Class AbstractTensor¶

Defined in File abstract_tensor.hpp

Inheritance Relationships¶

Derived Types¶

public sequant::NormalOperator< S > (Template Class NormalOperator)
public sequant::Tensor (Class Tensor)

Class Documentation¶

class AbstractTensor¶

AbstractTensor is a tensor over general (i.e., not necessarily commutative) rings. A tensor with \( k \geq 0 \) ket (see Dirac notation ) and \( b \geq 0 \) bra modes describes elements of a tensor product of \( b+k \) vector spaces. Equivalently it represents a linear map between the tensor product of \( k \) primal vector spaces to the tensor product of \( b \) dual vector spaces. Tensor modes are 1-to-1 represented by unique indices, represented by Index objects.

It is also necessary to support modes that are “array-like” in that they do not refer to a vector space or its dual; such modes can represent ordinal indices (e.g. to treat a collection/sequence of tensors as a single tensor) Thus each tensor has zero or more auxiliary (aux) modes. The aux modes are invariant under the transformations of vector spaces and do not contribute to the tensor symmetries.

Tensors can have the following symmetries:

Tensors can be symmetric or nonsymmetric with respect to the transposition of corresponding {bra,ket} modes in bra/ket mode ranges. This symmetry is used to treat particles as indistinguishable or distinguishable in physical simulation. See more below on how such mode bundles are handled.
Tensors can be symmetric, antisymmetric, and nonsymmetric with respect to the transposition of modes within the bra or ket sets. This symmetry is used to model the distinguishable and indistinguishable (bosonic and fermionic) degrees of freedom in many-body quantum mechanics context. More complicated symmetries are not yet supported.
Tensors can be symmetric, conjugate, or nonsymmetric with respect to swap of bra with ket. This symmetry corresponds to time reversal in physical simulation.

The supporting rings are not assumed to be scalars, hence tensor product supporting the concept of tensor is not necessarily commutative.

For some applications the pairing of bra and ket modes is important, hence it is necessary to support not only tensors where first bra mode is paired with the first ket, but it is then necessary to support bra and ket modes that are unpaired. This introduces notion of bra/ket slots. A slot is either occupied by a non-null Index (hence corresponds to a bra or ket mode), or empty (i.e., occupied by a null Index). Tensors with non-symmetric bras and kets can have empty slots in arbitrary positions in bra and ket slot bundles. Such tensors symmetric with respect to reordering of braket bundles (_column_symmetry()) assume the canonical order of slots, defined as follows:

paired braket slot bundles (both bra and ket slots are nonempty) appear first
unpaired bra slots appear next (with ket slots empty, or without altogether is there are no unpaired ket slots)
unpaired ket slots appear next (without matching bra slots).

Empty aux slots are not permitted.

Note

This interface class defines a Tensor concept. All Tensor objects must fulfill the is_tensor trait (see below). To adapt an existing class intrusively derive it from AbstractTensor and implement all member functions. This allows to implement heterogeneous containers of objects that meet the Tensor concept.

Subclassed by sequant::NormalOperator< S >, sequant::Tensor

Public Types

using const_any_view_rand = ranges::any_view<const Index&, ranges::category::random_access>¶

using const_any_view_randsz = ranges::any_view<const Index&, ranges::category::random_access | ranges::category::sized>¶

using any_view_rand = ranges::any_view<Index&, ranges::category::random_access>¶

using any_view_randsz = ranges::any_view<Index&, ranges::category::random_access | ranges::category::sized>¶

Public Functions

virtual ~AbstractTensor() = default¶

inline virtual AbstractTensor *_clone() const¶

clones this object /

Throws:: missing_instantiation_for – if not overloaded

inline virtual std::shared_ptr<AbstractTensor> _clone_shared() const¶: clones this object producing a shared_ptr<AbstractTensor> so that if the derived class is an Expr, hence derived from std::enable_shared_from_this, the weak pointer is set correctly

inline virtual const_any_view_randsz _bra() const¶

accessor for bra slots

Returns:: view of a contiguous range of bra Index objects; empty slots may be empty (i.e., occupied by null indices).

inline virtual const_any_view_randsz _ket() const¶

accesses ket slots

Returns:: view of a contiguous range of ket Index objects; empty slots may be empty (i.e., occupied by null indices).

inline virtual const_any_view_randsz _aux() const¶

accesses aux (non-vector-space) indices

Returns:: view of a contiguous range of aux Index objects

inline virtual const_any_view_rand _braket() const¶

accesses bra and ket slots

Returns:: concatenated (hence, non contiguous) view of bra and ket slots

inline virtual const_any_view_rand _braketaux() const¶

accesses bra, ket, and aux slots

Returns:: view of a not necessarily contiguous view of bra, ket, and aux slots

inline virtual const_any_view_rand _slots() const¶

accesses all slots

Returns:: view of a not necessarily contiguous range of Index objects

inline virtual std::size_t _bra_rank() const¶

Returns:: the number of bra slots (some may be empty, hence this is the gross rank)

inline virtual std::size_t _bra_net_rank() const¶

Returns:: the number of nonempty bra slots (i.e., nonnull bra indices)

inline virtual std::size_t _ket_rank() const¶

Returns:: the number of bra slots (some may be empty, hence this is the gross rank)

inline virtual std::size_t _ket_net_rank() const¶

Returns:: the number of nonempty ket slots (i.e., nonnull bra indices)

inline virtual std::size_t _aux_rank() const¶

Returns:: the number of aux slots

inline virtual std::size_t _num_slots() const¶

Returns:: the number of slots

inline virtual std::size_t _num_indices() const¶

Returns:: the number of indices

inline virtual Symmetry _symmetry() const¶

Returns:: the permutational symmetry of the vector space indices of the tensor

inline virtual BraKetSymmetry _braket_symmetry() const¶

Returns:: the symmetry of tensor under exchange of vectors space (bra) and its dual (ket)

inline virtual ColumnSymmetry _column_symmetry() const¶

Note

slots are left-aligned

Returns:: the symmetry of tensor under exchange of matching {bra,ket} slot pairs

inline virtual std::size_t _color() const¶

inline virtual bool _is_cnumber() const¶