tv_apply_transpose_derivatives_from_sweep#

t3toolbox.backend.sampling_derivatives.tv_apply_transpose_derivatives_from_sweep(c, ww, pp, frame, sweep, order, sum_over_probes=False)#
def tv_apply_transpose_derivatives_from_sweep(
        c:          NDArray,                # residual jet (scalar), shape=(order+1)+W+K+C
        ww:         typ.Sequence[NDArray],  # probe vectors X,        len=d, elm_shape=W+(Ni,)
        pp:         typ.Sequence[NDArray],  # perturbation vectors P, len=d, elm_shape=W+(Ni,)
        frame:       typ.Tuple[
            typ.Sequence[NDArray], typ.Sequence[NDArray],
            typ.Sequence[NDArray], typ.Sequence[NDArray],
        ],                                  # = T3Frame.data = (U, O, P, Q)
        sweep:      typ.Tuple[
            typ.Sequence[NDArray],          # xi_jets
            typ.Sequence[NDArray],          # mu_jets
        ],                                  # = tv_precompute_apply_frame_sweep_jets(frame, ww, pp, order)
        order:      int,                    # highest derivative order
        sum_over_probes: bool = False,      # True: sum the sample stack W (the J^T r back-projection)
) -> typ.Tuple[
    typ.Tuple[NDArray, ...],  # dU_tildes
    typ.Tuple[NDArray, ...],  # dG_tildes
]:                                          # = T3Variations.data

Variation gradient of tv_apply_derivatives_transpose() from a precomputed frame sweep: the c-seeded sigma_hat sweep + the single-term assembly, reusing the frame (xi, mu)_jets (w_jets is frame-free, recomputed here). The reuse hook for a fitting inner solve.

Parameters:

  • c (NDArray)

  • ww (t3toolbox.backend.common.typ.Sequence[NDArray])

  • pp (t3toolbox.backend.common.typ.Sequence[NDArray])

  • frame (t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray]])

  • sweep (t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray]])

  • order (int)

  • sum_over_probes (bool)

Return type:

t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Tuple[NDArray, Ellipsis], t3toolbox.backend.common.typ.Tuple[NDArray, Ellipsis]]