t3m_form_then_round
===================

.. py:function:: t3toolbox.backend.t3_linalg.t3m_form_then_round(x, y, max_tucker_ranks = None, max_tt_ranks = None, rtol = None, atol = None)

   .. code-block:: python

      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 (:py:func:`t3_mult`, multiplied ranks) and, if any
   truncation is requested, rounds it with :py:func:`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.