function koopman_matrix

deeptime.decomposition.deep.koopman_matrix(x: Tensor, y: Tensor, epsilon: float = 1e-06, mode: str = 'trunc', c_xx: Optional[Tuple[Tensor, Tensor, Tensor]] = None) → Tensor

Computes the Koopman matrix

\[K = C_{00}^{-1/2}C_{0t}C_{tt}^{-1/2} \]

based on data over which the covariance matrices \(C_{\cdot\cdot}\) are computed.

Parameters:

• x (torch.Tensor) – Instantaneous data.

• y (torch.Tensor) – Time-lagged data.

• epsilon (float, default=1e-6) – Cutoff parameter for small eigenvalues.

• mode (str, default='trunc') – Regularization mode for Hermetian inverse. See sym_inverse().

• c_xx (tuple of torch.Tensor, optional, default=None) – Tuple containing c00, c0t, ctt if already computed.

Returns:

K – The Koopman matrix.

Return type:

torch.Tensor