compute_xi

t3toolbox.backend.probing.compute_xi(up_tucker_cores, ww)

def compute_xi(
        up_tucker_cores:    typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=C+(nUi,Ni)
        ww:                 typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=W+(Ni,)
) -> typ.Union[typ.Sequence[NDArray], NDArray]: # xis. len=d, elm_shape=(...,nUi)

Compute upward 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:

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

• ww (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]