compute_mu

t3toolbox.backend.probing.compute_mu(left_tt_cores, xis)

def compute_mu(
        left_tt_cores:      typ.Union[typ.Sequence[NDArray], NDArray], # len=d-1. elm_shape=C+(rLi,nUi,rL(i+1))
        xis:                typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=W+C+(nUi,)
) -> typ.Union[typ.Sequence[NDArray], NDArray]: # mus. len=d, elm_shape=W+C+(rLi,)

Compute leftward edge variables associated with edges between 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:

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

• xis (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]