assemble_tt_variations

t3toolbox.backend.probing.assemble_tt_variations(sigma_tildes, tau_tildes, deta_tildes, xis, mus, nus, sum_over_probes=False, n_probe=0)

def assemble_tt_variations(
        sigma_tildes:   typ.Union[typ.Sequence[NDArray], NDArray],  # len=d, elm_shape=(...,rR(i+1))
        tau_tildes:     typ.Union[typ.Sequence[NDArray], NDArray],  # len=d, elm_shape=(...,rLi)
        deta_tildes:    typ.Union[typ.Sequence[NDArray], NDArray],  # len=d, elm_shape=(...,nUi)
        xis:            typ.Union[typ.Sequence[NDArray], NDArray],  # len=d, elm_shape=(...,nUi)
        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))
        sum_over_probes: bool = False,
        n_probe: int = 0,  # number of trailing probe-stack axes; only used when sum_over_probes
) -> typ.Union[typ.Sequence[NDArray], NDArray]: # dG_tildes. len=d, elm_shape=(...,rLi,nUi,rRi)

Assemble TT core variations, delta_G_tilde. Used for computing the transpose of the map from a tangent vector to its probes.

See Section 6.2.3, particularly Algorithm 8, 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:

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

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

• deta_tildes (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])

• 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])

• sum_over_probes (bool)

• n_probe (int)

Return type:

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