compute_eta

t3toolbox.backend.probing.compute_eta(down_tt_cores, mus, nus)

def compute_eta(
        down_tt_cores:         typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=C+(rLi,nOi,rR(i+1))
        mus:                    typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=W+C+(rLi,)
        nus:                    typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=(...,rR(i+1))
) -> typ.Union[typ.Sequence[NDArray], NDArray]: # etas. len=d, elm_shape=W+C+(nOi,)

Compute downward edge variables associated with edges between Tucker cores and adjacent TT-cores. Used for probing a Tucker tensor train.

See Section 6.2, particularly Figure 7 and Algorithm 5, in:

Alger, N., Christierson, B., Chen, P., & Ghattas, O. (2026). “Tucker Tensor Train Taylor Series.” arXiv preprint arXiv:2603.21141. https://arxiv.org/abs/2603.21141

Parameters:

• down_tt_cores (t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[NDArray], NDArray])

• mus (t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[NDArray], NDArray])

• nus (t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[NDArray], NDArray])

Return type:

t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[NDArray], NDArray]