tv_entries_derivatives#

t3toolbox.backend.sampling_derivatives.tv_entries_derivatives(index, pp, variation, frame, order)#

def tv_entries_derivatives(
        index:      NDArray,                # int, shape=(d,)+W -- the grid points
        pp:         typ.Sequence[NDArray],  # perturbation vectors P, len=d, elm_shape=W+(Ni,)
        variation:  typ.Tuple[
            typ.Sequence[NDArray],          # var_tucker_cores dU. len=d, elm_shape=K+C+(nOi,Ni)
            typ.Sequence[NDArray],          # var_tt_cores     dG. len=d, elm_shape=K+C+(rLi,nUi,rRi)
        ],                                  # = T3Variations.data
        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
        ],                                  # = T3Frame.data = (up, down, left, right) = (U, O, P, Q)
        order:      int,                    # highest derivative order
) -> NDArray:                               # entries-derivative jets, shape=(order+1,)+W+K+C

Symmetric derivatives of an entry of a tangent vector, in one repeated direction.

The entries analog of tv_apply_derivatives() – identical but with the frame/var up-index jets from slicing Tucker-core fibers at index (order 0) + contracting P (order 1). Stacks order + W + K + C. Verified vs dense_entries_derivatives() on the densified tangent.