T3Tangent.to_t3

t3toolbox.manifold.T3Tangent.to_t3(include_shift=False)

def to_t3(
        self,
        include_shift:  bool = False,  # False: tangent vector v. True: base point + v.
) -> t3.TuckerTensorTrain:  # doubled-rank Tucker tensor train

Doubled-rank TuckerTensorTrain representation of this tangent vector.

The Tucker and TT ranks are (roughly) doubled. With include_shift=True the result represents base point + v (the standard shifted embedding used by retract()).

This is the doubled-rank representation of Appendix A.3.1 (equations (50)-(53) and Figure 20) in Alger et al. (2026), “Tucker Tensor Train Taylor Series” (arXiv:2603.21141).

Parameters:

include_shift (bool)

Return type:

TuckerTensorTrain