Basis

class btensor.basis.Basis(argument, *, parent=None, metric=None, name=None, orthonormal=None)[source]

Class to represent a vector space basis, which can be used to define a Tensor object.

Parameters

argument (int | BasisArgument) – Integer to create a rootbasis or sequence, slice, or array to create a derived basis.
parent (Basis | None) – Parent basis object for the derived basis. If it is None, the basis is a root-basis. Default: None.
metric (np.ndarray | None) – Metric array, representing the inner product of the basis with itself. It is used to raise and lower tensor indices, if the basis is non-orthonormal. Default: None.
name (str | None) – Name of the basis, which is used for string representations of basis objects. Basis names are not required to be unique. Default: None.
orthonormal (bool | None) – Set True, if the basis is orthonormal, i.e. the metric is the identity matrix. If None, the basis is assumed orthonormal if a) it is a root basis without metric or b) it is a derived basis with an orthonormal parent basis, defined in terms of a permutation + selection (slice or 1D sequence). Default: None.

Return type

None

Methods

`__init__`	Initialize new Basis object.
`get_by_id`	Returns a previously defined basis based on its ID, if it exists.
`get_common_parent`	Find first common ancestor basis between multiple bases.
`get_overlap`	Get overlap matrix with another basis as a Tensor.
`get_parents`	Get list of parent bases ordered from direct parent to root basis.
`get_transformation`	Get transformation matrix to another basis as a Tensor with general variance.
`get_transformation_from`	Get transformation matrix from another basis as a Tensor with variance (-1, 1).
`get_transformation_to`	Get transformation matrix to another basis as a Tensor with variance (-1, 1).
`is_compatible_with`	Check if basis is compatible with another basis.
`is_derived_from`	Check if the basis is derived from a second basis.
`is_parent_of`	Check if the basis is parent of a second basis.
`is_root`	True if basis is a root-basis, False otherwise.
`make_intersect_basis`	Make the smallest orthonormal basis, which spans the intersecting space of both the basis and another basis.
`make_subbasis`	Make a new basis with coefficients or indices in reference to the current basis.
`make_union_basis`	Make the smallest orthonormal basis, which spans both the basis and one or more other bases.
`same_root`	Check if all bases have the same root.

Attributes

`T`	alias of TypeVar('T')
`id`	Unique ID of basis.
`is_orthonormal`	True if the basis is orthonormal.
`metric`	Metric matrix, used to raise and lower tensor indices.
`name`	Name of basis.
`parent`	Parent of basis or None, if the basis is a root-basis.
`root`	Root-basis of the basis or None, if the basis itself is the root-basis.
`size`	Size of basis.
`space`	Space spanned by basis.