TuckerTensorTrain.probe#

t3toolbox.tucker_tensor_train.TuckerTensorTrain.probe(ww)#

def probe(
    self,
    ww: Sequence[NDArray],  # len=d, elm_shape=W+(Ni,)
) -> Sequence[NDArray]:     # zz, len=d, elm_shape=X+W+(Ni,)

Probe a TuckerTensorTrain.

Parameters:

self (TuckerTensorTrain) – Tucker tensor train with shape=(N0,...,N(d-1))
ww (Sequence[NDArray]) – Vectors to probe self with len=d, elm_shape=W+(Ni,)

Returns:

Results of contracting self with the vectors in all but one index for all indices. Sequence of vectors if ww elements are vectors, and sequence of NDArray``s each with ``elm_shape=W+(Ni,) if ww elements are matrices.

Return type:

Sequence[NDArray]

Examples

Basic probing example:

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> np.random.seed(0)
>>> x = t3.TuckerTensorTrain.randn((10,11,12),(5,6,4),(2,3,4,2))
>>> ww = (np.random.randn(10), np.random.randn(11), np.random.randn(12))
>>> zz = x.probe(ww)                    # contract all-but-one index, for each index
>>> x_dense = x.to_dense()
>>> zz0_true = np.einsum('abc,b,c', x_dense, ww[1], ww[2])
>>> zz1_true = np.einsum('abc,a,c', x_dense, ww[0], ww[2])
>>> zz2_true = np.einsum('abc,a,b', x_dense, ww[0], ww[1])
>>> print(np.allclose(zz[0], zz0_true), np.allclose(zz[1], zz1_true), np.allclose(zz[2], zz2_true))
True True True

Probe with stacked vectors and stacked T3s – each probe is base-inner W + C + (Ni,):

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> np.random.seed(0)
>>> randn = np.random.randn
>>> stack_shape = (2,3)
>>> x = t3.TuckerTensorTrain.randn((14,15,16), (4,5,6), (2,3,2,1), stack_shape)
>>> vstack_shape = (4,5,1)
>>> ww = [randn(*(vstack_shape+(14,))), randn(*(vstack_shape+(15,))), randn(*(vstack_shape+(16,)))]
>>> result = x.probe(ww)
>>> print(result[0].shape)             # probe stack (4,5,1) outer, T3 stack (2,3) inner, then N0=14
(4, 5, 1, 2, 3, 14)
>>> ii, jj = 1, 2          # T3 (frame) stack index
>>> ll, mm, nn =  3, 2, 0  # vector (probe) stack index
>>> result_ij_lmn_0 = result[0][ll,mm,nn, ii,jj]
>>> result_ij_lmn_1 = result[1][ll,mm,nn, ii,jj]
>>> result_ij_lmn_2 = result[2][ll,mm,nn, ii,jj]
>>> x_ij_dense = x.to_dense()[ii,jj]
>>> result_ij_lmn_0_true = np.einsum('abc,b,c', x_ij_dense, ww[1][ll,mm,nn], ww[2][ll,mm,nn])
>>> result_ij_lmn_1_true = np.einsum('abc,a,c', x_ij_dense, ww[0][ll,mm,nn], ww[2][ll,mm,nn])
>>> result_ij_lmn_2_true = np.einsum('abc,a,b', x_ij_dense, ww[0][ll,mm,nn], ww[1][ll,mm,nn])
>>> print(np.allclose(result_ij_lmn_0, result_ij_lmn_0_true))
True
>>> print(np.allclose(result_ij_lmn_1, result_ij_lmn_1_true))
True
>>> print(np.allclose(result_ij_lmn_2, result_ij_lmn_2_true))
True