fv_weights_from_t3_weights

t3toolbox.backend.fv_operations.fv_weights_from_t3_weights(t3_weights)

def fv_weights_from_t3_weights(
        t3_weights: typ.Tuple[typ.Sequence[NDArray], typ.Sequence[NDArray]],  # (tucker_weights, tt_weights)
) -> typ.Tuple[
    typ.Tuple[NDArray, ...],  # up_weights    = tucker_weights
    typ.Tuple[NDArray, ...],  # down_weights  = tucker_weights
    typ.Tuple[NDArray, ...],  # left_weights  = tt_weights[:-1]
    typ.Tuple[NDArray, ...],  # right_weights = tt_weights[1:]
]:

Build frame weights (a tangent metric) from base-point edge weights (tucker_weights, tt_weights).

up = down = tucker_weights; left = tt_weights[:-1], right = tt_weights[1:]. The TT slicing encodes the convention that H_i’s left bond is TT bond i and its right bond is bond i+1 – non-obvious, hence a named function. The result is a valid T3FrameWeights; it pairs with a minimal-rank tangent (where the down/complement rank nD equals the Tucker rank nU, e.g. from t3svd). A non-minimal tangent has nD < nU and would mismatch the down family at use.

Parameters:

t3_weights (t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray]])

Return type:

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