t3m_inplace_fused#

t3toolbox.backend.t3_linalg.t3m_inplace_fused(x, y, max_tucker_ranks=None, max_tt_ranks=None, rtol=None, atol=None)#
def t3m_inplace_fused(
        x: typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # (tucker_cores_x, tt_cores_x)
        y: typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # (tucker_cores_y, tt_cores_y)

        max_tucker_ranks:   typ.Union[int, typ.Sequence[int], None] = None,  # scalar caps all, or len=d
        max_tt_ranks:       typ.Union[int, typ.Sequence[int], None] = None,  # scalar caps all, or len=d+1

        rtol:               typ.Optional[float] = None,  # requires unstacked (enforced by the frontend)
        atol:               typ.Optional[float] = None,
) -> typ.Tuple[
    typ.Tuple[NDArray, ...],  # x_times_y tucker_cores
    typ.Tuple[NDArray, ...],  # x_times_y tt_cores
]:

Elementwise product x ⊙ y – method (b): a fused left-to-right sweep that truncates as it goes, never materializing the full product (the workhorse; see docs/ttm_t3m_ht_note.tex).

Right-orthogonalizes the two central TTs separately (the Kronecker of right-canonical cores is right-canonical, so the product’s central TT is right-canonical without being formed), then sweeps left to right carrying the separate (r_x, r_y) bonds. At each mode it builds the product core on the fly, then does the joint per-site T3 truncation (the Tucker rank, weighted by the canonical environment, then the TT bond) – both truncations are optimal because the right side is right-canonical. O(d·r⁴), memory O(r̃·n²·r²) (one site). Stack-aware with max-rank truncation; rtol/atol require unstacked. No truncation requested -> the exact full product.

Parameters:

  • x (t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray]])

  • y (t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray]])

  • max_tucker_ranks (t3toolbox.backend.common.typ.Union[int, t3toolbox.backend.common.typ.Sequence[int], None])

  • max_tt_ranks (t3toolbox.backend.common.typ.Union[int, t3toolbox.backend.common.typ.Sequence[int], None])

  • rtol (t3toolbox.backend.common.typ.Optional[float])

  • atol (t3toolbox.backend.common.typ.Optional[float])

Return type:

t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Tuple[NDArray, Ellipsis], t3toolbox.backend.common.typ.Tuple[NDArray, Ellipsis]]