POD

modulo_vki.modulo.ModuloVKI.POD(self, SAVE_T_POD: bool = False, mode: str = 'K', verbose=True)

Compute the Proper Orthogonal Decomposition (POD) of a dataset.

The POD is computed using the snapshot approach, working on the temporal correlation matrix. The eigenvalue solver for this matrix is defined in the eig_solver attribute of the class.

Parameters:

• SAVE_T_POD (bool, optional) – Flag to save time-dependent POD data. Default is False.

• mode (str, optional) – The mode of POD computation. Must be either ‘K’ or ‘svd’. ‘K’ (default) uses the snapshot method on the temporal correlation matrix. ‘svd’ uses the SVD decomposition (full dataset must fit in memory).

Returns:

• Phi_P (numpy.ndarray) – POD temporal modes.

• Psi_P (numpy.ndarray) – POD spatial modes.

• Sigma_P (numpy.ndarray) – POD singular values (eigenvalues are Sigma_P**2).

Raises:

ValueError – If mode is not ‘k’ or ‘svd’.

Notes

A brief recall of the theoretical background of the POD is available at https://youtu.be/8fhupzhAR_M