t3toolbox.basis_variations_format.bv_to_t3
==========================================

.. py:function:: t3toolbox.basis_variations_format.bv_to_t3(index: t3toolbox.backend.common.typ.Tuple[bool, int], basis: T3Basis, variations: T3Variations) -> t3toolbox.tucker_tensor_train.TuckerTensorTrain

   Convert basis-variations representation to TuckerTensorTrain.

       If replacement_ind=1, replace_tt=True::

           1 -- L0 --(H1)-- R2 -- R3 -- 1
                |     |     |     |
                U0    U1    U2    U3
                |     |     |     |

       If replacement_ind=2, replace_tt=False::

           1 -- L0 -- L1 -- D2 -- R3 -- 1
                |     |     |     |
                U0    U1   (V2)   U3
                |     |     |     |

       Parameters
       ----------
       ii: int
           Index of variation. 0 <= replacement_ind < num_cores
       replace_tt: bool
           Indicates whether to use TT variation (True) or a Tucker variation (False)
       base: T3Basis
           Basis cores
       variations: T3Variations
           Variation cores

       Raises
       ------
       RuntimeError
           - Error raised if the basis and variations do not fit with each other

       Examples
       --------
   import t3toolbox.backend.basis_variations_format.bv_conversions    >>> import numpy as np
       >>> import t3toolbox.basis_variations_format as bvf
       >>> randn = np.random.randn # shorthand
       >>> (U0,U1,U2) = (randn(10, 14), randn(11, 15), randn(12, 16))
       >>> (L0,L1,L2) = (randn(1, 10, 2), randn(2, 11, 3), randn(3,12,4))
       >>> (R0,R1,R2) = (randn(2,10,4), randn(4, 11, 5), randn(5, 12, 1))
       >>> (D0,D1,D2) = (randn(1, 9, 4), randn(2, 8, 5), randn(3, 7, 1))
       >>> base = bvf.T3Basis((U0,U1,U2), (D0,D1,D2), (L0,L1,L2), (R0,R1,R2))
       >>> (V0,V1,V2) = (randn(9,14), randn(8,15), randn(7,16))
       >>> (H0,H1,H2) = (randn(1,10,4), randn(2,11,5), randn(3,12,1))
       >>> variations = bvf.T3Variations((V0,V1,V2), (H0,H1,H2))
       >>> ((B0, B1, B2), (G0, G1, G2)) = t3toolbox.backend.basis_variations_format.bv_conversions.bv_to_t3((True, 1), base, variations).data # replace index-1 TT-core
       >>> print(((B0,B1,B2), (G0,G1,G2)) == ((U0,U1,U2), (L0,H1,R2)))
       True
   import t3toolbox.backend.basis_variations_format.bv_conversions    >>> ((B0, B1, B2), (G0, G1, G2)) = t3toolbox.backend.basis_variations_format.bv_conversions.bv_to_t3((False, 1), base, variations).data # replace index-1 tucker core
       >>> print(((B0,B1,B2), (G0,G1,G2)) == ((U0,V1,U2), (L0,D1,R2)))
       True