compute_deta#

t3toolbox.backend.probing.compute_deta(var_tt_cores, left_tt_cores, right_tt_cores, mus, nus, sigmas, taus)#

def compute_deta(
        var_tt_cores:       typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(rLi,nUi,rR(i+1))
        left_tt_cores:      typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(rLi,nUi,rL(i+1))
        right_tt_cores:     typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(rRi,nUi,rR(i+1))
        mus:                typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,rLi)
        nus:                typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,rR(i+1))
        sigmas:             typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,rR(i+1))
        taus:               typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,rL(i+1))
) -> typ.Union[typ.Sequence[NDArray], NDArray]: # detas. len=d, elm_shape=(...,nUi)

Compute var-downward edge variables deta. Used for probing a tangent vector.

See Section 6.2.2, particularly Algorithm 7, 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