Source code for pymatgen.symmetry.settings

# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.

"""
This module provides classes for non-standard space-group settings
"""

from fractions import Fraction
import numpy as np
import re

from pymatgen.core import Lattice
from pymatgen.util.string import transformation_to_string
from pymatgen.core.operations import MagSymmOp, SymmOp

from typing import Union, List, Tuple

__author__ = "Matthew Horton"
__copyright__ = "Copyright 2017, The Materials Project"
__version__ = "0.1"
__maintainer__ = "Matthew Horton"
__email__ = "mkhorton@lbl.gov"
__status__ = "Development"
__date__ = "Apr 2017"


[docs]class JonesFaithfulTransformation: """ Transformation for space-groups defined in a non-standard setting """ def __init__(self, P, p): """ Transform between settings using matrix P and origin shift vector p, using same notation as reference. Should initialize using `from_transformation_string` in Jones faithful notation, given by a string specifying both a transformation matrix and an origin shift, with parts delimited by a semi-colon. Best shown by example: * `a,b,c;0,0,0` is the identity (no change) * `-b+c,a+c,-a+b+c;0,0,0` is R3:r to R3:h (rhombohedral to hexagonal setting) * `a,b,c;-1/4,-1/4,-1/4` is Pnnn:1 to Pnnn:2 (change in origin choice) * `b,c,a;-1/2,-1/2,-1/2` is Bbab:1 to Ccca:2 (change settin and origin) Can transform points (coords), lattices and symmetry operations. Used for transforming magnetic space groups since these are commonly used in multiple settings, due to needing to transform between magnetic and non-magnetic settings. See: International Tables for Crystallography (2016). Vol. A, Chapter 1.5, pp. 75–106. """ # using capital letters in violation of PEP8 to # be consistent with variables in supplied reference, # for easier debugging in future self._P, self._p = P, p
[docs] @classmethod def from_transformation_string(cls, transformation_string="a,b,c;0,0,0"): """ Construct SpaceGroupTransformation from its transformation string. :param P: matrix :param p: origin shift vector :return: """ P, p = JonesFaithfulTransformation.parse_transformation_string( transformation_string) return cls(P, p)
[docs] @classmethod def from_origin_shift(cls, origin_shift="0,0,0"): """ Construct SpaceGroupTransformation from its origin shift string. :param p: origin shift vector :return: """ P = np.identity(3) p = [float(Fraction(x)) for x in origin_shift.split(",")] return cls(P, p)
[docs] @staticmethod def parse_transformation_string(transformation_string="a,b,c;0,0,0"): # type: (str) -> Tuple[List[List[float]], List[float]] """ :return: transformation matrix & vector """ try: a = np.array([1, 0, 0]) b = np.array([0, 1, 0]) c = np.array([0, 0, 1]) b_change, o_shift = transformation_string.split(";") basis_change = b_change.split(",") origin_shift = o_shift.split(",") # add implicit multiplication symbols basis_change = [re.sub( r'(?<=\w|\))(?=\() | (?<=\))(?=\w) | (?<=(\d|a|b|c))(?=([abc]))', r'*', x, flags=re.X) for x in basis_change] # should be fine to use eval here but be mindful for security # reasons # see http://lybniz2.sourceforge.net/safeeval.html # could replace with regex? or sympy expression? P = np.array([eval(x, {"__builtins__": None}, {'a': a, 'b': b, 'c': c}) for x in basis_change]) P = P.transpose() # by convention p = [float(Fraction(x)) for x in origin_shift] return (P, p) except Exception: raise ValueError("Failed to parse transformation string.")
@property def P(self) -> List[List[float]]: """ :return: transformation matrix """ return self._P @property def p(self) -> List[float]: """ :return: translation vector """ return self._p @property def inverse(self) -> 'JonesFaithfulTransformation': """ :return: JonesFaithfulTransformation """ Q = np.linalg.inv(self.P) return JonesFaithfulTransformation(Q, -np.matmul(Q, self.p)) @property def transformation_string(self) -> str: """ :return: transformation string """ return self._get_transformation_string_from_Pp(self.P, self.p) @staticmethod def _get_transformation_string_from_Pp(P: List[List[float]], p: List[float]) -> str: P = np.array(P).transpose() P_string = transformation_to_string(P, components=('a', 'b', 'c')) p_string = transformation_to_string(np.zeros((3, 3)), p) return P_string + ";" + p_string
[docs] def transform_symmop(self, symmop: Union[SymmOp, MagSymmOp]) -> Union[SymmOp, MagSymmOp]: """ Takes a symmetry operation and transforms it. :param symmop: SymmOp or MagSymmOp :return: """ W = symmop.rotation_matrix w = symmop.translation_vector Q = np.linalg.inv(self.P) W_ = np.matmul(np.matmul(Q, W), self.P) I = np.identity(3) w_ = np.matmul(Q, (w + np.matmul(W - I, self.p))) w_ = np.mod(w_, 1.0) if isinstance(symmop, MagSymmOp): return MagSymmOp.from_rotation_and_translation_and_time_reversal( rotation_matrix=W_, translation_vec=w_, time_reversal=symmop.time_reversal, tol=symmop.tol) elif isinstance(symmop, SymmOp): return SymmOp.from_rotation_and_translation( rotation_matrix=W_, translation_vec=w_, tol=symmop.tol) raise RuntimeError
[docs] def transform_coords(self, coords: List[List[float]]) -> List[List[float]]: """ Takes a list of co-ordinates and transforms them. :param coords: List of coords :return: """ new_coords = [] for x in coords: x = np.array(x) Q = np.linalg.inv(self.P) x_ = np.matmul(Q, (x - self.p)) # type: ignore new_coords.append(x_.tolist()) return new_coords
[docs] def transform_lattice(self, lattice): # type: (Lattice) -> Lattice """ Takes a Lattice object and transforms it. :param lattice: Lattice :return: """ return Lattice(np.matmul(lattice.matrix, self.P))
def __eq__(self, other): return np.allclose(self.P, other.P) and np.allclose(self.p, other.p) def __str__(self): return str(JonesFaithfulTransformation.transformation_string) def __repr__(self): return "JonesFaithfulTransformation with P:\n{0}\nand p:\n{1}".format( self.P, self.p)