t3toolbox.backend.probing.probe_t3

t3toolbox.backend.probing.probe_t3(ww: t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.NDArray], x: t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray]], t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.NDArray, t3toolbox.backend.common.NDArray]], edge_weights: t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray]], t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.NDArray, t3toolbox.backend.common.NDArray, t3toolbox.backend.common.NDArray]] = (None, None, None), use_jax: bool = False) → t3toolbox.backend.common.typ.Union[t3toolbox.backend.common.typ.Sequence[t3toolbox.backend.common.NDArray], t3toolbox.backend.common.NDArray]

Probe a Tucker tensor train.

See Section 5.2, particularly Figure 9 in:

Alger, N., Christierson, B., Chen, P., & Ghattas, O. (2026). “Tucker Tensor Train Taylor Series.” arXiv preprint arXiv:2603.21141. https://arxiv.org/abs/2603.21141

Parameters:

• x (t3.TuckerTensorTrain) – Tucker tensor train to probe. structure=((N1,…,Nd),(n1,…,nd),(1,r1,…,r(d-1),1))

• ww (typ.Sequence[NDArray]) – input vectors to probe with. len=d, elm_shape=(…,Ni)

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

Returns:

Probes, zz. len=d, elm_shape=(…,Ni)

Return type:

typ.Tuple[NDArray,…]

See also

probe_tangent, probe_tangent_transpose, compute_xis, compute_mus, compute_nus, compute_etas, assemble_probes

Examples

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> import t3toolbox.backend.probing as t3p
>>> x = t3.t3_corewise_randn((10,11,12),(5,6,4),(2,3,4,2)).data
>>> ww = (np.random.randn(10), np.random.randn(11), np.random.randn(12))
>>> zz = t3p.t3_probe(ww, x)
>>> x_dense = t3.TuckerTensorTrain(*x).to_dense()
>>> zz2 = t3p.probe_dense(ww, x_dense)
>>> print([np.linalg.norm(z - z2) for z, z2 in zip(zz, zz2)])
[1.0259410400851746e-12, 1.0909087370186656e-12, 3.620283224238675e-13]

Vectorize over probes:

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> import t3toolbox.backend.probing as t3p
>>> x = t3.t3_corewise_randn((10,11,12),(5,6,4),(2,3,4,2)).data
>>> ww = (np.random.randn(2,3, 10), np.random.randn(2,3, 11), np.random.randn(2,3, 12))
>>> zz = t3p.t3_probe(ww, x)
>>> x_dense = t3.TuckerTensorTrain(*x).to_dense()
>>> zz2 = t3p.probe_dense(ww, x_dense)
>>> print([np.linalg.norm(z - z2) for z, z2 in zip(zz, zz2)])
[2.9290244450205316e-12, 2.0347746956505754e-12, 1.7784156096697445e-12]

Vectorize over probes and T3s:

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> import t3toolbox.backend.probing as t3p
>>> x = t3.t3_corewise_randn((10,11,12),(5,6,4),(2,3,4,2), stack_shape=(4,5)).data
>>> ww = (np.random.randn(2,3, 10), np.random.randn(2,3, 11), np.random.randn(2,3, 12))
>>> zz = t3p.t3_probe(ww, x)
>>> x_dense = t3.TuckerTensorTrain(*x).to_dense()
>>> zz2 = t3p.probe_dense(ww, x_dense)
>>> print([np.linalg.norm(z - z2) for z, z2 in zip(zz, zz2)])
[1.4471391818397927e-11, 1.0485601346346092e-11, 1.437623640611662e-11]

Using weights:

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> import t3toolbox.backend.probing as t3p
>>> randn = np.random.randn
>>> x0 = t3.t3_corewise_randn((10,11,12),(5,6,4),(2,3,4,2))
>>> (tucker_cores0, tt_cores0) = x0
>>> shape_weights = [randn(10), randn(11), randn(12)]
>>> tucker_weights = [randn(5), randn(6), randn(4)]
>>> tt_weights = [randn(2), randn(3), randn(4), randn(2)]
>>> edge_weights = (shape_weights, tucker_weights, tt_weights)
>>> ww = [np.random.randn(2,10), np.random.randn(2,11), np.random.randn(2,12)]
>>> zz = t3p.t3_probe(ww, x0,edge_weights=edge_weights)
>>> x = t3.absorb_edge_weights_into_cores(x0, edge_weights)
>>> zz2 = t3p.t3_probe(ww, x)
>>> print([np.linalg.norm(z - z2) for z, z2 in zip(zz, zz2)])
[3.372228193172379e-14, 3.826148129405782e-14, 2.294115439089251e-14]

For uniform T3:

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> import t3toolbox.backend.probing as t3p
>>> import t3toolbox.uniform as ut3
>>> import t3toolbox.corewise as cw
>>> x = t3.t3_corewise_randn((10,11,12),(5,6,4),(2,3,4,2))
>>> ww = (np.random.randn(2,10), np.random.randn(2,11), np.random.randn(2,12))
>>> uniform_x, masks = ut3.t3_to_ut3(x)
>>> inv_masks = cw.corewise_logical_not(masks)
>>> junk = ut3.uniform_randn(ut3.get_uniform_structure(uniform_x), masks=inv_masks)
>>> uniform_x = cw.corewise_add(uniform_x, junk) # Add random junk outside the masks
>>> uniform_ww = ut3.pack_tensors(ww)
>>> uniform_zz = t3p.t3_probe(uniform_ww, uniform_x, edge_weights=masks)
>>> zz = t3p.t3_probe(ww, x)
>>> uniform_zz2 = ut3.pack_tensors(zz)
>>> print(np.linalg.norm(uniform_zz - uniform_zz2))
0.0
>>> uniform_x_weighted = t3.absorb_edge_weights_into_cores(uniform_x, masks)
>>> uniform_zz3 = t3p.t3_probe(uniform_ww, uniform_x_weighted)
>>> print(np.linalg.norm(uniform_zz - uniform_zz3))
0.0