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