assemble_tangent_z

t3toolbox.backend.probing.assemble_tangent_z(tucker_cores, var_tucker_cores, etas, detas)

def assemble_tangent_z(
        tucker_cores:       typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=(nUi,Ni)
        var_tucker_cores:   typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=(nOi,Ni)
        etas:               typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,nOi)
        detas:              typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,nUi)
) -> typ.Union[typ.Sequence[NDArray], NDArray]: # zs. len=d, elm_shape=(...,Ni)

Assemble tangent vector probes from edge variables.

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

See also

compute_dxi, compute_sigma, compute_tau, compute_deta, tv_probe

Parameters:

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

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

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

• detas (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]