class LatticeBase(BaseClass):
"""Base class for crystallographic lattice objects.
Parameters
----------
nd : int
cell_matrix : array_like
orientation_matrix : array_like, optional
offset : array_like, optional
"""
def __init__(self,
nd=None,
cell_matrix=None,
orientation_matrix=None,
offset=None):
super().__init__()
self.nd = nd
self.offset = Point(offset, nd=3)
if cell_matrix is not None and orientation_matrix is None:
orientation_matrix = cell_matrix.T * self.fractional_matrix
if orientation_matrix is None:
orientation_matrix = np.asmatrix(np.identity(3))
self.orientation_matrix = np.asmatrix(orientation_matrix)
self.lattice_type = None
def __dir__(self):
return ['nd', 'offset', 'orientation_matrix']
def __eq__(self, other):
if isinstance(other, type(self)):
return self is other or \
all([np.allclose(getattr(self, attr), getattr(other, attr))
for attr in dir(self)])
def __lt__(self, other):
if isinstance(other, type(self)):
try:
return self.cell_volume < other.cell_volume
except AttributeError:
return self.cell_area < other.cell_area
@property
def cell_matrix(self):
"""Matrix of lattice row vectors.
Same as :attr:`Crystal2DLattice.ortho_matrix`\ .T or
:attr:`Crystal3DLattice.ortho_matrix`\ .T.
"""
return (self.orientation_matrix * self.ortho_matrix).T
@property
def matrix(self):
"""Alias for \
:attr:`~sknano.core.crystallography.LatticeBase.cell_matrix`."""
return self.cell_matrix
@property
def fractional_matrix(self):
"""Transformation matrix to convert from cartesian coordinates to \
fractional coordinates."""
return np.linalg.inv(self.ortho_matrix)
@property
def metric_tensor(self):
"""Metric tensor."""
return self.cell_matrix * self.cell_matrix.T
def fractional_to_cartesian(self, fcoords):
"""Convert fractional coordinate to cartesian coordinate.
Parameters
----------
fcoords : array_like
Returns
-------
:class:`~numpy:numpy.ndarray`
"""
ccoords = self.orientation_matrix * self.ortho_matrix * \
np.asmatrix(fcoords).T + self.offset.column_matrix
try:
return ccoords.T.A.reshape((3, ))
except ValueError:
return ccoords.T.A.reshape((len(fcoords), 3))
def cartesian_to_fractional(self, ccoords):
"""Convert cartesian coordinate to fractional coordinate.
Parameters
----------
ccoords : array_like
Returns
-------
:class:`~numpy:numpy.ndarray`
"""
fcoords = np.linalg.inv(self.ortho_matrix) * \
np.linalg.inv(self.orientation_matrix) * \
(np.asmatrix(ccoords).T - self.offset.column_matrix)
try:
return fcoords.T.A.reshape((3, ))
except ValueError:
return fcoords.T.A.reshape((len(ccoords), 3))
def wrap_fractional_coordinate(self, p, epsilon=1e-6, pbc=None):
"""Wrap fractional coordinate to lie within unit cell.
Parameters
----------
p : array_like
Returns
-------
:class:`~numpy:numpy.ndarray`
"""
if pbc is None:
pbc = np.asarray(np.ones(3), dtype=bool)
p = np.ma.array(p, mask=~pbc)
p = np.ma.fmod(p, 1)
p[np.ma.where(p < 0)] += 1
p[np.ma.where(p > 1 - epsilon)] -= 1
p[np.ma.where(np.logical_or((p > 1 - epsilon), (p < epsilon)))] = 0
p.mask = np.ma.nomask
return p.tolist()
def wrap_cartesian_coordinate(self, p, pbc=None):
"""Wrap cartesian coordinate to lie within unit cell.
Parameters
----------
p : array_like
Returns
-------
:class:`~numpy:numpy.ndarray`
"""
return self.fractional_to_cartesian(
self.wrap_fractional_coordinate(self.cartesian_to_fractional(p),
pbc=pbc))
def rotate(self,
angle=None,
axis=None,
anchor_point=None,
rot_point=None,
from_vector=None,
to_vector=None,
degrees=False,
transform_matrix=None,
verbose=False,
**kwargs):
"""Rotate unit cell.
Parameters
----------
angle : float
axis : :class:`~sknano.core.math.Vector`, optional
anchor_point : :class:`~sknano.core.math.Point`, optional
rot_point : :class:`~sknano.core.math.Point`, optional
from_vector, to_vector : :class:`~sknano.core.math.Vector`, optional
degrees : bool, optional
transform_matrix : :class:`~numpy:numpy.ndarray`
See Also
--------
core.math.rotate
"""
if self.nd == 2:
axis = 'z'
if transform_matrix is None:
transform_matrix = \
np.asmatrix(
rotation_matrix(angle=angle, axis=axis,
anchor_point=anchor_point,
rot_point=rot_point,
from_vector=from_vector,
to_vector=to_vector, degrees=degrees,
verbose=verbose, **kwargs))
# print('transform_matrix: {}'.format(transform_matrix))
# transform_matrix = \
# transformation_matrix(angle=angle, axis=axis,
# anchor_point=anchor_point,
# rot_point=rot_point,
# from_vector=from_vector,
# to_vector=to_vector, degrees=degrees,
# verbose=verbose, **kwargs)
self.orientation_matrix = \
transform_matrix * self.orientation_matrix
def translate(self, t):
"""Translate lattice.
Parameters
----------
t : :class:`Vector`
See Also
--------
core.math.translate
"""
self.offset.translate(t)
class LatticeBase(BaseClass):
"""Base class for crystallographic lattice objects.
Parameters
----------
nd : int
cell_matrix : array_like
orientation_matrix : array_like, optional
offset : array_like, optional
"""
def __init__(self, nd=None, cell_matrix=None, orientation_matrix=None,
offset=None):
super().__init__()
self.nd = nd
self.offset = Point(offset, nd=3)
if cell_matrix is not None and orientation_matrix is None:
orientation_matrix = cell_matrix.T * self.fractional_matrix
if orientation_matrix is None:
orientation_matrix = np.asmatrix(np.identity(3))
self.orientation_matrix = np.asmatrix(orientation_matrix)
self.lattice_type = None
def __dir__(self):
return ['nd', 'offset', 'orientation_matrix']
def __eq__(self, other):
if isinstance(other, type(self)):
return self is other or \
all([np.allclose(getattr(self, attr), getattr(other, attr))
for attr in dir(self)])
def __lt__(self, other):
if isinstance(other, type(self)):
try:
return self.cell_volume < other.cell_volume
except AttributeError:
return self.cell_area < other.cell_area
@property
def cell_matrix(self):
"""Matrix of lattice row vectors.
Same as :attr:`Crystal2DLattice.ortho_matrix`\ .T or
:attr:`Crystal3DLattice.ortho_matrix`\ .T.
"""
return (self.orientation_matrix * self.ortho_matrix).T
@property
def matrix(self):
"""Alias for \
:attr:`~sknano.core.crystallography.LatticeBase.cell_matrix`."""
return self.cell_matrix
@property
def fractional_matrix(self):
"""Transformation matrix to convert from cartesian coordinates to \
fractional coordinates."""
return np.linalg.inv(self.ortho_matrix)
@property
def metric_tensor(self):
"""Metric tensor."""
return self.cell_matrix * self.cell_matrix.T
def fractional_to_cartesian(self, fcoords):
"""Convert fractional coordinate to cartesian coordinate.
Parameters
----------
fcoords : array_like
Returns
-------
:class:`~numpy:numpy.ndarray`
"""
ccoords = self.orientation_matrix * self.ortho_matrix * \
np.asmatrix(fcoords).T + self.offset.column_matrix
try:
return ccoords.T.A.reshape((3, ))
except ValueError:
return ccoords.T.A.reshape((len(fcoords), 3))
def cartesian_to_fractional(self, ccoords):
"""Convert cartesian coordinate to fractional coordinate.
Parameters
----------
ccoords : array_like
Returns
-------
:class:`~numpy:numpy.ndarray`
"""
fcoords = np.linalg.inv(self.ortho_matrix) * \
np.linalg.inv(self.orientation_matrix) * \
(np.asmatrix(ccoords).T - self.offset.column_matrix)
try:
return fcoords.T.A.reshape((3, ))
except ValueError:
return fcoords.T.A.reshape((len(ccoords), 3))
def wrap_fractional_coordinate(self, p, epsilon=1e-6, pbc=None):
"""Wrap fractional coordinate to lie within unit cell.
Parameters
----------
p : array_like
Returns
-------
:class:`~numpy:numpy.ndarray`
"""
if pbc is None:
pbc = np.asarray(np.ones(3), dtype=bool)
p = np.ma.array(p, mask=~pbc)
p = np.ma.fmod(p, 1)
p[np.ma.where(p < 0)] += 1
p[np.ma.where(p > 1 - epsilon)] -= 1
p[np.ma.where(np.logical_or((p > 1 - epsilon), (p < epsilon)))] = 0
p.mask = np.ma.nomask
return p.tolist()
def wrap_cartesian_coordinate(self, p, pbc=None):
"""Wrap cartesian coordinate to lie within unit cell.
Parameters
----------
p : array_like
Returns
-------
:class:`~numpy:numpy.ndarray`
"""
return self.fractional_to_cartesian(
self.wrap_fractional_coordinate(self.cartesian_to_fractional(p),
pbc=pbc))
def rotate(self, angle=None, axis=None, anchor_point=None,
rot_point=None, from_vector=None, to_vector=None, degrees=False,
transform_matrix=None, verbose=False, **kwargs):
"""Rotate unit cell.
Parameters
----------
angle : float
axis : :class:`~sknano.core.math.Vector`, optional
anchor_point : :class:`~sknano.core.math.Point`, optional
rot_point : :class:`~sknano.core.math.Point`, optional
from_vector, to_vector : :class:`~sknano.core.math.Vector`, optional
degrees : bool, optional
transform_matrix : :class:`~numpy:numpy.ndarray`
See Also
--------
core.math.rotate
"""
if self.nd == 2:
axis = 'z'
if transform_matrix is None:
transform_matrix = \
np.asmatrix(
rotation_matrix(angle=angle, axis=axis,
anchor_point=anchor_point,
rot_point=rot_point,
from_vector=from_vector,
to_vector=to_vector, degrees=degrees,
verbose=verbose, **kwargs))
# print('transform_matrix: {}'.format(transform_matrix))
# transform_matrix = \
# transformation_matrix(angle=angle, axis=axis,
# anchor_point=anchor_point,
# rot_point=rot_point,
# from_vector=from_vector,
# to_vector=to_vector, degrees=degrees,
# verbose=verbose, **kwargs)
self.orientation_matrix = \
transform_matrix * self.orientation_matrix
def translate(self, t):
"""Translate lattice.
Parameters
----------
t : :class:`Vector`
See Also
--------
core.math.translate
"""
self.offset.translate(t)
