spd_learn.functional.transport_tangent_vector#

spd_learn.functional.transport_tangent_vector(v, p, q, metric='airm', **kwargs)[source]#

Parallel transport of tangent vector with metric selection.

A convenience function that allows selecting the transport method via a string argument.

Parameters:

v (torch.Tensor) – Tangent vector at p to be transported, shape (…, n, n).
p (torch.Tensor) – Source point on SPD manifold, shape (…, n, n).
q (torch.Tensor) – Target point on SPD manifold, shape (…, n, n).
metric (str, optional) – The Riemannian metric to use. Options are: - “airm”: Affine-Invariant Riemannian Metric (closed-form) - “lem” or “log_euclidean”: Log-Euclidean Metric (Frechet derivatives) - “log_cholesky”: Log-Cholesky Metric (Cholesky decomposition) - “schild”: Schild’s ladder approximation - “pole”: Pole ladder approximation Default is “airm”.
**kwargs (dict) – Additional keyword arguments passed to the transport function. For example, n_steps for schild_ladder.

Returns:

Transported tangent vector at q, shape (…, n, n).

Return type:

torch.Tensor

Examples

>>> import torch
>>> from spd_learn.functional import transport_tangent_vector
>>> n = 3
>>> A = torch.randn(n, n)
>>> p = A @ A.T + torch.eye(n)
>>> B = torch.randn(n, n)
>>> q = B @ B.T + torch.eye(n)
>>> v = torch.randn(n, n)
>>> v = (v + v.T) / 2
>>> # Use different transport methods
>>> v_airm = transport_tangent_vector(v, p, q, metric="airm")
>>> v_lem = transport_tangent_vector(v, p, q, metric="lem")
>>> v_schild = transport_tangent_vector(v, p, q, metric="schild", n_steps=10)