compute_deta_tilde

t3toolbox.backend.probing.compute_deta_tilde(up_tucker_cores, ztildes)

def compute_deta_tilde(
        up_tucker_cores:    typ.Union[typ.Sequence[NDArray], NDArray],  # len=d, elm_shape=(nUi,Ni)
        ztildes:            typ.Union[typ.Sequence[NDArray], NDArray],  # len=d, elm_shape=(...,Ni)
) -> typ.Union[typ.Sequence[NDArray], NDArray]: # len=d, elm_shape=(...,nUi)

Adjoint-var-upward edge variables deta_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:

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

• ztildes (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]