TuckerTensorTrain.norm
======================

.. py:method:: t3toolbox.tucker_tensor_train.TuckerTensorTrain.norm(use_orthogonalization = True)

   .. code-block:: python

      def norm(
              self,
              use_orthogonalization: bool = True, # for numerical stability
      ):


   Compute Hilbert-Schmidt (Frobenius) norm of this TuckerTensorTrain.

   The Hilbert-Schmidt norm is defined with respect to the dense ``N0 x ... x N(d-1)`` tensor
   that is *represented* by the TuckerTensorTrain.

   ``x.norm() = np.linalg.norm(x.to_dense())``

   For corewise norm, see :func:`t3toolbox.corewise.corewise_norm`

   :param use_orthogonalization: If True, compute norm by orthogonalizing (more stable).
                                 If False, compute norm with conventional zippering (faster, more suited for automatic differentiation).
                                 Default: ``use_orthogonalization=True``.
   :type use_orthogonalization: bool, optional

   :returns: **result** -- Hilbert-Schmidt (Frobenius) norm of Tucker tensor train, ||x||_HS.
             If stacked, ``result.shape=self.stack_shape``. Otherwise, result is scalar.
   :rtype: scalar or NDArray

   .. seealso:: :py:meth:`.TuckerTensorTrain.__add__`, :py:meth:`.TuckerTensorTrain.__sub__`, :py:meth:`.TuckerTensorTrain.__neg__`, :py:meth:`.TuckerTensorTrain.__mul__`, :py:meth:`.TuckerTensorTrain.inner`, :py:meth:`.TuckerTensorTrain.sum`

   .. 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), (2,3,2,2))
   >>> print(np.allclose(x.norm(), np.linalg.norm(x.to_dense())))
   True

   Stacked -- ``norm()`` returns an array of shape ``stack_shape``, one norm per slice:

   >>> 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), (2,3,2,2), stack_shape=(2,3))
   >>> norms_x = x.norm(use_orthogonalization=True)
   >>> print(norms_x.shape)
   (2, 3)
   >>> x_dense = x.to_dense()
   >>> norms_x_dense = np.sqrt(np.sum(x_dense**2, axis=(-3,-2,-1)))
   >>> print(np.allclose(norms_x, norms_x_dense))
   True