ut3_weighted_norm#

t3toolbox.backend.ut3_linalg.ut3_weighted_norm(x, weights, use_orthogonalization=True)#
def ut3_weighted_norm(
        x:       UT3Data,                              # (tucker_supercore, tt_supercore, shape, masks)
        weights: ut3_operations.UT3WeightsData,        # (tucker_weight_supercore, tt_weight_supercore, masks)
        use_orthogonalization: bool = True,            # for numerical stability
) -> NDArray:                                          # weighted HS norm, shape=stack_shape

Weighted Hilbert-Schmidt norm of a uniform Tucker tensor train – the norm of the fully-weighted network, norm(absorb(x, weights)). Uniform twin of t3_weighted_norm.

The plain norm squares the inserted diagonals, so weights = 1/sigma penalises by 1/sigma^2. Absorbing breaks any orthogonality x had (that is what the weights do), so the orthogonalization here runs on the weighted train, as in ragged.

Weighting does not mask, but the norm does: the reduction is the existing plain uniform norm, which masks its own input on entry – so the garbage padding absorb passes through is zeroed there, where reductions are, not here (docs/contributor/weighted_internals.md §2).

Precondition: weights’ masks must equal x’s masks (ut3_weights_consistent()); the frontend enforces it.

Parameters:

  • x (UT3Data)

  • weights (t3toolbox.backend.ut3_operations.UT3WeightsData)

  • use_orthogonalization (bool)

Return type:

NDArray