 'C7', 'C8',
'D5', 'D7', 'D8',
'C5v', 'C7v', 'C8v',
'C5h',
'D5h', 'D7h', 'D8h',
'D4d', 'D5d', 'D6d', 'D7d', 'D8d',
'S6', 'S8', 'S10', 'S12',
'I', 'Ih',
'C*', 'C*h']
"""List of chemically important point groups, based on:
http://symmetry.jacobs-university.de/ """
pgdict = {}
"""Dict of crystallographic point group symbols and their corresponding numbers
(the number for initializing a Group object)"""
for i, symbol in enumerate(pglist):
pgdict[i+1] = symbol
"""Dict of crystallographic point groups, with the numbers used by PyXtal"""
def __str__(self):
try:
return self.string
except:
if self.dim == 0:
#TODO: implement point group symbols
s = "-- Point group --"
elif self.dim == 3:
s = "-- Space group --"
elif self.dim == 2:
s = "-- Layer group --"
elif self.dim == 1:
s = "-- Rod group --"
else:
return "Error: invalid crystal dimension. Must be a number between 0 and 3."
s += "# "+str(self.number)+" ("+self.symbol+")--"
#TODO: implement H-M symbol
for wp in self.Wyckoff_positions:
s += "\n "+str(wp.multiplicity)+wp.letter+"\tsite symm: " + ss_string_from_ops(wp.symmetry_m[0], self.number, dim=self.dim)
#for op in wp.ops:
# s += "\n" + op.as_xyz_string()
self.string = s
return self.string
def __repr__(self):
return str(self)
def __init__(self, group, dim=3):
self.dim = dim
#TODO: get symbol from number
self.symbol, self.number = get_symbol_and_number(group, dim)
number = self.number #QZ: needs to clean up
if dim == 3:
if self.number not in range(1, 231):
printx("Error: invalid symmetry group "+str(group)+" for dimension "+str(self.dim), priority=1)
return
self.PBC = [1,1,1]
self.wyckoffs = get_wyckoffs(self.number)
"""The Wyckoff positions for the crystal's spacegroup."""
self.w_symm = get_wyckoff_symmetry(self.number)
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=False)"""
self.w_symm_m = get_wyckoff_symmetry(self.number, molecular=True)
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=True)"""
self.wyckoff_generators = get_wyckoff_generators(self.number)
"""A list of Wyckoff generators (molecular=False)"""
self.wyckoff_generators_m = get_wyckoff_generators(self.number, molecular=True)
"""A list of Wyckoff generators (molecular=True)"""
self.inverse_generators = get_inverse_ops(self.wyckoff_generators)
"""A list of inverses of the generators (molecular=False)"""
self.inverse_generators_m = get_inverse_ops(self.wyckoff_generators_m)
"""A list of inverses of the generators (molecular=True)"""
if self.number <= 2:
self.lattice_type = "triclinic"
elif self.number <= 15:
self.lattice_type = "monoclinic"
elif self.number <= 74:
self.lattice_type = "orthorhombic"
elif self.number <= 142:
self.lattice_type = "tetragonal"
elif self.number <= 194:
self.lattice_type = "hexagonal"
elif self.number <= 230:
self.lattice_type = "cubic"
elif dim == 2:
if self.number not in range(1, 81):
printx("Error: invalid symmetry group "+str(group)+" for dimension "+str(self.dim), priority=1)
return
self.PBC = [1,1,0]
self.wyckoffs = get_layer(self.number)
"""The Wyckoff positions for the crystal's spacegroup."""
self.w_symm = get_layer_symmetry(self.number)
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=False)."""
self.w_symm_m = get_layer_symmetry(self.number, molecular=True)
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=True)"""
self.wyckoff_generators = get_layer_generators(self.number)
"""A list of Wyckoff generators (molecular=False)"""
self.wyckoff_generators_m = get_layer_generators(self.number, molecular=True)
"""A list of Wyckoff generators (molecular=True)"""
self.inverse_generators = get_inverse_ops(self.wyckoff_generators)
"""A list of inverses of the generators (molecular=False)"""
self.inverse_generators_m = get_inverse_ops(self.wyckoff_generators_m)
"""A list of inverses of the generators (molecular=True)"""
if self.number <= 2:
self.lattice_type = "triclinic"
elif self.number <= 18:
self.lattice_type = "monoclinic"
elif self.number <= 48:
self.lattice_type = "orthorhombic"
elif self.number <= 64:
self.lattice_type = "tetragonal"
elif self.number <= 80:
self.lattice_type = "hexagonal"
elif dim == 1:
if self.number not in range(1, 76):
printx("Error: invalid symmetry group "+str(group)+" for dimension "+str(self.dim), priority=1)
return
self.PBC = [0,0,1]
self.wyckoffs = get_rod(self.number)
"""The Wyckoff positions for the crystal's spacegroup."""
self.w_symm = get_rod_symmetry(self.number)
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=False)"""
self.w_symm_m = get_rod_symmetry(self.number, molecular=True)
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=True)"""
self.wyckoff_generators = get_rod_generators(self.number)
"""A list of Wyckoff generators (molecular=False)"""
self.wyckoff_generators_m = get_rod_generators(self.number, molecular=True)
"""A list of Wyckoff generators (molecular=True)"""
self.inverse_generators = get_inverse_ops(self.wyckoff_generators)
"""A list of inverses of the generators (molecular=False)"""
self.inverse_generators_m = get_inverse_ops(self.wyckoff_generators_m)
"""A list of inverses of the generators (molecular=True)"""
if self.number <= 2:
self.lattice_type = "triclinic"
elif self.number <= 12:
self.lattice_type = "monoclinic"
elif self.number <= 22:
self.lattice_type = "orthorhombic"
elif self.number <= 41:
self.lattice_type = "tetragonal"
elif self.number <= 75:
self.lattice_type = "hexagonal"
elif dim == 0:
#0-D clusters. Except for group "I" and "Ih", z axis is the high-symmetry axis
#https://en.wikipedia.org/wiki/Schoenflies_notation#Point_groups
self.dim = 0
self.PBC = [0,0,0]
#Check if string is for crystallographic point group
if type(group) == str:
if group in pglist:
group = pglist.index(group) + 1
#Get crystallographic point group
if type(group) == int or type(group) == float:
if number in range(1, 57):
self.symbol = pglist[number-1]
symbol = self.symbol
#Retrive symmetry info from database
self.wyckoffs = get_point(self.number)
"""The Wyckoff positions for the crystal's spacegroup."""
self.w_symm = get_point_symmetry(self.number)
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=False)"""
self.w_symm_m = deepcopy(self.w_symm)
"""A list of site symmetry operations for the Wyckoff positions, obtained
from get_wyckoff_symmetry (molecular=True)"""
self.wyckoff_generators = get_point_generators(self.number)
"""A list of Wyckoff generators (molecular=False)"""
self.wyckoff_generators_m = deepcopy(self.wyckoff_generators)
"""A list of Wyckoff generators (molecular=True)"""
self.inverse_generators = get_inverse_ops(self.wyckoff_generators)
"""A list of inverses of the generators (molecular=False)"""
self.inverse_generators_m = deepcopy(self.inverse_generators)
"""A list of inverses of the generators (molecular=True)"""
#Assign lattice type
if self.symbol in ["C1","Ci""D2","D2h","T","Th","O","Td","Oh","I","Ih"]:
self.lattice_type = "spherical"
else:
self.lattice_type = "ellipsoidal"
else:
printx("Error: invalid symmetry group "+str(group)+" for dimension "+str(self.dim), priority=1)
return
#Get other point groups
#Should be elif
if type(group) == str:
#Remove whitespace
symbol = ''.join(c for c in symbol if not c.isspace())
#Find rotation order from symbol
num_str = ''.join(c for c in symbol if not c.isalpha())
if num_str == "*":
num = 0 #infinite rotation order
elif num_str == "":
num = 1 #No rotation order
else:
try:
num = int(num_str) #rotation order
1 / num
except:
printx("Error: invalid rotation order for point group symbol.", priority=1)
return
gens = [Identity] # List of generator SymmOps
generate = True
#interpret symbol
if symbol[0] == "I":
#Icosohedral
self.lattice_type = "spherical"
#Add 2, 3, and 5-fold rotations
gens.append(SymmOp.from_xyz_string('-x,-y,z'))
gens.append(SymmOp.from_xyz_string('z,x,y'))
tau = 0.5*(math.sqrt(5)+1)
m = aa2matrix([1., tau, 0.], 2*pi/5)
gens.append(SymmOp.from_rotation_and_translation(m, [0,0,0]))
#Add Wyckoff generating operations
op_c = SymmOp.from_xyz_string('x,0,0')
op_b = SymmOp.from_xyz_string('x,x,x')
m = [[0,0,0,0],[0,1,0,0],[0,tau,0,0],[0,0,0,0]]
op_a = SymmOp(m)
gen_ops = [Identity, op_c, op_b, op_a, op_o]
if symbol == "Ih":
#Add horizontal mirror plane
mirror = SymmOp.from_xyz_string('x,y,-z') #m x,y,0
gens.append(mirror)
op_d = SymmOp.from_xyz_string('0,y,z')
gen_ops = [Identity, op_d, op_c, op_b, op_a, op_o]
elif symbol[0] == "C" and symbol[-1] != "i":
#n-fold rotation
if num == 1:
self.lattice_type = "spherical"
else:
self.lattice_type = "ellipsoidal"
op_b = SymmOp.from_xyz_string('0,y,z')
op_c = SymmOp.from_xyz_string('x,0,z')
op_d = SymmOp.from_xyz_string('x,x,z')
if symbol[-1] == "d":
printx("Error: Invalid point group symbol.", priority=1)
return
if num == 0:
#infinite-order rotation
self.symbol = "C*"
generate=False
pass
else:
#Add rotation
self.symbol = "C" + str(num)
m = aa2matrix([0.,0.,1.], 2*pi/num)
gens.append(SymmOp.from_rotation_and_translation(m, [0.,0.,0.]))
if num != 1:
gen_ops = [Identity, op_z]
elif num == 1:
gen_ops = [Identity]
if symbol[-1] == "v":
#Add vertical mirror plane
gens.append(SymmOp.from_xyz_string('-x,y,z')) #m 0,y,z
self.symbol += "v"
if num == 2:
gen_ops = [Identity, op_b, op_c, op_z]
elif num == 4:
gen_ops = [Identity, op_c, op_d, op_z]
else:
gen_ops = [Identity, op_b, op_z]
if symbol[-1] == "h":
#Add horizontal mirror plane
gens.append(SymmOp.from_xyz_string('x,y,-z')) #m x,y,0
self.symbol += "h"
op_xy = SymmOp.from_xyz_string('x,y,0')
gen_ops = [Identity, op_xy, op_z, op_o]
if symbol == "Cs":
gens = [Identity, SymmOp.from_xyz_string('x,y,-z')]
gen_ops = [Identity, SymmOp.from_xyz_string('x,y,0')]
elif symbol[0] == "C" and symbol[-1] == "i":
#n-fold rotinversion, usually just Ci
if num == 1:
self.lattice_type = "spherical"
else:
self.lattice_type = "ellipsoidal"
if "d" in symbol or "h" in symbol or "v" in symbol:
printx("Error: Invalid point group symbol.", priority=1)
return
if num == 0:
#infinite-order rotation
gens.append(SymmOp.from_xyz_string('-x,-y,-z'))
gens.append(SymmOp.from_xyz_string('x,y,-z'))
self.symbol = "C*i"
generate = False
else:
#Add rotoinversion
m = np.dot(aa2matrix([0.,0.,1.], 2*pi/num), [[-1.,0.,0.],[0.,-1.,0.],[0.,0.,-1.]])
gens.append(SymmOp.from_rotation_and_translation(m, [0.,0.,0.]))
if num == 1:
self.symbol = "Ci"
else:
self.symbol = "C" + str(num) + "i"
if num != 1:
gen_ops = [Identity, op_z, op_o]
elif num == 1:
gen_ops = [Identity, op_o]
elif (symbol[0] == "D") and ("v" not in symbol) and ("i" not in symbol):
#n-fold rotation and n 2-fold perpendicular rotations
if num == 2 and symbol[-1] == "h":
self.lattice_type = "spherical"
else:
self.lattice_type = "ellipsoidal"
if num == 0:
#infinite-order rotation
self.symbol = "D*"
generate = False
else:
#Add rotation
self.symbol = "D" + str(num)
#Rotation angle
angle = 2*pi/num
#Add n-fold rotation
m = aa2matrix([0.,0.,1.], angle)
gens.append(SymmOp.from_rotation_and_translation(m, [0.,0.,0.]))
#Add 2-fold rotation
gens.append(SymmOp.from_xyz_string('x,-y,-z'))
#Initialize gen_ops
gen_ops = [Identity]
if symbol[-1] == "d":
#Add half-angle plane
m_ref = [[math.cos(0.5*angle),math.sin(0.5*angle),0],[math.sin(0.5*angle),-math.cos(0.5*angle),0],[0,0,1]]
gens.append(SymmOp.from_rotation_and_translation(m_ref, [0.,0.,0.]))
self.symbol += "d"
#Add quarter-angle plane
m_ref = [[math.cos(0.25*angle),0,0],[math.sin(0.25*angle),0,0],[0,0,1]]
if np.isclose(m_ref[0][0],0,rtol=.001,atol=.001):
m_ref = [[0,0,0],[0,math.sin(0.25*angle),0],[0,0,1]]
gen_ops.append(SymmOp.from_rotation_and_translation(m_ref, [0.,0.,0.]))
elif symbol[-1] == "h":
#Add horizontal mirror plane
gens.append(SymmOp.from_xyz_string('x,y,-z')) #m x,y,0
self.symbol += "h"
#Add horizontal plane
gen_ops.append(SymmOp.from_xyz_string('x,y,0'))
#Add vertical plane
gen_ops.append(SymmOp.from_xyz_string('x,0,z'))
if num % 2 == 0:
#Add extra plane
m_ref = [[math.cos(0.5*angle),0,0],[math.sin(0.5*angle),0,0],[0,0,1]]
if np.isclose(m_ref[0][0],0,rtol=.001,atol=.001):
m_ref = [[0,0,0],[0,math.sin(0.5*angle),0],[0,0,1]]
gen_ops.append(SymmOp.from_rotation_and_translation(m_ref, [0.,0.,0.]))
#Add extra axis
m = aa2matrix([0.,0.,1.], 0.5*angle)
axis = np.dot(m, [1,0,0])
gen_ops.append(symmetry_element_from_axis(axis))
#Add generator op for axis, as well as z-axis and origin
else:
if num % 2 == 0:
m = aa2matrix([0.,0.,1.], 0.5*angle)
axis = np.dot(m, [1,0,0])
gen_ops.append(symmetry_element_from_axis(axis))
#Add common special positions
gen_ops += [op_x, op_z, op_o]
elif symbol[0] == "S":
#2n-fold rotation-reflection axis
self.lattice_type = "ellipsoidal"
#Equivalent to Cnh for odd n
if num == 0 or symbol[-1]=="v" or symbol[-1]=="i" or symbol[-1]=="h" or symbol[-1]=="d":
printx("Error: invalid point group symbol.", priority=1)
return
m = np.dot(aa2matrix([0.,0.,1.], 2*pi/num), [[1.,0.,0.],[0.,1.,0.],[0.,0.,-1.]])
gens.append(SymmOp.from_rotation_and_translation(m, [0.,0.,0.]))
if num % 2 == 1:
op_xy = SymmOp.from_xyz_string('x,y,0')
gen_ops = [Identity, op_xy, op_z, op_o]
elif num % 2 == 0:
gen_ops = [Identity, op_z, op_o]
else:
printx("Error: Invalid point group symbol.", priority=1)
return
#Generate full set of SymmOps
if generate is True:
gen_pos = generate_full_symmops(gens, 0.03)
if "*" not in self.symbol:
#Calculate Wyckoff positions
self.wyckoffs = []
for op in gen_ops:
wp = Wyckoff_position.wyckoff_from_generating_op(op, gen_pos)
self.wyckoffs.append(wp)
#Calculate site symmetry and generators
self.w_symm = []
for wp in self.wyckoffs:
self.w_symm.append(Wyckoff_position.symmetry_from_wyckoff(wp, gen_pos))
self.w_symm_m = deepcopy(self.w_symm)
self.wyckoff_generators = [calculate_generators(wp, self.wyckoffs[0]) for wp in self.wyckoffs]
self.wyckoff_generators_m = deepcopy(self.wyckoff_generators)
self.inverse_generators = get_inverse_ops(self.wyckoff_generators)
self.inverse_generators_m = get_inverse_ops(self.wyckoff_generators_m)
elif "*" in self.symbol:
#infinite rotational groups
"""C* and C*h are the prototypes; the rest are redundant for molecules:
C*v = C*
S* = C*h
D* = C*h
D*h = C*h"""
if self.symbol in ['C*', 'C*v']:
self.symbol = 'C*'
self.number = pglist.index(self.symbol) + 1
#Linear, no reflection
self.wyckoffs = [[SymmOp.from_xyz_string('0,0,z')]]
self.w_symm = [[[Identity]]]
self.w_symm_m = deepcopy(self.w_symm)
self.wyckoff_generators = [[Identity]]
self.wyckoff_generators_m = [[Identity]]
self.inverse_generators = [[Identity]]
self.inverse_generators_m = [[Identity]]
elif self.symbol in ['C*h', 'S*', 'D*', 'D*h']:
self.symbol = 'C*h'
self.number = pglist.index(self.symbol) + 1
#Linear, with reflection
self.wyckoffs = [[op_z, SymmOp.from_xyz_string('0,0,-z')],[op_o]]
self.w_symm = [[[Identity],[Identity]],[[Identity, SymmOp.from_xyz_string('0,0,-z')]]]
self.w_symm_m = deepcopy(self.w_symm)
self.wyckoff_generators = [[Identity, SymmOp.from_xyz_string('x,y,-z')],[Identity]]
self.wyckoff_generators_m = [[Identity, SymmOp.from_xyz_string('x,y,-z')],[Identity]]
self.inverse_generators = [[Identity, SymmOp.from_xyz_string('x,y,-z')],[Identity]]
self.inverse_generators_m = [[Identity, SymmOp.from_xyz_string('x,y,-z')],[Identity]]
else:
printx("Error: Invalid point group symbol.", priority=1)
#TODO: Add self.symbol to dictionary
wpdicts = [{"index": i, "letter": letter_from_index(i, self.wyckoffs, dim=self.dim), "ops": self.wyckoffs[i],
"multiplicity": len(self.wyckoffs[i]), "symmetry": self.w_symm[i], "symmetry_m": self.w_symm_m[i],
"generators": self.wyckoff_generators[i], "generators_m": self.wyckoff_generators_m[i],
"inverse_generators": self.inverse_generators[i], "inverse_generators_m": self.inverse_generators_m[i],
"PBC": self.PBC, "dim": self.dim, "number": self.number, "symbol": self.symbol} for i in range(len(self.wyckoffs))]
self.Wyckoff_positions = [Wyckoff_position.from_dict(wpdict) for wpdict in wpdicts]
"""A list of Wyckoff_position objects, sorted by descending multiplicity"""
self.wyckoffs_organized = organized_wyckoffs(self)
"""A 2D list of Wyckoff_position objects, grouped and sorted by
multiplicity."""
def get_wyckoff_position(self, index):
"""
Returns a single Wyckoff_position object
Args:
index: the index of the Wyckoff position within the group
The largest position is always 0
Returns: a Wyckoff_position object
"""
if type(index) == int:
pass
elif type(index) == str:
#Extract letter from number-letter combinations ("4d"->"d")
for c in index:
if c.isalpha():
letter = c
break
index = index_from_letter(letter, self.wyckoffs, dim=self.dim)
return self.Wyckoff_positions[index]
def get_wyckoff_symmetry(self, index, molecular=False):
"""
Returns the site symmetry symbol for the Wyckoff position
Args:
index: the index of the Wyckoff position within the group
The largest position is always 0
molecular: whether to use the Euclidean operations or not (for hexagonal groups)
Returns: a Hermann-Mauguin style string for the site symmetry
"""
if type(index) == int:
pass
elif type(index) == str:
#Extract letter from number-letter combinations ("4d"->"d")
for c in index:
if c.isalpha():
letter = c
break
index = index_from_letter(letter, self.wyckoffs, dim=self.dim)
if molecular is False:
ops = self.w_symm[index][0]
if molecular is True:
ops = self.w_symm_m[index][0]
return ss_string_from_ops(ops, self.number, dim=self.dim)
def get_wyckoff_symmetry_m(self, index):
"""
Returns the site symmetry symbol for the Wyckoff position (with molecular=True)
Args:
index: the index of the Wyckoff position within the group
The largest position is always 0
Returns: a Hermann-Mauguin style string for the site symmetry
"""
return self.get_wyckoff_symmetry(index, molecular=True)
def __iter__(self):
yield from self.Wyckoff_positions
def __getitem__(self, index):
return self.get_wyckoff_position(index)
def __len__(self):
return len(self.wyckoffs)
def print_all(self):
"""
Prints useful information about the Group.
"""
try:
print(self.string_long)
except:
if self.dim == 3:
s = "-- Space "
elif self.dim == 2:
s = "-- Layer "
elif self.dim == 1:
s = "-- Rod "
elif self.dim == 0:
s = "-- Point "
s += "group # "+str(self.number)+" ("+self.symbol+")--"
for wp in self.Wyckoff_positions:
s += "\n"+str(wp.multiplicity)+wp.letter+" site symm: "
s += ss_string_from_ops(wp.symmetry_m[0], self.number, dim=self.dim)
for op in wp.ops:
s += "\n " + op.as_xyz_string()
self.string_long = s
print(self.string_long)
def gen_pos(self):
"""
Returns the general Wyckoff position
"""
return self.Wyckoff_positions[0]
def get_symbol_and_number(group, dim=3):
"""
Function for quick conversion between symbols and numbers
Args:
group: the group symbol or international number
dim: the periodic dimension of the group
"""
keys = {3: 'space_group',
2: 'layer_group',
1: 'rod_group',
0: 'point_group',
}
found = False
lists = symbols[keys[dim]]
number = None
symbol = None
if dim not in [0, 1, 2, 3]:
raise ValueError('Dimension ({:d}) should in [0, 1, 2, 3] '.format(dim))
if type(group) == int:
if 0 < group < len(lists) + 1:
number = group
symbol = lists[number-1]
else:
raise ValueError('group ({:d}) should between 0 and {:d} for {:s}'.\
format(group, len(lists), keys[dim]))
else:
for i, _symbol in enumerate(lists):
if _symbol == group:
number = i + 1
symbol = group
found = True
break
if not found:
raise ValueError('group ({:s}) not found for any of {:d} {:s}s'.\
format(group, len(lists), keys[dim]))
return symbol, number
def list_groups(dim=3):
"""
Function for quick print of groups and symbols
Args:
group: the group symbol or international number
dim: the periodic dimension of the group
"""
import pandas as pd
keys = {3: 'space_group',
2: 'layer_group',
1: 'rod_group',
0: 'point_group',
}
data = symbols[keys[dim]]
df = pd.DataFrame(index=range(1, len(data)+1),
data=data,
columns=[keys[dim]])
pd.set_option('display.max_rows', len(df))
#df.set_index('Number')
print(df)
