t3m_form_then_round#

t3toolbox.backend.t3_linalg.t3m_form_then_round(x, y, max_tucker_ranks=None, max_tt_ranks=None, rtol=None, atol=None)#
def t3m_form_then_round(
        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 (a): form the full product, then round.

Forms the full Khatri-Rao/Kronecker product (t3_mult(), multiplied ranks) and, if any truncation is requested, rounds it with t3svd(); with no truncation it returns the exact full product directly. The forming step is embarrassingly parallel (no sweep) but materializes the whole product – see docs/ttm_t3m_ht_note.tex for the cost trade-off vs the fused / swap methods. Stack-aware with max-rank truncation; rtol/atol require unstacked.

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]]