Modal Decomposition¶

mrpod.modal_decomposition.mrpod_detail_bundle(data_array, *args, num_of_modes=50, seg=10, subtract_avg=False, reflect=False, normalize_mode=True, full_path_write=None, **kwargs)¶

Computes MRPOD modes, eigvals and proj coeffs from a dataset arranged in an ndarray of the shape of NxM0xM1x…, with N being the dimension that will be wavelet transformed.

Other Parameters:
Parameters:	data_array : ndarray data array arranged in a dimension of NxM0xM1x…, such as a time series (N) of multi- dimensional scalar/vector fields. num_of_modes : 50, int, optional Number of modes to be computed (from the most energetic Mode 1). By default, all the valid modes are computed. seg : 10, int, optional In case of insufficient computer RAM, the `data_array` can be segmented along the M dimension of the reshaped NxM and pieced together after the filtering. subtract_avg : False, bool, optional If True, the ensemble average of the `data_array` along N is subtracted from the dataset. reflect : False, bool, optional If True, the cross-correlation matrix as well as the dataset is padded symmetrically along the sample axis. normalize_mode : True, bool, optional If True, the magnitudes of the modes will be normalized by their corresponding eingenvalues and the sample size. full_path_write : None, path obj, optional If provided, the output is saved locally in the specified directory.
Returns:	dict A dictionary containing the eigenvalues, projection coefficients, POD modes, and the cross- correlation matrix.
	**kwargs : Keyword arguments from `mrpod_eigendecomp()` necessary to perform a wavelet transform.

mrpod.modal_decomposition.mrpod_eigendecomp(corr_mat, js, scales, pod_fcn=None, reflect=False, **kwargs)¶

Apply eigenvalue decomposition to cross-correlation matrices reconstructed in specific bandpasses using WaveletTranform.

Other Parameters:
Parameters:	corr_mat : ndarray Cross-correlation matrix with a dimension of NxN js : 1d arrray of int The correponding decomposition levels. Different j levels are admissible for “max-overlap”. scales : 1d array of int All the scales included in the reconstruction. Discrete scales are admissible. pod_fcn : function object Function to solve the eigenvalue problem by taking in a pre-computed cross-correlation matrix. The output must conform to [eigvals, proj_coeffs]. If None, the built-in solver `pod_eigendecomp` is used. reflect : False, bool, optional If true, the corr_mat is padded symmetrically along both axes and is truncated after reconstruction and before eigenvalue decomposition. Such measure helps reducing the effect of uneven boundaries in the wavelet transform process. reflected : False, bool, optional If true, the supplied corr_mat has already been padded and is truncated before fed into the eigenvalue solver.
Returns:	eigvals : 1d array Eigenvalues from the decomposition proj_coeffs : ndarray Projection coefficients (temporal modes) of the shape of NxN K : ndarray Reconstructed cross-correlation matrix within the designed bandpasses.
	**kwargs : Keyword arguments from `WaveletTransform` necessary to perform a wavelet transform.

mrpod.modal_decomposition.ortho_check(v1, v2)¶: Check the orthogonality of two vectors.

mrpod.modal_decomposition.pod_eigendecomp(corr_mat, tol=1e-14)¶

Solving the eigenvalue problem of AX=Lambda.

Parameters:	corr_mat : ndarray Cross-correlation matrix with a dimension of NxN.
Returns:	eigvals : 1d array Eigenvalues from the decomposition. proj_coeffs: ndarray Projection coefficients (temporal modes) of the shape of NxN.

mrpod.modal_decomposition.pod_modes(data_array, pod_fcn=None, eigvals=None, proj_coeffs=None, num_of_modes=None, normalize_mode=True)¶

Calculate the POD modes based on the eigenvalue decomposition.

Parameters:

data_array : ndarray: Data array arranged in a dimension of NxM0xM1x…, such as a time series (N) of multi- dimensional scalar/vector fields.
pod_fcn : function object: Function to solve the eigenvalue problem by taking in a pre-computed cross-correlation matrix. The output must conform to [eigvals, proj_coeffs]. If None, the built-in solver pod_eigendecomp is used.
eigvals : 1d array: Eigenvalues from the decomposition.
proj_coeffs: ndarray: Projection coefficients (temporal modes) of the shape of NxN.
num_of_modes : None, int, optional: Number of modes to be computed (from the most energetic Mode 1). By default, all the valid modes are computed.
normalize_mode : True, bool, optional: If True, the magnitudes of the modes will be normalized by their corresponding eingenvalues and the sample size.

Returns:

dict: A dictionary containing the eigenvalues, projection coefficients, POD modes, and the cross- correlation matrix.