t3toolbox.tucker_tensor_train.t3_sub
====================================

.. py:function:: t3toolbox.tucker_tensor_train.t3_sub(x: t3toolbox.backend.common.typ.Union[TuckerTensorTrain, t3toolbox.backend.common.NDArray], y: t3toolbox.backend.common.typ.Union[TuckerTensorTrain, t3toolbox.backend.common.NDArray], squash: bool = True, use_jax: bool = False) -> t3toolbox.backend.common.typ.Union[TuckerTensorTrain, t3toolbox.backend.common.NDArray]

   Subtract Tucker tensor trains, x - y, yielding a Tucker tensor train with summed ranks.

   Subtraction is defined with respect to the dense N0 x ... x N(d-1) tensors that
   are *represented* by the Tucker tensor trains, even though these dense tensors
   are not formed during computations.

   For corewise subtraction, see :func:`t3toolbox.corewise.corewise_sub`

   T3 + T3 = T3
   T3 + dense = dense
   dense + T3 = dense
   dense + dense = dense

   :param x: First summand. structure=((N0,...,N(d-1)), (n1,...,nd), (r0, r1,...,rd))
   :type x: TuckerTensorTrain
   :param y: Second summand. structure=((N0,...,N(d-1)), (m1,...,md), (q0, q1,...,qd))
   :type y: TuckerTensorTrain
   :param squash: Squash the first and last TT cores so that r0=rd=1 in the result. Default: True.
   :type squash: bool
   :param xnp: Linear algebra backend. Default: np (numpy)

   :returns:

             Difference of Tucker tensor trains, x-y.
                 - shape=(N0,...,N(d-1),
                 - tucker_ranks=(n0+m0,...,n(d-1)+m(d-1),
                 - TT ranks=(1, r1+q1,...,r(d-1)+q(d-1),1)) if squash=True,
                 or (r0+q0, r1+q1,...,r(d-1)+q(d-1),rd+qd)) if squash=False.
   :rtype: TuckerTensorTrain

   :raises ValueError: - Error raised if either of the TuckerTensorTrains are internally inconsistent
       - Error raised if the TuckerTensorTrains have different shapes.

   .. seealso:: :py:obj:`TuckerTensorTrain`, :py:obj:`t3_shape`, :py:obj:`t3_add`, :py:obj:`t3_scale`, :py:obj:`t3_neg`, :func:`~t3toolbox.corewise.corewise_neg`

   .. rubric:: Examples

   >>> import numpy as np
   >>> import t3toolbox.tucker_tensor_train as t3
   >>> x = t3.t3_corewise_randn((14,15,16), (4,5,6), (1,3,2,1))
   >>> y = t3.t3_corewise_randn((14,15,16), (3,7,2), (1,5,6,1))
   >>> x_minus_y = t3.t3_sub(x, y)
   >>> print(x_minus_y.uniform_structure)
   ((14, 15, 16), (7, 12, 8), (2, 8, 8, 2), ())
   >>> print(np.linalg.norm(x.to_dense() - y.to_dense() - x_minus_y.to_dense()))
   3.5875705233607603e-13