def test_init(self):
for test_string, test_Pp in zip(self.test_strings, self.test_Pps):
jft = JonesFaithfulTransformation.from_transformation_string(test_string)
jft2 = JonesFaithfulTransformation(test_Pp[0], test_Pp[1])
self.assertTrue(np.allclose(jft.P, jft2.P))
self.assertTrue(np.allclose(jft.p, jft2.p))
self.assertEqual(test_string, jft.transformation_string)
self.assertEqual(test_string, jft2.transformation_string)
def test_transform_lattice(self):
lattice = Lattice.cubic(5)
all_ref_lattices = [
[[5.0, 0.0, 0.0], [0.0, 5.0, 0.0], [0.0, 0.0, 5.0]],
[[5.0, 5.0, 0.0], [-5.0, 5.0, 0.0], [0.0, 0.0, 10.0]],
[[1.25, 1.25, -2.5], [1.25, -1.25, -2.5], [-2.5, 0.0, 0.0]],
[[5.0, 0.0, 0.0], [0.0, 5.0, 0.0], [0.0, 0.0, 5.0]],
]
for ref_lattice, (P, p) in zip(all_ref_lattices, self.test_Pps):
jft = JonesFaithfulTransformation(P, p)
self.assertTrue(np.allclose(jft.transform_lattice(lattice).matrix, ref_lattice))
def test_transform_coords(self):
coords = [[0, 0, 0], [0.5, 0.5, 0.5]]
all_ref_coords = [
[[0.0, 0.0, 0.0], [0.5, 0.5, 0.5]],
[[0.0, 0.0, -0.25], [0.0, 0.5, 0.0]],
[[0.0, 0.0, 0.0], [-1.0, 0.0, -1.5]],
[[-0.25, -0.5, -0.75], [0.25, 0.0, -0.25]],
]
for ref_coords, (P, p) in zip(all_ref_coords, self.test_Pps):
jft = JonesFaithfulTransformation(P, p)
transformed_coords = jft.transform_coords(coords)
for coord, ref_coord in zip(transformed_coords, ref_coords):
self.assertTrue(np.allclose(coord, ref_coord))
def test_transform_symmops(self):
# reference data for this test taken from GENPOS
# http://cryst.ehu.es/cryst/get_gen.html
# Fm-3m
input_symmops = """x,y,z
-x,-y,z
-x,y,-z
x,-y,-z
z,x,y
z,-x,-y
-z,-x,y
-z,x,-y
y,z,x
-y,z,-x
y,-z,-x
-y,-z,x
y,x,-z
-y,-x,-z
y,-x,z
-y,x,z
x,z,-y
-x,z,y
-x,-z,-y
x,-z,y
z,y,-x
z,-y,x
-z,y,x
-z,-y,-x
-x,-y,-z
x,y,-z
x,-y,z
-x,y,z
-z,-x,-y
-z,x,y
z,x,-y
z,-x,y
-y,-z,-x
y,-z,x
-y,z,x
y,z,-x
-y,-x,z
y,x,z
-y,x,-z
y,-x,-z
-x,-z,y
x,-z,-y
x,z,y
-x,z,-y
-z,-y,x
-z,y,-x
z,-y,-x
z,y,x"""
# Fm-3m transformed by (a-b,a+b,2c;0,0,1/2)
ref_transformed_symmops = """x,y,z
-x,-y,z
-y,-x,-z+1/2
y,x,-z+1/2
-1/2x-1/2y+z+1/4,1/2x+1/2y+z+1/4,-1/2x+1/2y+3/4
1/2x+1/2y+z+1/4,-1/2x-1/2y+z+1/4,1/2x-1/2y+3/4
1/2x+1/2y-z+3/4,-1/2x-1/2y-z+3/4,-1/2x+1/2y+3/4
-1/2x-1/2y-z+3/4,1/2x+1/2y-z+3/4,1/2x-1/2y+3/4
-1/2x+1/2y-z+3/4,-1/2x+1/2y+z+1/4,1/2x+1/2y+3/4
1/2x-1/2y-z+3/4,1/2x-1/2y+z+1/4,-1/2x-1/2y+3/4
-1/2x+1/2y+z+1/4,-1/2x+1/2y-z+3/4,-1/2x-1/2y+3/4
1/2x-1/2y+z+1/4,1/2x-1/2y-z+3/4,1/2x+1/2y+3/4
-x,y,-z+1/2
x,-y,-z+1/2
y,-x,z
-y,x,z
1/2x+1/2y-z+3/4,1/2x+1/2y+z+1/4,1/2x-1/2y+3/4
-1/2x-1/2y-z+3/4,-1/2x-1/2y+z+1/4,-1/2x+1/2y+3/4
-1/2x-1/2y+z+1/4,-1/2x-1/2y-z+3/4,1/2x-1/2y+3/4
1/2x+1/2y+z+1/4,1/2x+1/2y-z+3/4,-1/2x+1/2y+3/4
1/2x-1/2y+z+1/4,-1/2x+1/2y+z+1/4,-1/2x-1/2y+3/4
-1/2x+1/2y+z+1/4,1/2x-1/2y+z+1/4,1/2x+1/2y+3/4
1/2x-1/2y-z+3/4,-1/2x+1/2y-z+3/4,1/2x+1/2y+3/4
-1/2x+1/2y-z+3/4,1/2x-1/2y-z+3/4,-1/2x-1/2y+3/4
-x,-y,-z+1/2
x,y,-z+1/2
y,x,z
-y,-x,z
1/2x+1/2y-z+3/4,-1/2x-1/2y-z+3/4,1/2x-1/2y+3/4
-1/2x-1/2y-z+3/4,1/2x+1/2y-z+3/4,-1/2x+1/2y+3/4
-1/2x-1/2y+z+1/4,1/2x+1/2y+z+1/4,1/2x-1/2y+3/4
1/2x+1/2y+z+1/4,-1/2x-1/2y+z+1/4,-1/2x+1/2y+3/4
1/2x-1/2y+z+1/4,1/2x-1/2y-z+3/4,-1/2x-1/2y+3/4
-1/2x+1/2y+z+1/4,-1/2x+1/2y-z+3/4,1/2x+1/2y+3/4
1/2x-1/2y-z+3/4,1/2x-1/2y+z+1/4,1/2x+1/2y+3/4
-1/2x+1/2y-z+3/4,-1/2x+1/2y+z+1/4,-1/2x-1/2y+3/4
x,-y,z
-x,y,z
-y,x,-z+1/2
y,-x,-z+1/2
-1/2x-1/2y+z+1/4,-1/2x-1/2y-z+3/4,-1/2x+1/2y+3/4
1/2x+1/2y+z+1/4,1/2x+1/2y-z+3/4,1/2x-1/2y+3/4
1/2x+1/2y-z+3/4,1/2x+1/2y+z+1/4,-1/2x+1/2y+3/4
-1/2x-1/2y-z+3/4,-1/2x-1/2y+z+1/4,1/2x-1/2y+3/4
-1/2x+1/2y-z+3/4,1/2x-1/2y-z+3/4,1/2x+1/2y+3/4
1/2x-1/2y-z+3/4,-1/2x+1/2y-z+3/4,-1/2x-1/2y+3/4
-1/2x+1/2y+z+1/4,1/2x-1/2y+z+1/4,-1/2x-1/2y+3/4
1/2x-1/2y+z+1/4,-1/2x+1/2y+z+1/4,1/2x+1/2y+3/4"""
jft = JonesFaithfulTransformation.from_transformation_string(self.test_strings[1])
input_symmops = [SymmOp.from_xyz_string(s) for s in input_symmops.split()]
ref_transformed_symmops = [SymmOp.from_xyz_string(s) for s in ref_transformed_symmops.split()]
transformed_symmops = [jft.transform_symmop(op) for op in input_symmops]
for transformed_op, ref_transformed_op in zip(transformed_symmops, ref_transformed_symmops):
self.assertEqual(transformed_op, ref_transformed_op)
def test_inverse(self):
for test_string in self.test_strings:
jft = JonesFaithfulTransformation.from_transformation_string(test_string)
self.assertEqual(jft, jft.inverse.inverse)
self.assertEqual(jft.transformation_string, jft.inverse.inverse.transformation_string)
def data_str(self, include_og=True):
"""
Get description of all data, including information for OG setting.
:return: str
"""
# __str__() omits information on OG setting to reduce confusion
# as to which set of symops are active, this property gives
# all stored data including OG setting
desc = {} # dictionary to hold description strings
description = ""
# parse data into strings
# indicate if non-standard setting specified
if self.jf != JonesFaithfulTransformation.from_transformation_string(
"a,b,c;0,0,0"):
description += "Non-standard setting: .....\n"
description += self.jf.__repr__()
description += "\n\nStandard setting information: \n"
desc["magtype"] = self._data["magtype"]
desc["bns_number"] = ".".join(map(str, self._data["bns_number"]))
desc["bns_label"] = self._data["bns_label"]
desc["og_id"] = ("\t\tOG: " +
".".join(map(str, self._data["og_number"])) + " " +
self._data["og_label"] if include_og else "")
desc["bns_operators"] = " ".join(
[op_data["str"] for op_data in self._data["bns_operators"]])
desc["bns_lattice"] = (" ".join([
lattice_data["str"]
for lattice_data in self._data["bns_lattice"][3:]
]) if len(self._data["bns_lattice"]) > 3 else ""
) # don't show (1,0,0)+ (0,1,0)+ (0,0,1)+
desc["bns_wyckoff"] = "\n".join([
textwrap.fill(
wyckoff_data["str"],
initial_indent=wyckoff_data["label"] + " ",
subsequent_indent=" " * len(wyckoff_data["label"] + " "),
break_long_words=False,
break_on_hyphens=False,
) for wyckoff_data in self._data["bns_wyckoff"]
])
desc["og_bns_transformation"] = ("OG-BNS Transform: ({})\n".format(
self._data["og_bns_transform"]) if desc["magtype"] == 4
and include_og else "")
bns_operators_prefix = "Operators{}: ".format(
" (BNS)" if desc["magtype"] == 4 and include_og else "")
bns_wyckoff_prefix = "Wyckoff Positions{}: ".format(
" (BNS)" if desc["magtype"] == 4 and include_og else "")
# apply textwrap on long lines
desc["bns_operators"] = textwrap.fill(
desc["bns_operators"],
initial_indent=bns_operators_prefix,
subsequent_indent=" " * len(bns_operators_prefix),
break_long_words=False,
break_on_hyphens=False,
)
description += ("BNS: {d[bns_number]} {d[bns_label]}{d[og_id]}\n"
"{d[og_bns_transformation]}"
"{d[bns_operators]}\n"
"{bns_wyckoff_prefix}{d[bns_lattice]}\n"
"{d[bns_wyckoff]}").format(
d=desc, bns_wyckoff_prefix=bns_wyckoff_prefix)
if desc["magtype"] == 4 and include_og:
desc["og_operators"] = " ".join(
[op_data["str"] for op_data in self._data["og_operators"]])
# include all lattice vectors because (1,0,0)+ (0,1,0)+ (0,0,1)+
# not always present in OG setting
desc["og_lattice"] = " ".join([
lattice_data["str"]
for lattice_data in self._data["og_lattice"]
])
desc["og_wyckoff"] = "\n".join([
textwrap.fill(
wyckoff_data["str"],
initial_indent=wyckoff_data["label"] + " ",
subsequent_indent=" " * len(wyckoff_data["label"] + " "),
break_long_words=False,
break_on_hyphens=False,
) for wyckoff_data in self._data["og_wyckoff"]
])
og_operators_prefix = "Operators (OG): "
# apply textwrap on long lines
desc["og_operators"] = textwrap.fill(
desc["og_operators"],
initial_indent=og_operators_prefix,
subsequent_indent=" " * len(og_operators_prefix),
break_long_words=False,
break_on_hyphens=False,
)
description += ("\n{d[og_operators]}\n"
"Wyckoff Positions (OG): {d[og_lattice]}\n"
"{d[og_wyckoff]}").format(d=desc)
elif desc["magtype"] == 4:
description += "\nAlternative OG setting exists for this space group."
return description
def __init__(self, id, setting_transformation="a,b,c;0,0,0"):
"""
Initializes a MagneticSpaceGroup from its Belov, Neronova and
Smirnova (BNS) number supplied as a list or its label supplied
as a string. To create a magnetic structure in pymatgen, the
Structure.from_magnetic_spacegroup() method can be used, which
relies on this class.
The main difference between magnetic space groups and normal
crystallographic space groups is the inclusion of a time reversal
operator that acts on an atom's magnetic moment. This is
indicated by a prime symbol (') next to the respective symmetry
operation in its label, e.g. the standard crystallographic
space group Pnma has magnetic subgroups Pn'ma, Pnm'a, Pnma',
Pn'm'a, Pnm'a', Pn'ma', Pn'm'a'.
The magnetic space groups are classified as one of 4 types
where G = magnetic space group, and F = parent crystallographic
space group:
1. G=F no time reversal, i.e. the same as corresponding
crystallographic group
2. G=F+F1', "grey" groups, where avg. magnetic moment is zero,
e.g. a paramagnet in zero ext. mag. field
3. G=D+(F-D)1', where D is an equi-translation subgroup of F of
index 2, lattice translations do not include time reversal
4. G=D+(F-D)1', where D is an equi-class subgroup of F of index 2
There are two common settings for magnetic space groups, BNS
and OG. In case 4, the BNS setting != OG setting, and so a
transformation to go between the two settings is required:
specifically, the BNS setting is derived from D, and the OG
setting is derived from F.
This means that the OG setting refers to the unit cell if magnetic
order is neglected, and requires multiple unit cells to reproduce
the full crystal periodicity when magnetic moments are present.
This does not make the OG setting, in general, useful for
electronic structure calculations and the BNS setting is preferred.
However, this class does contain information on the OG setting and
can be initialized from OG labels or numbers if required.
Conventions: ITC monoclinic unique axis b, monoclinic cell choice 1,
hexagonal axis for trigonal groups, origin choice 2 for groups with
more than one origin choice (ISO-MAG).
Raw data comes from ISO-MAG, ISOTROPY Software Suite, iso.byu.edu
http://stokes.byu.edu/iso/magnetic_data.txt
with kind permission from Professor Branton Campbell, BYU
Data originally compiled from:
(1) Daniel B. Litvin, Magnetic Group Tables (International Union
of Crystallography, 2013) www.iucr.org/publ/978-0-9553602-2-0.
(2) C. J. Bradley and A. P. Cracknell, The Mathematical Theory of
Symmetry in Solids (Clarendon Press, Oxford, 1972).
See http://stokes.byu.edu/iso/magneticspacegroupshelp.php for more
information on magnetic symmetry.
:param id: BNS number supplied as list of 2 ints or BNS label as
str or index as int (1-1651) to iterate over all space groups"""
self._data = {}
# Datafile is stored as sqlite3 database since (a) it can be easily
# queried for various different indexes (BNS/OG number/labels) and (b)
# allows binary data to be stored in a compact form similar to that in
# the source data file, significantly reducing file size.
# Note that a human-readable JSON format was tested first but was 20x
# larger and required *much* longer initial loading times.
# retrieve raw data
db = sqlite3.connect(MAGSYMM_DATA)
c = db.cursor()
if isinstance(id, str):
id = "".join(id.split()) # remove any white space
c.execute("SELECT * FROM space_groups WHERE BNS_label=?;", (id, ))
elif isinstance(id, list):
c.execute("SELECT * FROM space_groups WHERE BNS1=? AND BNS2=?;",
(id[0], id[1]))
elif isinstance(id, int):
# OG3 index is a 'master' index, going from 1 to 1651
c.execute("SELECT * FROM space_groups WHERE OG3=?;", (id, ))
raw_data = list(c.fetchone())
# Jones Faithful transformation
self.jf = JonesFaithfulTransformation.from_transformation_string(
"a,b,c;0,0,0")
if isinstance(setting_transformation, str):
if setting_transformation != "a,b,c;0,0,0":
self.jf = JonesFaithfulTransformation.from_transformation_string(
setting_transformation)
elif isinstance(setting_transformation, JonesFaithfulTransformation):
if setting_transformation != self.jf:
self.jf = setting_transformation
self._data["magtype"] = raw_data[0] # int from 1 to 4
self._data["bns_number"] = [raw_data[1], raw_data[2]]
self._data["bns_label"] = raw_data[3]
self._data["og_number"] = [raw_data[4], raw_data[5], raw_data[6]]
self._data["og_label"] = raw_data[7] # can differ from BNS_label
def _get_point_operator(idx):
"""Retrieve information on point operator (rotation matrix and Seitz label)."""
hex = self._data["bns_number"][0] >= 143 and self._data[
"bns_number"][0] <= 194
c.execute(
"SELECT symbol, matrix FROM point_operators WHERE idx=? AND hex=?;",
(idx - 1, hex),
)
op = c.fetchone()
op = {
"symbol": op[0],
"matrix": np.array(op[1].split(","), dtype="f").reshape(3, 3),
}
return op
def _parse_operators(b):
"""Parses compact binary representation into list of MagSymmOps."""
if len(
b
) == 0: # e.g. if magtype != 4, OG setting == BNS setting, and b == [] for OG symmops
return None
raw_symops = [b[i:i + 6] for i in range(0, len(b), 6)]
symops = []
for r in raw_symops:
point_operator = _get_point_operator(r[0])
translation_vec = [r[1] / r[4], r[2] / r[4], r[3] / r[4]]
time_reversal = r[5]
op = MagSymmOp.from_rotation_and_translation_and_time_reversal(
rotation_matrix=point_operator["matrix"],
translation_vec=translation_vec,
time_reversal=time_reversal,
)
# store string representation, e.g. (2x|1/2,1/2,1/2)'
seitz = "({0}|{1},{2},{3})".format(
point_operator["symbol"],
Fraction(translation_vec[0]),
Fraction(translation_vec[1]),
Fraction(translation_vec[2]),
)
if time_reversal == -1:
seitz += "'"
symops.append({"op": op, "str": seitz})
return symops
def _parse_wyckoff(b):
"""Parses compact binary representation into list of Wyckoff sites."""
if len(b) == 0:
return None
wyckoff_sites = []
def get_label(idx):
if idx <= 25:
return chr(97 + idx) # returns a-z when idx 0-25
return "alpha" # when a-z labels exhausted, use alpha, only relevant for a few space groups
o = 0 # offset
n = 1 # nth Wyckoff site
num_wyckoff = b[0]
while len(wyckoff_sites) < num_wyckoff:
m = b[1 + o] # multiplicity
label = str(b[2 + o] * m) + get_label(num_wyckoff - n)
sites = []
for j in range(m):
s = b[
3 + o + (j * 22):3 + o + (j * 22) +
22] # data corresponding to specific Wyckoff position
translation_vec = [s[0] / s[3], s[1] / s[3], s[2] / s[3]]
matrix = [
[s[4], s[7], s[10]],
[s[5], s[8], s[11]],
[s[6], s[9], s[12]],
]
matrix_magmom = [
[s[13], s[16], s[19]],
[s[14], s[17], s[20]],
[s[15], s[18], s[21]],
]
# store string representation, e.g. (x,y,z;mx,my,mz)
wyckoff_str = "({};{})".format(
transformation_to_string(matrix, translation_vec),
transformation_to_string(matrix_magmom, c="m"),
)
sites.append({
"translation_vec": translation_vec,
"matrix": matrix,
"matrix_magnetic": matrix_magmom,
"str": wyckoff_str,
})
# only keeping string representation of Wyckoff sites for now
# could do something else with these in future
wyckoff_sites.append({
"label": label,
"str": " ".join([s["str"] for s in sites])
})
n += 1
o += m * 22 + 2
return wyckoff_sites
def _parse_lattice(b):
"""Parses compact binary representation into list of lattice vectors/centerings."""
if len(b) == 0:
return None
raw_lattice = [b[i:i + 4] for i in range(0, len(b), 4)]
lattice = []
for r in raw_lattice:
lattice.append({
"vector": [r[0] / r[3], r[1] / r[3], r[2] / r[3]],
"str":
"({0},{1},{2})+".format(
Fraction(r[0] / r[3]).limit_denominator(),
Fraction(r[1] / r[3]).limit_denominator(),
Fraction(r[2] / r[3]).limit_denominator(),
),
})
return lattice
def _parse_transformation(b):
"""Parses compact binary representation into transformation between OG and BNS settings."""
if len(b) == 0:
return None
# capital letters used here by convention,
# IUCr defines P and p specifically
P = [[b[0], b[3], b[6]], [b[1], b[4], b[7]], [b[2], b[5], b[8]]]
p = [b[9] / b[12], b[10] / b[12], b[11] / b[12]]
P = np.array(P).transpose()
P_string = transformation_to_string(P, components=("a", "b", "c"))
p_string = "{},{},{}".format(
Fraction(p[0]).limit_denominator(),
Fraction(p[1]).limit_denominator(),
Fraction(p[2]).limit_denominator(),
)
return P_string + ";" + p_string
for i in range(8, 15):
try:
raw_data[i] = array(
"b", raw_data[i]) # construct array from sql binary blobs
except Exception:
# array() behavior changed, need to explicitly convert buffer to str in earlier Python
raw_data[i] = array("b", str(raw_data[i]))
self._data["og_bns_transform"] = _parse_transformation(raw_data[8])
self._data["bns_operators"] = _parse_operators(raw_data[9])
self._data["bns_lattice"] = _parse_lattice(raw_data[10])
self._data["bns_wyckoff"] = _parse_wyckoff(raw_data[11])
self._data["og_operators"] = _parse_operators(raw_data[12])
self._data["og_lattice"] = _parse_lattice(raw_data[13])
self._data["og_wyckoff"] = _parse_wyckoff(raw_data[14])
db.close()