compute_dxi

t3toolbox.backend.probing.compute_dxi(var_tucker_cores, ww)

def compute_dxi(
        var_tucker_cores:       typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=(nOi,Ni)
        ww:                     typ.Union[typ.Sequence[NDArray], NDArray], # len=d. elm_shape=(...,Ni)
) -> typ.Union[typ.Sequence[NDArray], NDArray]: # dxis. len=d, elm_shape=(...,nOi)

Compute var-upward edge variables dxi. Used for probing a tangent vector.

Same as compute_xi(), except with var_tucker_cores in place of tucker_cores.

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_xi, compute_sigma, compute_tau, compute_deta, assemble_tangent_z, tv_probe

Parameters:

• var_tucker_cores (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])

Return type:

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