TuckerTensorTrain.entries_derivatives
=====================================

.. py:method:: t3toolbox.tucker_tensor_train.TuckerTensorTrain.entries_derivatives(index, pp, order)

   .. code-block:: python

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


   Symmetric directional derivatives of this T3's entries at ``index``, in direction ``P``.

   The Taylor data of the represented tensor's multilinear extension at grid corner ``index``, in
   direction ``P``: ``y^(t) = d^t/ds^t apply(e_{index} + s P)|_0``. Index ``0`` is the ordinary
   :py:meth:`entries`. Stacks ``order + W + C``. ``index`` and ``P`` share ``W``.

   .. seealso:: :py:obj:`entries`, :py:obj:`apply_derivatives`, :py:obj:`entries_corewise_derivatives_transpose`

   .. rubric:: Examples

   >>> import numpy as np
   >>> import t3toolbox.tucker_tensor_train as t3
   >>> np.random.seed(0)
   >>> x = t3.TuckerTensorTrain.randn((14, 15, 16), (4, 5, 6), (1, 3, 2, 1))
   >>> index = np.array([3, 5, 7])
   >>> pp = (np.random.randn(14), np.random.randn(15), np.random.randn(16))
   >>> yj = x.entries_derivatives(index, pp, 3)
   >>> print(yj.shape)
   (4,)
   >>> print(bool(np.allclose(yj[0], x.entries(index))))   # order 0 == entries
   True