t3toolbox.weighted_tucker_tensor_train.WeightedTuckerTensorTrain
================================================================

.. py:class:: t3toolbox.weighted_tucker_tensor_train.WeightedTuckerTensorTrain

   Class for Tucker tensor trains with weights on internal edges.

   Tensor network diagrams illustrating weights::

   1--t0--G0--t1--G1-- ... --G(d-1)--td--1
          |       |          |
          s0      s1         s(d-1)
          |       |          |
          B0      B1         B(d-1)
          |       |          |

   Most functions is performed by:
       1) absorb weights into cores, yielding an (unweighted) TuckerTensorTrain
       2) apply the operation to the TuckerTensorTrain

   Addition, subtraction are performed by:
       1) Add TuckerTensorTrain component
       2) Concatenate weights

   Scaling and negation are performed by scaling the TuckerTensorTrain component only.

   .. rubric:: Examples

   >>> import numpy as np
   >>> import t3toolbox.tucker_tensor_train as t3
   >>> import t3toolbox.weighted_tucker_tensor_train as wt3
   >>> randn = np.random.randn
   >>> x0 = t3.t3_corewise_randn((6,7,8), (5,6,7), (2,3,3,1), stack_shape=(4,))
   >>> tucker_vectors = tuple([randn(4, 5), randn(4, 6), randn(4, 7)])
   >>> tt_vectors = tuple([randn(4, 2), randn(4, 3), randn(4, 3), randn(4, 1)])
   >>> weights = wt3.EdgeVectors(tucker_vectors, tt_vectors)
   >>> x = wt3.WeightedTuckerTensorTrain(x0, weights)
   >>> dense_x = x.to_dense()
   >>> all_x_vars = x0.tucker_cores + x0.tt_cores + tucker_vectors + tt_vectors
   >>> einsum_str = 'qix,qjy,qkz,qaib,qbjc,qckd,qi,qj,qk,qa,qb,qc,qd->qxyz'
   >>> dense_x2 = np.einsum(einsum_str, *all_x_vars)
   >>> print(np.linalg.norm(dense_x - dense_x2))
   2.0706421599518804e-12


   .. py:attribute:: x0
      :type:  t3toolbox.tucker_tensor_train.TuckerTensorTrain


   .. py:attribute:: edge_weights
      :type:  EdgeVectors


   .. py:method:: data()


   .. py:method:: validate()


   .. py:method:: __post_init__()


   .. py:method:: contract_edge_weights_into_cores(use_jax: bool = False) -> t3toolbox.tucker_tensor_train.TuckerTensorTrain

      Contract each edge vector into a neighboring backend.

      Tensor network diagram illustrating groupings::

               ____     ____     ________
              /    \   /    \   /                    1---w---G0---w---G1---w---G2---w---1
                  |        |        |
                / w      / w      / w
                | |      | |      | |
                \ B0     \ B1     \ B2
                  |        |        |
                  w        w        w
                  |        |        |

      .. rubric:: Examples

      >>> import numpy as np
      >>> import t3toolbox.tucker_tensor_train as t3
      >>> import t3toolbox.weighted_tucker_tensor_train as wt3
      >>> randn = np.random.randn
      >>> x0 = t3.t3_corewise_randn((6,7,8), (5,6,7), (2,3,3,1), stack_shape=(4,))
      >>> tucker_vectors = tuple([randn(4, 5), randn(4, 6), randn(4, 7)])
      >>> tt_vectors = tuple([randn(4, 2), randn(4, 3), randn(4, 3), randn(4, 1)])
      >>> weights = wt3.EdgeVectors(tucker_vectors, tt_vectors)
      >>> x0_w = wt3.WeightedTuckerTensorTrain(x0, weights)
      >>> x = x0_w.contract_edge_weights_into_cores()
      >>> dense_x = x.to_dense()
      >>> all_x_vars = x0.tucker_cores + x0.tt_cores + tucker_vectors + tt_vectors
      >>> einsum_str = 'qix,qjy,qkz,qaib,qbjc,qckd,qi,qj,qk,qa,qb,qc,qd->qxyz'
      >>> dense_x2 = np.einsum(einsum_str, *all_x_vars)
      >>> print(np.linalg.norm(dense_x - dense_x2))
      4.7254283984394845e-12



   .. py:method:: squash_tails(use_jax: bool = False) -> WeightedTuckerTensorTrain


   .. py:method:: reverse() -> WeightedTuckerTensorTrain

      Reverse the weighted Tucker tensor train.




   .. py:method:: __neg__() -> WeightedTuckerTensorTrain


   .. py:method:: __mul__(other) -> WeightedTuckerTensorTrain


   .. py:method:: __add__(other, squash: bool = True, use_jax: bool = False)


   .. py:method:: __sub__(other, squash: bool = True, use_jax: bool = False)


   .. py:method:: norm(use_orthogonalization: bool = True, use_jax: bool = False)

      Computes the Hilbert-Schmidt norm of the weighted Tucker tensor train.

      .. rubric:: Examples

      >>> import numpy as np
      >>> import t3toolbox.tucker_tensor_train as t3
      >>> import t3toolbox.weighted_tucker_tensor_train as wt3
      >>> randn = np.random.randn
      >>> x0 = t3.t3_corewise_randn((6,7,8), (5,6,7), (2,3,3,1), stack_shape=(4,))
      >>> x_tucker_vectors = tuple([randn(4, 5), randn(4, 6), randn(4, 7)])
      >>> x_tt_vectors = tuple([randn(4, 2), randn(4, 3), randn(4, 3), randn(4, 1)])
      >>> x_weights = wt3.EdgeVectors(x_tucker_vectors, x_tt_vectors)
      >>> x = wt3.WeightedTuckerTensorTrain(x0, x_weights)
      >>> print(x.norm())
      [ 31.94684693   0.68957189 100.53306804  35.34732966]
      >>> x_dense = x.contract_edge_weights_into_cores().to_dense()
      >>> print(np.array([np.linalg.norm(x_dense[ii]) for ii in range(4)]))
      [ 31.94684693   0.68957189 100.53306804  35.34732966]



   .. py:method:: to_dense(use_jax: bool = False) -> t3toolbox.backend.common.NDArray

      Convert the weighted Tucker tensor train to a dense array.

      .. rubric:: Examples

      >>> import numpy as np
      >>> import t3toolbox.tucker_tensor_train as t3
      >>> import t3toolbox.weighted_tucker_tensor_train as wt3
      >>> randn = np.random.randn
      >>> x0 = t3.t3_corewise_randn((6,7,8), (5,6,7), (2,3,3,1), stack_shape=(4,))
      >>> tucker_vectors = tuple([randn(4, 5), randn(4, 6), randn(4, 7)])
      >>> tt_vectors = tuple([randn(4, 2), randn(4, 3), randn(4, 3), randn(4, 1)])
      >>> weights = wt3.EdgeVectors(tucker_vectors, tt_vectors)
      >>> x0_w = wt3.WeightedTuckerTensorTrain(x0, weights)
      >>> dense_x = x0_w.to_dense()
      >>> all_x_vars = x0.tucker_cores + x0.tt_cores + tucker_vectors + tt_vectors
      >>> einsum_str = 'qix,qjy,qkz,qaib,qbjc,qckd,qi,qj,qk,qa,qb,qc,qd->qxyz'
      >>> dense_x2 = np.einsum(einsum_str, *all_x_vars)
      >>> print(np.linalg.norm(dense_x - dense_x2))
      2.8199489101171104e-12