def point_group(self):
"""
:return: get the point group in :math:`O(3)` of a 3D lattice, in :math:`O(2)` of a 2D lattice
:rtype: :py:class:`MatrixGroup <structrans.crystallography.MatrixGroup>`
:raises AttributeError: Point groups for other than 2D and 3D lattices are not implemented yet.
"""
if not self.dimension() in [2, 3]:
raise AttributeError(
'Point groups for other than 2D and 3D lattices are not implemented yet.'
)
if self.__pointGroup is None and self.__N == 3:
lg = np.array(self.Laue_group().matrices())
self.__pointGroup = MatrixGroup(np.append(lg, -lg, axis=0))
elif self.__pointGroup is None and self.__N == 2:
self.__pointGroup = MatrixGroup(
np.array([
Q for Q in SQUARE_EXT_GROUP.matrices()
if self.inpointgroup(Q)
]))
if self.__pointGroup.order() == 4:
hexGroup = MatrixGroup(
np.array([
Q for Q in HEX2D_EXT_GROUP.matrices()
if self.inpointgroup(Q)
]))
if hexGroup.order() > self.__pointGroup.order():
self.__pointGroup = hexGroup
return self.__pointGroup
def Laue_group(self):
'''
:return: get the Laue group in :math:`SO(3)` of a 3D lattice, in :math:`SO(2)` of a 2D lattice.
:rtype: :py:class:`MatrixGroup <structrans.crystallography.MatrixGroup>`
:raises AttributeError: Laue groups for other than 2D and 3D lattices are not implemented yet.
'''
if not self.dimension() in [2, 3]:
raise AttributeError(
'Laue groups for other than 2D and 3D lattices are not implemented yet.'
)
if self.__LaueGroup is None and self.dimension() == 3:
self.__LaueGroup = MatrixGroup(
np.array([
Q for Q in CUBIC_LAUE_GROUP.matrices()
if self.inpointgroup(Q)
]))
if self.__LaueGroup.order() == 4:
hexgroup = MatrixGroup(
np.array([
Q for Q in HEX_LAUE_GROUP.matrices()
if self.inpointgroup(Q)
]))
if hexgroup.order() > self.__LaueGroup.order():
self.__LaueGroup = hexgroup
if self.__LaueGroup is None and self.dimension() == 2:
self.__LaueGroup = MatrixGroup(
np.array([
Q for Q in SQUARE_GROUP.matrices() if self.inpointgroup(Q)
]))
if self.__LaueGroup.order() == 2:
hexGroup = MatrixGroup(
np.array([
Q for Q in HEX2D_GROUP.matrices()
if self.inpointgroup(Q)
]))
if hexGroup.order() > self.__LaueGroup.order():
self.__LaueGroup = hexGroup
return self.__LaueGroup
def lattice_group(self):
"""
:return: get the lattice group in :math:`GL(3, \mathbb Z)` of a 3D lattice
:rtype: :py:class:`MatrixGroup <structrans.crystallography.MatrixGroup>`
:raises AttributeError: Lattice groups for other than 2D and 3D lattices are not implemented yet.
"""
if not self.dimension() in [2, 3]:
raise AttributeError(
'Lattice groups for other than 2D and 3D lattices are not implemented yet.'
)
if self.__specLatticeGroup is None:
E = self.__E
Einv = la.inv(E)
mats = np.array([
np.rint(Einv.dot(Q.dot(E)))
for Q in self.point_group().matrices()
],
dtype='int')
return MatrixGroup(mats)
