TuckerTensorTrain.apply_derivatives
===================================

.. py:method:: t3toolbox.tucker_tensor_train.TuckerTensorTrain.apply_derivatives(ww, pp, order)

   .. code-block:: python

      def apply_derivatives(
              self,
              ww:     Sequence[NDArray],  # apply vectors X,        len=d, elm_shape=W+(Ni,)
              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 applying this T3 in all modes, in one repeated direction.

   The all-modes analogue of :py:meth:`probe_derivatives` (derivative analogue of :py:meth:`apply`):
   ``y^(t) = d^t/ds^t apply(X + s P)|_0`` for ``t=0..order`` (a scalar per stack element). Stacks
   ``order + W + C``. ``X`` and ``P`` share the sample stack ``W``.

   .. seealso:: :py:obj:`apply`, :py:obj:`probe_derivatives`, :py:obj:`apply_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))
   >>> ww = (np.random.randn(14), np.random.randn(15), np.random.randn(16))
   >>> pp = (np.random.randn(14), np.random.randn(15), np.random.randn(16))
   >>> yj = x.apply_derivatives(ww, pp, 3)
   >>> print(yj.shape)                        # (order+1,)
   (4,)
   >>> print(bool(np.allclose(yj[0], x.apply(ww))))     # order 0 == apply
   True