T3Tangent.entries
=================

.. py:method:: t3toolbox.manifold.T3Tangent.entries(index)

   .. code-block:: python

      def entries(
              self,
              index:      NDArray,  # int, shape=(d,)+W (a stack W of multi-indices)
      ) -> NDArray:                 # entries of the dense tangent at ``index``; shape=W+K+C


   Extract entries of the dense tangent at ``index`` (without forming the dense tangent).

   The tangent analogue of :py:meth:`.TuckerTensorTrain.entries`, and the all-modes special case
   of :py:meth:`probe` with unit vectors -- computed by **slicing** Tucker-core fibers (no
   contraction, no ``N`` factor), then the same left-to-right sweep as :py:meth:`apply`. ``index``
   is ``(d,) + W``: ``index[m]`` holds the (stack ``W`` of) indices into mode ``m``. Result
   stacked ``W + K + C``.

   .. seealso:: :py:obj:`apply`, :py:obj:`probe`

   .. rubric:: Examples

   >>> import numpy as np
   >>> import t3toolbox.tucker_tensor_train as t3
   >>> import t3toolbox.frame_variations_format as bvf
   >>> import t3toolbox.manifold as t3m
   >>> x = t3.TuckerTensorTrain.randn((10, 11, 12), (5, 6, 4), (1, 2, 3, 1))
   >>> frame, variations = bvf.t3_orthogonal_representations(x)
   >>> v = t3m.T3Tangent(frame, variations)
   >>> idx = (3, 5, 7)
   >>> print(bool(abs(float(v.entries(idx)) - float(v.to_dense()[idx])) < 1e-9))
   True