def gen_cuboid(self, cuboid, periodicity=None):
"""Generates list of lattice points containing all points in a cuboid.
Args:
cuboid: lower and upper ends of the cuboid.
periodicity: periodicity object.
Returns:
Cartesian coordinates of the grid points.
"""
# Get the 8 corners of the cuboid
mesh = np.mgrid[0:2, 0:2, 0:2].reshape(3, -1).transpose()
abc_corners = [[cuboid[mm[0], 0], cuboid[mm[1], 1], cuboid[mm[2], 2]]
for mm in mesh]
# Get corners of the containing parallelepiped in relative coordinates
invlatvecs = np.linalg.inv(self.latvecs)
nmo_corners = np.dot(abc_corners, invlatvecs)
nmo_mininds = np.floor(nmo_corners.min(axis=0)).astype(int)
nmo_maxinds = np.floor(nmo_corners.max(axis=0)).astype(int)
# Generate mesh indexing all points inside the parallelepiped
nallpoint = np.abs(np.prod(nmo_maxinds - nmo_mininds))
printstatus("Number of necessary grid points: {:d}".format(
int(nallpoint)),
indentlevel=1)
nmo = np.mgrid[nmo_mininds[0]:nmo_maxinds[0] + 1,
nmo_mininds[1]:nmo_maxinds[1] + 1,
nmo_mininds[2]:nmo_maxinds[2] + 1, ]
nmo = nmo.reshape(3, -1).transpose()
# Throw away points in the parallelepiped which are farther away from
# the cuboid as the maximal size of the unit cell along given direction
abc = np.dot(nmo, self.latvecs)
buffer = np.max(np.abs(self.latvecs), axis=0)
cond1 = np.all(abc < cuboid[0] - buffer, axis=1)
cond2 = np.all(abc > cuboid[1] + buffer, axis=1)
inside = np.logical_not(np.logical_or(cond1, cond2))
return np.dot(nmo[inside], self.latvecs)
def gen_cuboid(self, cuboid, periodicity=None):
"""Generates list of lattice points containing all points in a cuboid.
Args:
cuboid: lower and upper ends of the cuboid.
periodicity: periodicity object.
Returns:
Cartesian coordinates of the grid points.
"""
# Get the 8 corners of the cuboid
mesh = np.mgrid[0:2,0:2,0:2].reshape(3, -1).transpose()
abc_corners = [ [ cuboid[mm[0],0], cuboid[mm[1],1], cuboid[mm[2],2] ]
for mm in mesh ]
# Get corners of the containing parallelepiped in relative coordinates
invlatvecs = np.linalg.inv(self.latvecs)
nmo_corners = np.dot(abc_corners, invlatvecs)
nmo_mininds = np.floor(nmo_corners.min(axis=0)).astype(int)
nmo_maxinds = np.floor(nmo_corners.max(axis=0)).astype(int)
# Generate mesh indexing all points inside the parallelepiped
nallpoint = np.abs(np.prod(nmo_maxinds - nmo_mininds))
printstatus(
"Number of necessary grid points: {:d}".format(int(nallpoint)),
indentlevel=1)
nmo = np.mgrid[nmo_mininds[0]:nmo_maxinds[0]+1,
nmo_mininds[1]:nmo_maxinds[1]+1,
nmo_mininds[2]:nmo_maxinds[2]+1, ]
nmo = nmo.reshape(3, -1).transpose()
# Throw away points in the parallelepiped which are farther away from
# the cuboid as the maximal size of the unit cell along given direction
abc = np.dot(nmo, self.latvecs)
buffer = np.max(np.abs(self.latvecs), axis=0)
cond1 = np.all(abc < cuboid[0] - buffer, axis=1)
cond2 = np.all(abc > cuboid[1] + buffer, axis=1)
inside = np.logical_not(np.logical_or(cond1, cond2))
return np.dot(nmo[inside], self.latvecs)
def fromdict(cls, geometry, inidict):
"""Builds instance from dictionary."""
period_type = inidict.get("period_type", "0D")
if period_type not in ["0D", "1D", "2D", "3D"]:
error("Invalid periodicty type '" + period_type + "'")
# 0D periodicity
if period_type == "0D":
return cls(geometry, "0D")
# 1D periodicity
if period_type == "1D":
axis = inidict.get("axis", None)
if axis is None:
error("Missing axis specification for 1D periodicity.")
try:
axis = np.array([int(s) for s in axis.split()])
axis.shape = (1, 3)
except ValueError:
error("Invalid axis specification.")
if np.all(axis == 0):
error("Invalid axis direction.")
# 2D periodicity
elif period_type == "2D":
axis = inidict.get("axis", None)
miller = inidict.get("miller_indices", None)
if axis is None and miller is None:
error("Either 'axis' or 'miller_indices' needed for "
"periodicity specification.")
elif axis is not None and miller is not None:
error(
"Only one of the keywords 'axis' or 'miller_indices' can "
"be used for periodicity specification.")
if miller:
try:
miller = np.array([int(s) for s in miller.split()])
miller.shape = (3, )
except ValueError:
error("Invalid miller index for 2D periodicity")
if np.all(miller == 0):
error("Invalid miller index for 2D periodicity")
axis = plane_axis_from_miller(miller)
else:
try:
axis = np.array([int(s) for s in axis.split()])
axis.shape = (2, 3)
except ValueError:
error("Invalid axis specification.")
if np.all(axis == 0):
error("Invalid axis direction.")
if np.all(np.cross(axis[0], axis[1]) == 0):
error("Axis are parallel.")
# 3D periodicity
else:
axis = inidict.get("axis", None)
superlattice = inidict.get("superlattice", None)
if axis is None and superlattice is None:
error("Either 'axis' or 'superlattice' needed for "
"periodicity specification.")
elif axis is not None and superlattice is not None:
error("Only one of the keywords 'axis' or 'superlattice'"
"can be used for periodicity specification.")
if superlattice:
try:
superlattice = np.array(
[float(s) for s in superlattice.split()])
superlattice.shape = (3, 3)
except ValueError:
error("Invalid superlattice specification")
if np.abs(np.linalg.det(superlattice)) < nc.EPSILON:
error("Linearly dependent superlattice vectors")
axis = cell_axis_from_superlattice(
superlattice,
np.dot(geometry.bravais_cell, geometry.latvecs))
else:
try:
axis = np.array([int(s) for s in axis.split()])
axis.shape = (3, 3)
except ValueError:
error("Invalid axis specification.")
if np.all(axis == 0):
error("Invalid axis direction.")
if np.abs(np.linalg.det(axis)) < nc.EPSILON:
error("Linearly dependent axis")
# Switch back to primitive lattice, if necessary
if np.any(geometry.bravais_cell != np.eye(3, dtype=int)):
printstatus("Axis with respect to Bravais lattice:")
for vec in axis:
printstatus(
"{:3d} {:3d} {:3d}".format(*[int(ss) for ss in vec]),
indentlevel=1)
axis = np.dot(axis, geometry.bravais_cell)
# Get smallest possible unit cell
for ii in range(len(axis)):
divisor = gcd(abs(axis[ii]))
axis[ii] = axis[ii] // divisor
printstatus("Axis with respect to primitive lattice:")
for vec in axis:
printstatus("{:3d} {:3d} {:3d}".format(*[int(ss) for ss in vec]),
indentlevel=1)
# Repeat unit cell
cellrep = inidict.get("axis_repetition", None)
if cellrep:
try:
cellrep = np.array([float(s) for s in cellrep.split()])
cellrep.shape = (int(period_type[0]), )
except ValueError:
error("Invalid axis repetition specification.")
axis = np.array(axis * cellrep[:, np.newaxis], int)
printstatus("Axis repetition:" +
" ".join(["{:3d}".format(int(s)) for s in cellrep]))
return cls(geometry, period_type, axis)
def fromdict(cls, geometry, inidict):
"""Builds instance from dictionary."""
period_type = inidict.get("period_type", "0D")
if period_type not in [ "0D", "1D", "2D", "3D"]:
error("Invalid periodicty type '" + period_type + "'")
# 0D periodicity
if period_type == "0D":
return cls(geometry, "0D")
# 1D periodicity
if period_type == "1D":
axis = inidict.get("axis", None)
if axis is None:
error("Missing axis specification for 1D periodicity.")
try:
axis = np.array([ int(s) for s in axis.split() ])
axis.shape = (1, 3)
except ValueError:
error("Invalid axis specification.")
if np.all(axis == 0):
error("Invalid axis direction.")
# 2D periodicity
elif period_type == "2D":
axis = inidict.get("axis", None)
miller = inidict.get("miller_indices", None)
if axis is None and miller is None:
error("Either 'axis' or 'miller_indices' needed for "
"periodicity specification.")
elif axis is not None and miller is not None:
error("Only one of the keywords 'axis' or 'miller_indices' can "
"be used for periodicity specification.")
if miller:
try:
miller = np.array([ int(s) for s in miller.split() ])
miller.shape = (3, )
except ValueError:
error("Invalid miller index for 2D periodicity")
if np.all(miller == 0):
error("Invalid miller index for 2D periodicity")
axis = plane_axis_from_miller(miller)
else:
try:
axis = np.array([ int(s) for s in axis.split() ])
axis.shape = (2, 3)
except ValueError:
error("Invalid axis specification.")
if np.all(axis == 0):
error("Invalid axis direction.")
if np.all(np.cross(axis[0], axis[1]) == 0):
error("Axis are parallel.")
# 3D periodicity
else:
axis = inidict.get("axis", None)
superlattice = inidict.get("superlattice", None)
if axis is None and superlattice is None:
error("Either 'axis' or 'superlattice' needed for "
"periodicity specification.")
elif axis is not None and superlattice is not None:
error("Only one of the keywords 'axis' or 'superlattice'"
"can be used for periodicity specification.")
if superlattice:
try:
superlattice = np.array([ float(s)
for s in superlattice.split() ])
superlattice.shape = (3, 3)
except ValueError:
error("Invalid superlattice specification")
if np.abs(np.linalg.det(superlattice)) < nc.EPSILON:
error("Linearly dependent superlattice vectors")
axis = cell_axis_from_superlattice(superlattice,
np.dot(geometry.bravais_cell, geometry.latvecs))
else:
try:
axis = np.array([ int(s) for s in axis.split() ])
axis.shape = (3, 3)
except ValueError:
error("Invalid axis specification.")
if np.all(axis == 0):
error("Invalid axis direction.")
if np.abs(np.linalg.det(axis)) < nc.EPSILON:
error("Linearly dependent axis")
# Switch back to primitive lattice, if necessary
if np.any(geometry.bravais_cell != np.eye(3, dtype=int)):
printstatus("Axis with respect to Bravais lattice:")
for vec in axis:
printstatus("{:3d} {:3d} {:3d}".format(
*[ int(ss) for ss in vec ]), indentlevel=1)
axis = np.dot(axis, geometry.bravais_cell)
# Get smallest possible unit cell
for ii in range(len(axis)):
divisor = gcd(abs(axis[ii]))
axis[ii] /= divisor
printstatus("Axis with respect to primitive lattice:")
for vec in axis:
printstatus("{:3d} {:3d} {:3d}".format(
*[ int(ss) for ss in vec ]), indentlevel=1)
# Repeat unit cell
cellrep = inidict.get("axis_repetition", None)
if cellrep:
try:
cellrep = np.array([ float(s) for s in cellrep.split() ])
cellrep.shape = (int(period_type[0]), )
except ValueError:
error("Invalid axis repetition specification.")
axis *= cellrep[:,np.newaxis]
printstatus("Axis repetition:"
+ " ".join([ "{:3d}".format(int(s)) for s in cellrep ]))
return cls(geometry, period_type, axis)
