TuckerTensorTrain.probe_derivatives
===================================

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

   .. code-block:: python

      def probe_derivatives(
              self,
              ww:     Sequence[NDArray],  # probe 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
      ) -> Sequence[NDArray]:             # len=d, elm_shape=(order+1,)+W+C+(Ni,)


   Symmetric directional derivatives of probing this Tucker tensor train, in one repeated direction.

   Returns, for each mode ``i``, the stack ``y_i^(t) = d^t/ds^t [probe(X + s P)]_i|_0`` for
   ``t=0..order`` -- the derivative analogue of :py:meth:`probe`, perturbing every probe vector in
   the same direction ``P``. Index ``0`` is the ordinary :py:meth:`probe`. Stacks ``order + W + C``
   (order outermost; probe stack ``W``, T3 stack ``C``). ``X`` (``ww``) and ``P`` (``pp``) must
   share the sample stack ``W``. (For the gradient w.r.t. the cores, see
   :py:meth:`probe_corewise_derivatives_transpose`; for the Riemannian Jacobian use
   ``T3Tangent.probe_derivatives``.) See ``docs/symmetric_probe_derivatives.tex``.

   .. seealso:: :py:obj:`probe`, :py:obj:`apply_derivatives`, :py:obj:`probe_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))
   >>> zj = x.probe_derivatives(ww, pp, 3)
   >>> print([z.shape for z in zj])           # (order+1,) + (Ni,)
   [(4, 14), (4, 15), (4, 16)]
   >>> print([bool(np.allclose(z[0], z0)) for z, z0 in zip(zj, x.probe(ww))])  # order 0 == probe
   [True, True, True]