t3toolbox.basis_variations_format.T3Variations
==============================================

.. py:class:: t3toolbox.basis_variations_format.T3Variations

   Tuple containing variation cores for basis-variation representations of TuckerTensorTrains.

   *Components*
       - tucker_variations    = (V0, ..., V(d-1)), elm_shape=(nDi, Ni)
       - tt_variations        = (H0, ..., H(d-1)), elm_shape=(rLi, nUi, rRi)

   The variations should fit in the "holes" of a T3Basis.

   .. seealso:: :py:obj:`T3Basis`

   .. rubric:: Examples

   >>> import numpy as np
   >>> import t3toolbox.basis_variations_format as bvf
   >>> ss = (2,3) # stack shape
   >>> up_tucker_cores = (np.ones(ss+(10, 14)), np.ones(ss+(11, 15)), np.ones(ss+(12, 16)))
   >>> left_tt_cores = (np.ones(ss+(1, 10, 2)), np.ones(ss+(2, 11, 3)), np.ones(ss+(3,12,5)))
   >>> right_tt_cores = (np.ones(ss+(2, 10, 4)), np.ones(ss+(4, 11, 5)), np.ones(ss+(5, 12, 1)))
   >>> down_tt_cores = (np.ones(ss+(1, 9, 4)), np.ones(ss+(2, 8, 5)), np.ones(ss+(3, 7, 1)))
   >>> base = bvf.T3Basis(up_tucker_cores, down_tt_cores, left_tt_cores, right_tt_cores)
   >>> print(base.variation_shapes)
   (((9, 14), (8, 15), (7, 16)), ((1, 10, 4), (2, 11, 5), (3, 12, 1)))
   >>> tucker_variations = tuple([np.ones(ss + B_shape) for B_shape in base.variation_shapes[0]])
   >>> tt_variations = tuple([np.ones(ss + G_shape) for G_shape in base.variation_shapes[1]])
   >>> variations = bvf.T3Variations(tucker_variations, tt_variations) # variation that fits with base
   >>> print(variations.variation_shapes) # same as base, except first right tt rank and last left tt rank, which are None
   (((9, 14), (8, 15), (7, 16)), ((1, 10, 4), (2, 11, 5), (3, 12, 1)))


   .. py:attribute:: tucker_variations
      :type:  t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.NDArray, Ellipsis]


   .. py:attribute:: tt_variations
      :type:  t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.NDArray, Ellipsis]


   .. py:method:: d() -> int


   .. py:method:: shape() -> t3toolbox.backend.common.typ.Tuple[int, Ellipsis]


   .. py:method:: stack_shape() -> t3toolbox.backend.common.typ.Tuple[int, Ellipsis]


   .. py:method:: variation_shapes() -> t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Tuple[int, Ellipsis], Ellipsis], t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Tuple[int, Ellipsis], Ellipsis]]

      T3Variations shapes that fit with this T3Basis.

      Shapes of the "holes" in the following tensor diagrams::

          1 -- L0 -- ( ) -- R2 -- R3 -- 1
               |      |      |      |
               U0     U1     U2     U3
               |      |      |      |

          1 -- L0 -- L1 -- O2 -- R3 -- 1
               |     |     |     |
               U0    U1    ( )   U3
               |     |     |     |



   .. py:method:: data() -> t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.NDArray, Ellipsis], t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.NDArray, Ellipsis]]


   .. py:method:: validate() -> None

      Check rank and shape consistency of Tucker tensor train variations (`T3Variations`).

      :param self:
      :type self: T3Variations

      :raises ValueError: Error raised if the cores of the T3Variations have inconsistent shapes.

      .. seealso:: :py:obj:`T3Basis`, :py:obj:`T3Variations`



   .. py:method:: __post_init__()