expm_frechet

torch_sim.math.expm_frechet(A, E, method=None, compute_expm=True, check_finite=True)[source]

Frechet derivative of the matrix exponential of A in the direction E.

Parameters:

  • A (Tensor) – (N, N) array_like. Matrix of which to take the matrix exponential.

  • E (Tensor) – (N, N) array_like. Matrix direction in which to take the Frechet derivative.

  • method (str | None) – str, optional. Choice of algorithm. Should be one of - SPS (default) - blockEnlarge

  • compute_expm (bool) – bool, optional. Whether to compute also expm_A in addition to expm_frechet_AE. Default is True.

  • check_finite (bool) – bool, optional. Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns:

expm_A: ndarray. Matrix exponential of A.
expm_frechet_AE: ndarray. Frechet derivative of the matrix exponential of A

in the direction E.

Otherwise:
expm_frechet_AE: ndarray. Frechet derivative of the matrix exponential of A

in the direction E.

Return type:

If compute_expm is True