TuckerTensorTrain.from_canonical

static t3toolbox.tucker_tensor_train.TuckerTensorTrain.from_canonical(factors)

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.

Parameters:

factors (Sequence[NDArray]) – Canonical factors. len(factors)=d, factors[ii].shape=stack_shape+(canonical_rank, Ni).

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.

Return type:

TuckerTensorTrain

Raises:

ValueError – If factor matrices in factors have inconsistent shapes.

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)