utils.reduced_basis.svd

utils.reduced_basis.svd

Functions

Name	Description
svd_mode_selector	Select SVD modes based on relative reconstruction-error tolerance and plot the error.
svd_mode_selector_var	Select SVD modes based on an uncaptured variance tolerance and plot the uncaptured variance.

svd_mode_selector

utils.reduced_basis.svd.svd_mode_selector(
    data,
    tolerance=0.001,
    modes=False,
    **kwargs,
)

Select SVD modes based on relative reconstruction-error tolerance and plot the error.

Parameters

Name	Type	Description	Default
data	(array_like, shape(n_samples, n_features) or (n_features, n_samples))	Input data matrix. Columns (or rows) represent snapshots or observations.	required
tolerance	float	Maximum allowed relative reconstruction error (L2-norm) for the selected modes. Defaults to 1e-3.	0.001
modes	bool	If True, prints the number of selected modes. Defaults to False.	False
**kwargs		Additional keyword arguments passed to the plot (e.g., marker style, line width).	{}

Returns

Name	Type	Description
num_selected_modes	int	Number of SVD modes required to meet the specified reconstruction-error tolerance.
U	(ndarray, shape(n_features, n_features))	Matrix of left singular vectors from the SVD of the input data.

Notes

• Singular values are flipped to compute residual energy from smallest to largest modes.
• Relative reconstruction error is defined as the square-root of uncaptured energy divided by total energy.

Examples

>>> num_modes, U = svd_mode_selector(data_matrix, tolerance=1e-2)
>>> print(num_modes)
4

[Author: Suparno Bhattacharyya]

svd_mode_selector_var

utils.reduced_basis.svd.svd_mode_selector_var(
    data,
    tolerance=0.001,
    modes=False,
    **kwargs,
)

Select SVD modes based on an uncaptured variance tolerance and plot the uncaptured variance.

Parameters

Name	Type	Description	Default
data	(array_like, shape(n_samples, n_features) or (n_features, n_samples))	Input data matrix. Columns (or rows) represent snapshots or observations.	required
tolerance	float	Maximum allowed fraction of total variance that remains uncaptured by the selected modes. Defaults to 1e-3.	0.001
modes	bool	If True, prints the number of selected modes. Defaults to False.	False
**kwargs		Additional keyword arguments passed to the plot (e.g., marker style, line width).	{}

Returns

Name	Type	Description
num_selected_modes	int	Number of SVD modes required to meet the specified uncaptured variance tolerance.
U	(ndarray, shape(n_features, n_features))	Matrix of left singular vectors from the SVD of the input data.

Notes

• The function computes the full SVD of the (transposed) data matrix and calculates the cumulative sum of squared singular values to measure variance content.
• Uncaptured variance is defined as one minus the cumulative energy.
• A horizontal line at y = tolerance is drawn on the semilog plot for reference.

Examples

>>> num_modes, U = svd_mode_selector_var(data_matrix, tolerance=1e-2)
>>> print(num_modes)
5

[Author: Suparno Bhattacharyya]