tv_precompute_apply_frame_sweep#

t3toolbox.backend.apply.tv_precompute_apply_frame_sweep(frame, ww)#

def tv_precompute_apply_frame_sweep(
        frame:   typ.Tuple[
            typ.Sequence[NDArray],          # up_tucker_cores  U. len=d
            typ.Sequence[NDArray],          # down_tt_cores    O. len=d
            typ.Sequence[NDArray],          # left_tt_cores    P. len=d
            typ.Sequence[NDArray],          # right_tt_cores   Q. len=d
        ],                                  # frame order = T3Frame.data = (up, down, left, right)
        ww:     typ.Sequence[NDArray],      # apply vectors, len=d, elm_shape=W+(Ni,)
) -> typ.Tuple[
    typ.Sequence[NDArray],  # xis. len=d, elm_shape=W+C+(nUi,)
    typ.Sequence[NDArray],  # mus. len=d, elm_shape=W+C+(rLi,)
]:                                          # lean frame sweep -- (xis, mus) only

The all-modes apply frame sweep (lean): the frame edge variables (xi-hat, mu-hat) that depend only on the frame frame and the apply vectors ww – NOT on the tangent or residual. Computing them is the expensive, W-scaled part of the apply Jacobian; precomputed once per frame and reused across every J / Jᵀ of an inner solve (the reuse hook for fitting.py).

Lean ``(xis, mus)`` only (not the right nu / down eta sweeps): the all-modes apply forward AND its adjoint-state transpose use only (xi, mu) – the transpose recomputes the right context as sigma_hat from the residual rather than storing nu/eta, halving the W-scaling memory (apply on the manifold, §6.2.2 of Alger et al. (2026)). Probe, which leaves a mode free, needs the full sweep – tv_precompute_probe_frame_sweep().