TuckerTensorTrain.t3m

t3toolbox.tucker_tensor_train.TuckerTensorTrain.t3m(other, method='inplace_fused', max_tucker_ranks=None, max_tt_ranks=None, rtol=None, atol=None, oversample=1)

def t3m(
        self,
        other:              'TuckerTensorTrain',    # same shape & stack_shape
        method:             str = 'inplace_fused',  # the memory-light default for large d

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

        rtol:               typ.Optional[float] = None,  # requires unstacked
        atol:               typ.Optional[float] = None,  # requires unstacked

        oversample:         float = 1,  # method='swap' only; intermediate-rank relaxation
) -> 'TuckerTensorTrain':

Elementwise (Hadamard) product self ⊙ other with optional rank truncation.

Like self * other (whose ranks multiply: n_x·n_y Tucker, r_x·r_y TT) but able to truncate the result. method selects the algorithm – all give the same product, with different cost/memory trade-offs (see docs/ttm_t3m_ht_note.tex):

• 'form_then_round' – form the full product, then round. Parallel forming; cheapest to run for small bonds. This is what * uses.

• 'inplace_fused' (default) – a fused sweep that never materializes the full product; the right default for large d.

• 'swap' – the swap-based TTM generalization; best when the TT bond r greatly exceeds the number of modes d (O(d²·r³) compute, O(r̃²) memory).

Truncation (any combination; default none ⇒ exact full product): max_tucker_ranks / max_tt_ranks (a scalar caps every position, or a per-position sequence) and rtol / atol (per-step relative/absolute tolerances).

oversample (method='swap' only, >= 1, default 1 = off): relaxes the intermediate ranks/tolerances by this factor during the swaps and runs a final t3svd cleanup at the exact targets. 1 is the lowest-memory / lowest-quality corner; a modest 2 is a good default for near-form_then_round quality at a small memory cost; quality approaches form_then_round as oversample → ∞. See docs/ttm_t3m_ht_note.tex for why this is needed (the Tucker leaf-frame coupling).

Warning

rtol/atol are not supported for stacked Tucker tensor trains (different stack elements could truncate to different ranks). Use max_*_ranks for stacked input, or unstack first. Max-rank truncation is stacking-compatible.

Parameters:

• other (TuckerTensorTrain)

• method (str)

• max_tucker_ranks (Union[int, collections.abc.Sequence[int], None])

• max_tt_ranks (Union[int, collections.abc.Sequence[int], None])

• rtol (Optional[float])

• atol (Optional[float])

• oversample (float)

Return type:

TuckerTensorTrain