UT3Tangent.probe

t3toolbox.uniform_manifold.UT3Tangent.probe(ww)

def probe(
        self,
        ww:  typ.Sequence[NDArray],  # probe vectors, len=d, ith elm_shape=W+(Ni,)
) -> typ.Tuple[NDArray, ...]:        # d probes, ith elm_shape=W+K+C+(Ni,)

Probe this tangent vector: the single-sample Riemannian Jacobian 𝒥 (contract all-but-one mode, for each mode). Uniform mirror of probe(); ww is packed at the boundary and the d probes come back as ragged-width vectors, stacked W+K+C. The bare 𝒥 (no gauge projector Π).

Examples

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> import t3toolbox.uniform_tucker_tensor_train as ut3
>>> import t3toolbox.uniform_manifold as ut3m
>>> import t3toolbox.backend.probing as t3p
>>> np.random.seed(0)
>>> x = ut3.UniformTuckerTensorTrain.from_t3(t3.TuckerTensorTrain.randn((10, 11, 12), (5, 6, 4), (1, 2, 3, 1)))
>>> v = ut3m.UNIFORM_COREWISE.randn(ut3m.UNIFORM_MANIFOLD.frame(x))
>>> ww = (np.random.randn(2, 10), np.random.randn(2, 11), np.random.randn(2, 12))   # probe stack W=(2,)
>>> zz = v.probe(ww)
>>> print(zz[0].shape)                                     # W + K + C + (N0,) = (2,) + () + () + (10,)
(2, 10)
>>> print(bool(max(float(np.linalg.norm(a - b))
...                for a, b in zip(zz, t3p.dense_probe(ww, v.to_dense()))) < 1e-9))   # dense reference
True

Parameters:

ww (t3toolbox.backend.common.typ.Sequence[NDArray])

Return type:

t3toolbox.backend.common.typ.Tuple[NDArray, Ellipsis]