t3toolbox.tucker_tensor_train.t3_add

t3toolbox.tucker_tensor_train.t3_add(x: TuckerTensorTrain, y: TuckerTensorTrain, squash: bool = True, use_jax: bool = False) → TuckerTensorTrain

Add Tucker tensor trains x and y, yielding a Tucker tensor train x+y with summed ranks.

Addition 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 addition, see t3toolbox.corewise.corewise_add()

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

Parameters:

• other (TuckerTensorTrain) – The other Tucker tensor train to add to this one. structure=((N0,…,N(d-1)), (m0,…,m(d-1)), (q0, q1,…,qd))

• squash (bool) – Squash the first and last TT cores so that r0=rd=1 in the result. Default: True.

• xnp – Linear algebra backend. Default: np (numpy)

Returns:

Sum 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.

Return type:

TuckerTensorTrain

Raises:

ValueError –

• Error raised if either of the TuckerTensorTrains are internally inconsistent

• Error raised if the TuckerTensorTrains have different shapes.

See also

TuckerTensorTrain, __scale__, __sub__, __neg__, squash_tails, corewise_add()

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))
>>> z = t3.t3_add(x, y)
>>> print(z.uniform_structure)
((14, 15, 16), (7, 12, 8), (1, 8, 8, 1), ())
>>> print(np.linalg.norm(x.to_dense() + y.to_dense() - z.to_dense()))
6.524094086845177e-13

With vectorized TuckerTensorTrains

>>> 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), stack_shape=(2,3))
>>> y = t3.t3_corewise_randn((14,15,16), (3,7,2), (1,5,6,1), stack_shape=(2,3))
>>> z = t3.t3_add(x, y)
>>> print(z.uniform_structure)
((14, 15, 16), (7, 12, 8), (1, 8, 8, 1), (2, 3))
>>> print(np.linalg.norm(x.to_dense() + y.to_dense() - z.to_dense()))

Adding dense + T3

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> x = np.random.randn(14,15,16)
>>> y = t3.t3_corewise_randn((14,15,16), (4,5,6), (1,3,2,1))
>>> z = t3.t3_add(x, y)
>>> print(type(z))
<class 'numpy.ndarray'>
>>> print(np.linalg.norm(x + y.to_dense() - z))

Adding dense + T3 with stacking

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> s = (14,15,16)
>>> vs = (2,3)
>>> x = np.random.randn(2,3, 14,15,16)
>>> y = t3.t3_corewise_randn((14,15,16), (4,5,6), (1,3,2,1), stack_shape=(2,3))
>>> z = t3.t3_add(x, y)
>>> print(type(z))
<class 'numpy.ndarray'>
>>> print(np.linalg.norm(x + y.to_dense() - z))
0.0