TuckerTensorTrain.sum_stack#

t3toolbox.tucker_tensor_train.TuckerTensorTrain.sum_stack(axis=None)#

def sum_stack(
        self,
        axis = None, # stack axis or axes to sum over. None: sum over all stack axes
) -> 'TuckerTensorTrain':

Sum the tensors represented by a stacked TuckerTensorTrain over one or more stack axes.

This is the genuine tensor sum: the result represents the sum of the dense tensors over the chosen stack axes,

result.to_dense() = self.to_dense().sum(axis=stack axes).

The summed-over stack axes are removed; any remaining stack axes are kept. For a corewise sum of the core arrays instead, see sum_stack_corewise().

Warning

Ranks grow. Summing over stack axes whose sizes multiply to S multiplies every Tucker and TT rank by S (this is the S-fold generalization of __add__(), which is the S=2 case). Follow with t3svd() to truncate the ranks if needed.

Parameters:: axis (int or Sequence[int], optional) – Stack axis or axes to sum over, indexed within stack_shape. Default (axis=None): sum over all stack axes (the result is unstacked).
Returns:: Tucker tensor train representing the sum over the chosen stack axes. Its stack_shape consists of the un-summed stack axes.
Return type:: TuckerTensorTrain

Examples

Sum over all stack axes (the result is unstacked):

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> np.random.seed(0)
>>> x = t3.TuckerTensorTrain.randn((4,5,6), (2,3,2), (1,2,2,1), stack_shape=(3,))
>>> y = x.sum_stack()
>>> print(y.stack_shape)
()
>>> print(np.allclose(y.to_dense(), x.to_dense().sum(axis=0)))
True

Ranks grow by the summed stack size (here S=3):

>>> print(x.tucker_ranks, '->', y.tucker_ranks)
(2, 3, 2) -> (6, 9, 6)
>>> print(x.tt_ranks, '->', y.tt_ranks)
(1, 2, 2, 1) -> (1, 6, 6, 1)

Sum over one of several stack axes (the rest are kept):

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> np.random.seed(0)
>>> x = t3.TuckerTensorTrain.randn((4,5,6), (2,3,2), (1,2,2,1), stack_shape=(2,3))
>>> y = x.sum_stack(axis=0)
>>> print(y.stack_shape)
(3,)
>>> print(np.allclose(y.to_dense(), x.to_dense().sum(axis=0)))
True