t3toolbox.manifold.tangent_zeros#

t3toolbox.manifold.tangent_zeros(base: t3toolbox.basis_coordinates_format.T3Base, use_jax: bool = False) → t3toolbox.basis_coordinates_format.T3Variation#

Construct the zero vector in a Tucker tensor train tangent space.

Parameters:

  • base (T3Base) – Representations of base point on manifold where tangent space is attached

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

Returns:

Variation representing the zero vector in the tangent space

Return type:

T3Variation

See also

t3tangent_randn

Examples

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> import t3toolbox.manifold as t3m
>>> import t3toolbox.orthogonalization as orth
>>> p = t3.t3_corewise_randn(((14,15,16), (4,5,6), (1,3,2,1)))
>>> base, _ = orth.orthogonal_representations(p)
>>> z = t3m.tangent_zeros(base)
>>> print(np.linalg.norm(t3m.tangent_to_dense(z, base)))
0.0