treams.Lattice

class treams.Lattice(arr, alignment=None)

Lattice definition.

The lattice can be one-, two-, or three-dimensional. If it is not three-dimensional it is required to be embedded into a lower dimensional subspace that is aligned with the Cartesian axes. The default alignment for one-dimensional lattices is along the z-axis and for two-dimensional lattices it is in the x-y-plane.

For a one-dimensional lattice the definition consists of simply the value of the lattice pitch. Higher-dimensional lattices are defined by (2, 2)- or (3, 3)-arrays. If the arrays are diagonal it is sufficient to specify the (2,)- or (3,)-array diagonals. Alternatively, if another instance of a Lattice is given, the defined alignment is extracted, which can be used to separate a lower-dimensional sublattice.

Lattices are immutable objects.

Example

>>> Lattice([1, 2])
Lattice([[1. 0.]
         [0. 2.]], alignment='xy')
>>> Lattice(_, 'x')
Lattice(1.0, alignment='x')

Parameters:

• arr (float, array, Lattice) – Lattice definition. Each row corresponds to one lattice vector, each column to the axis defined in alignment.

• alignment (str, optional) – Alignment of the lattice. Possible values are ‘x’, ‘y’, ‘z’, ‘xy’, ‘yz’, ‘zx’, and ‘xyz’.

Attributes

alignment	The alignment of the lattice in three-dimensional space.
dim	Dimension of the lattice.
reciprocal	Reciprocal lattice.
volume	(Generalized) volume of the lattice.

Methods

__and__(other)	Intersect two lattices.
__eq__(other)	Equality.
__ge__(value, /)	Return self>=value.
__getitem__(idx)	Index into the lattice.
__gt__(value, /)	Return self>value.
__le__(other)	Test if one lattice includes another.
__lt__(value, /)	Return self<value.
__ne__(value, /)	Return self!=value.
__or__(other)	Merge two lattices.
__repr__()	Representation.
__str__()	String representation.
cubic(pitch[, alignment])	Create a three-dimensional cubic lattice.
hexagonal(pitch[, height, alignment])	Create a hexagonal lattice.
isdisjoint(other)	Test if lattices are disjoint.
orthorhombic(x, y, z[, alignment])	Create a three-dimensional orthorhombic lattice.
permute([n])	Permute the lattice orientation.
rectangular(x, y[, alignment])	Create a two-dimensional rectangular lattice.
square(pitch[, alignment])	Create a two-dimensional square lattice.
__lt__(value, /)	Return self<value.
__ge__(value, /)	Return self>=value.
__ne__(value, /)	Return self!=value.
__gt__(value, /)	Return self>value.