pod_basis()

pod_basis()#

pod_basis(states, num_vectors: int = None, svdval_threshold: float = None, cumulative_energy: float = None, residual_energy: float = None, projection_error: float = None, svdsolver: str = 'dense', weights: ndarray = None, return_rightvecs: bool = False, **svdsolver_options)[source]#

Compute a POD basis from the given states.

Parameters

states(n, k) ndarray: Matrix of \(k\) \(n\)-dimensional snapshots.
return_rightvecbool: If True, return the right singular vectors as well.

Returns

basis(n, r) ndarray: POD basis matrix, the first \(r\) left singular vectors of the states.
svdvals(n,), (k,), or (r,) ndarray: Normalized singular values in descending order. Always returns as many as are calculated: \(\min\{n, k\}\) for svdsolver="dense", \(r\) for svdsolver="randomized".
rightvecs(k, r) ndarray: First \(r\) right singular vectors, as columns. NOTE: only returned if return_rightvecs=True.

Notes

See PODBasis for the mathematical definition of POD and for details on other constructor arguments.