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 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)
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
class Lattice():
"""
This is the base class of lattices.
:attribute E: two-dimensional square matrix (any type can be converted to :py:class:`numpy.ndarray`)
"""
def __init__(self, E):
# check if E is a square matrix
try:
if not isinstance(E, np.ndarray):
E = np.array(E)
if not _is_square_mat(E):
raise ValueError('Base is not a square matrix')
if la.det(E)**2 <= 0.0:
raise ValueError('Bae matrix is singular')
except Exception:
raise ValueError('Base is not a square matrix')
self.__E = E
self.__N = len(E)
self.__LaueGroup = None
self.__pointGroup = None
self.__latticeGroup = None
self.__specLatticeGroup = None
def base(self):
"""
:return: the base matrix
:rtype: :py:class:`numpy.ndarray`
"""
E = np.empty_like(self.__E)
E[:] = self.__E
return E
def getbase(self):
warn("getbase() is deprecated, please use base() instead.", DeprecationWarning)
return self.base()
def dimension(self):
"""
Get the dimenstion of the lattice.
:return: (*integer*) - the dimenstion of the lattice
"""
return self.__N
def inpointgroup(self, Q):
"""
Check if `Q` is in the point group of the lattice.
This method works for lattices in any dimension.
"""
# if Q is not an orthogonal matrix, return false
try:
Q = np.array(Q)
except Exception:
return False
if not _in_O3(Q):
return False
if len(Q) != self.__N:
return False
return self == Lattice(np.dot(Q, self.__E))
def inlatticegroup(self, M):
"""
Check if `M` is in the lattice group of the lattice.
This method works for lattices in any dimension.
"""
# if Q is not an orthogonal matrix, return false
try:
M = np.array(M)
except Exception:
return False
M_int = np.rint(M)
if not np.allclose(M, M_int, atol=1E-8):
return False
# QE = EM
E = self.base()
Q = E.dot(M).dot(la.inv(E))
return _in_O3(Q)
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 getLauegroup(self):
warn("getLauegroup() is deprecated, please use Laue_group() instead.", DeprecationWarning)
return self.Laue_group()
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 getpointgroup(self):
warn("getpointgroup() is deprecated, please use point_group() instead.", DeprecationWarning)
return self.point_group()
def special_lattice_group(self):
"""
:return: get the special lattice group in :math:`SL(3, \mathbb Z)` of a 3D lattice
:rtype: :py:class:`MatrixGroup <structrans.crystallography.MatrixGroup>`
:raises AttributeError: Special lattice groups for other than 2D and 3D lattices are not implemented yet.
"""
if not self.dimension() in [2, 3]:
raise AttributeError('Special 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.Laue_group().matrices()], dtype='int')
return MatrixGroup(mats)
def getspeciallatticegroup(self):
warn("getspeciallatticegroup() is deprecated, please use special_lattice_group() instead.", DeprecationWarning)
return self.special_lattice_group()
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)
def getlatticegroup(self):
warn("getlatticegroup() is deprecated, please use lattice_group() instead.", DeprecationWarning)
return self.special_lattice_group()
def __eq__(self, other):
if not isinstance(other, Lattice):
return False
if not self.dimension() == other.dimension():
return False
E1 = self.base()
E2 = other.base()
# E1 A = E2
A = np.dot(la.inv(E1), E2)
A_int = np.rint(A)
return np.allclose(A, A_int, atol=1E-8)
def __str__(self):
des_str = '{:d} dimensional lattice:'.format(self.__N)
for i in range(self.__N):
des_str = des_str + '\n e_{:d} = {:s}'.format(i+1, str(self.__E[:, i]))
return des_str
class Lattice():
"""
This is the base class of lattices.
:attribute E: two-dimensional square matrix (any type can be converted to :py:class:`numpy.ndarray`)
"""
def __init__(self, E):
# check if E is a square matrix
try:
if not isinstance(E, np.ndarray):
E = np.array(E)
if not _is_square_mat(E):
raise ValueError('Base is not a square matrix')
if la.det(E)**2 <= 0.0:
raise ValueError('Bae matrix is singular')
except Exception:
raise ValueError('Base is not a square matrix')
self.__E = E
self.__N = len(E)
self.__LaueGroup = None
self.__pointGroup = None
self.__latticeGroup = None
self.__specLatticeGroup = None
def base(self):
"""
:return: the base matrix
:rtype: :py:class:`numpy.ndarray`
"""
E = np.empty_like(self.__E)
E[:] = self.__E
return E
def getbase(self):
warn("getbase() is deprecated, please use base() instead.",
DeprecationWarning)
return self.base()
def dimension(self):
"""
Get the dimenstion of the lattice.
:return: (*integer*) - the dimenstion of the lattice
"""
return self.__N
def inpointgroup(self, Q):
"""
Check if `Q` is in the point group of the lattice.
This method works for lattices in any dimension.
"""
# if Q is not an orthogonal matrix, return false
try:
Q = np.array(Q)
except Exception:
return False
if not _in_O3(Q):
return False
if len(Q) != self.__N:
return False
return self == Lattice(np.dot(Q, self.__E))
def inlatticegroup(self, M):
"""
Check if `M` is in the lattice group of the lattice.
This method works for lattices in any dimension.
"""
# if Q is not an orthogonal matrix, return false
try:
M = np.array(M)
except Exception:
return False
M_int = np.rint(M)
if not np.allclose(M, M_int, atol=1E-8):
return False
# QE = EM
E = self.base()
Q = E.dot(M).dot(la.inv(E))
return _in_O3(Q)
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 getLauegroup(self):
warn("getLauegroup() is deprecated, please use Laue_group() instead.",
DeprecationWarning)
return self.Laue_group()
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 getpointgroup(self):
warn(
"getpointgroup() is deprecated, please use point_group() instead.",
DeprecationWarning)
return self.point_group()
def special_lattice_group(self):
"""
:return: get the special lattice group in :math:`SL(3, \mathbb Z)` of a 3D lattice
:rtype: :py:class:`MatrixGroup <structrans.crystallography.MatrixGroup>`
:raises AttributeError: Special lattice groups for other than 2D and 3D lattices are not implemented yet.
"""
if not self.dimension() in [2, 3]:
raise AttributeError(
'Special 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.Laue_group().matrices()
],
dtype='int')
return MatrixGroup(mats)
def getspeciallatticegroup(self):
warn(
"getspeciallatticegroup() is deprecated, please use special_lattice_group() instead.",
DeprecationWarning)
return self.special_lattice_group()
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)
def getlatticegroup(self):
warn(
"getlatticegroup() is deprecated, please use lattice_group() instead.",
DeprecationWarning)
return self.special_lattice_group()
def __eq__(self, other):
if not isinstance(other, Lattice):
return False
if not self.dimension() == other.dimension():
return False
E1 = self.base()
E2 = other.base()
# E1 A = E2
A = np.dot(la.inv(E1), E2)
A_int = np.rint(A)
return np.allclose(A, A_int, atol=1E-8)
def __str__(self):
des_str = '{:d} dimensional lattice:'.format(self.__N)
for i in range(self.__N):
des_str = des_str + '\n e_{:d} = {:s}'.format(
i + 1, str(self.__E[:, i]))
return des_str