TuckerTensorTrain.from_canonical
================================

.. py:method:: t3toolbox.tucker_tensor_train.TuckerTensorTrain.from_canonical(factors)
   :staticmethod:


   .. code-block:: python

      def from_canonical(
              factors: Sequence[NDArray], # elm_shape = stack_shape + (canonical_rank, Ni)
      ) -> 'TuckerTensorTrain':


   Constructs TuckerTensorTrain from Canonical decomposition.

   Canonical decomposition represents a tensor X as a sum of rank-1 tensors of the form

       X[i1, ..., id] = sum_j F0[j,i1] * ... * F(d-1)[j,id],

   where F0,...,F(d-1) are the canonical factor matrices.

   :param factors: Canonical factors. ``len(factors)=d``, ``factors[ii].shape=stack_shape+(canonical_rank, Ni)``.
   :type factors: Sequence[NDArray]

   :returns: **T** -- TuckerTensorTrain representation of dense tensor which is represented by provided canonical decomposition.
             ``T.to_dense()[S,i1,...,id] = sum(factors[S,:,i1]*...*factors[S,:,id])``. Here ``S`` is a stack index.
   :rtype: TuckerTensorTrain

   :raises ValueError: If factor matrices in factors have inconsistent shapes.

   .. rubric:: Examples

   >>> import numpy as np
   >>> import t3toolbox.tucker_tensor_train as t3
   >>> rank = 3
   >>> shape = (5,6,7)
   >>> stack_shape = (2,3)
   >>> FF = [np.random.randn(*(stack_shape+(rank, N))) for N in shape]
   >>> x = t3.TuckerTensorTrain.from_canonical(FF)
   >>> x_dense = x.to_dense()
   >>> x_dense2 = np.einsum('abri,abrj,abrk->abijk', FF[0], FF[1], FF[2])
   >>> print(np.linalg.norm(x_dense - x_dense2))
   0.0
   >>> print(x.tucker_ranks)
   (3, 3, 3)
   >>> print(x.tt_ranks)
   (3, 3, 3, 3)