ut3svd_supercores#

t3toolbox.backend.ut3_svd.ut3svd_supercores(cores, rank_truncation_masks, squash_tails_first=True, skip_orthogonalization=False, content=None)#
def ut3svd_supercores(
        cores: typ.Tuple[
            NDArray,  # tucker_supercore (assumed masked)
            NDArray,  # tt_supercore
        ],
        rank_truncation_masks: typ.Tuple[
            NDArray,  # tucker_edge_mask -- prefix truncation masks
            NDArray,  # tt_edge_mask
        ],
        squash_tails_first: bool = True,
        skip_orthogonalization: bool = False,  # assume input already right-orthogonal (Tucker down + TT right)

        content: typ.Optional[typ.Tuple[typ.Sequence[int], NDArray, NDArray]] = None,
                 # (shape, tucker_edge_mask, tt_edge_mask) of the INPUT -- HOST. Given -> every
                 # kept-basis SVD (pre-orthogonalization + scan) is PAD-SAFE (review S1b).
) -> typ.Tuple[
    typ.Tuple[NDArray, NDArray],  # (tucker_supercore, tt_supercore) at the INPUT padded (n, r)
    NDArray,  # frame_singular_values, shape=(d,)+stack+(n,)
    NDArray,  # tt_singular_values,    shape=(d+1,)+stack+(r,)
]:

The T3-SVD sweep: orthogonalize, then a left-to-right scan that SVDs each Tucker/TT edge, pads the factors back to the padded size, and multiplies by the prefix truncation masks. Operates at the input padded (n, r); ut3svd() builds the masks and shrinks afterward.

skip_orthogonalization=True assumes the input is already right-orthogonal (Tucker down-orthogonal, TT right-orthogonal – the gauge the L->R scan needs) and skips the orthogonalization passes. Silently wrong if the input is not in that form (not checked).

Parameters:

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

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

  • squash_tails_first (bool)

  • skip_orthogonalization (bool)

  • content (t3toolbox.backend.common.typ.Optional[t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[int], NDArray, NDArray]])

Return type:

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