set_dimension()

PODBasis.set_dimension(num_vectors: int = None, svdval_threshold: float = None, cumulative_energy: float = None, residual_energy: float = None, projection_error: float = None)

Set the reduced state dimension \(r\). Exactly one argument should be specified

Parameters:

num_vectorsint

Set \(r\) to num_vectors.

svdval_thresholdfloat

Choose \(r\) as the number of normalized POD singular values that are greater than the given threshold, i.e., \(\sigma_{i}/\sigma_{1} \ge\) svdval_threshold for \(i=1,\ldots,r\).

cumulative_energyfloat

Choose \(r\) as the smallest integer such that \(\sum_{i=1}^{r}\sigma_i^2\big/\sum_{j=1}^{k}\sigma_j^2\) is greater than or equal to cumulative_energy.

residual_energyfloat

Choose \(r\) as the smallest integer such that \(\sum_{i=r+1}^k\sigma_i^2\big/\sum_{j=1}^k\sigma_j^2\) is less than or equal to residual_energy.

projection_errorfloat

Choose \(r\) as the smallest integer such that \(\|\Q - \Vr\Vr\trp\Q\|_F \big/ \|\Q\|_F\) is less than or equal to projection_error, where \(\Q\) is the matrix of training snapshots.