UT3Tangent.entries_derivatives
==============================

.. py:method:: t3toolbox.uniform_manifold.UT3Tangent.entries_derivatives(index, pp, order)

   .. code-block:: python

      def entries_derivatives(
              self,
              index:  NDArray,                # int, shape=(d,)+W -- the grid points
              pp:     typ.Sequence[NDArray],  # perturbation vectors P, len=d, elm_shape=W+(Ni,)
              order:  int,                    # highest derivative order
      ) -> NDArray:                           # scalar jets, shape=(order+1,)+W+K+C


   Symmetric entry derivatives at ``index`` in direction ``P`` (derivative twin of :py:meth:`entries`;
   the bare ``𝒥``). ``index`` and ``pp`` share ``W``. Uniform mirror of
   :py:meth:`~t3toolbox.manifold.T3Tangent.entries_derivatives`.

   .. rubric:: Examples

   >>> import numpy as np
   >>> import t3toolbox.tucker_tensor_train as t3
   >>> import t3toolbox.uniform_tucker_tensor_train as ut3
   >>> import t3toolbox.uniform_manifold as ut3m
   >>> np.random.seed(0)
   >>> x = ut3.UniformTuckerTensorTrain.from_t3(t3.TuckerTensorTrain.randn((10, 11, 12), (5, 6, 4), (1, 2, 3, 1)))
   >>> v = ut3m.UNIFORM_COREWISE.randn(ut3m.UNIFORM_MANIFOLD.frame(x))
   >>> pp = (np.random.randn(10), np.random.randn(11), np.random.randn(12))
   >>> yj = v.entries_derivatives(np.array([3, 5, 7]), pp, 3)
   >>> print(yj.shape, bool(np.allclose(yj[0], v.entries((3, 5, 7)))))  # (order+1,); order 0 == entries
   (4,) True