assemble_tucker_variations

t3toolbox.backend.probing.assemble_tucker_variations(ztildes, dxi_tildes, ww, etas, sum_over_probes=False)

def assemble_tucker_variations(
        ztildes:    typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,Ni)
        dxi_tildes: typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,nOi)
        ww:         typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,Ni)
        etas:       typ.Union[typ.Sequence[NDArray], NDArray], # len=d, elm_shape=(...,nOi)
        sum_over_probes: bool = False,
) -> typ.Union[typ.Sequence[NDArray], NDArray]: # dU_tildes. len=d, elm_shape=(...,nOi,Ni)

Assemble Tucker core variations, delta_U_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:

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

• dxi_tildes (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])

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

• sum_over_probes (bool)

Return type:

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