tv_entries_derivatives_transpose#

t3toolbox.backend.sampling_derivatives.tv_entries_derivatives_transpose(c, index, pp, frame, order, sum_over_probes=False)#

def tv_entries_derivatives_transpose(
        c:          NDArray,                # residual jet (scalar), shape=(order+1)+W+K+C
        index:      NDArray,                # int, shape=(d,)+W -- the grid points
        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)
        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

Transpose of tv_entries_derivatives(): scatter residual jets c at index into a variation gradient. Identical to tv_apply_derivatives_transpose() with the frame up-index jet from fiber slicing at index (order 0) + contracting P (order 1), and the ambient w_jet from the unit vectors e_{index} (order 0) + P (order 1) – so the Tucker-variation gradient scatters onto the indexed rows.