spd_learn.functional.frechet_derivative_exp#

spd_learn.functional.frechet_derivative_exp(X, W)[source]#

Frechet derivative of the matrix exponential at X in direction W.

Computes \(D\exp(X)[W]\), the directional derivative of the matrix exponential at symmetric matrix \(X\) (need not be SPD) in direction \(W\). Delegates to pyriemann.geometry.base.ddexpm(), which evaluates the Daleckii-Krein (Loewner divided-difference) form on the Array API backend.

Parameters:

  • X (torch.Tensor) – Symmetric matrix, shape (…, n, n). Need not be SPD.

  • W (torch.Tensor) – Symmetric matrix (tangent direction), shape (…, n, n).

Returns:

The Frechet derivative \(D\exp(X)[W]\), shape (…, n, n).

Return type:

torch.Tensor