wf_psf.utils.graph_utils module

class wf_psf.utils.graph_utils.GraphBuilder(obs_data, obs_pos, obs_weights, n_comp, n_eigenvects=None, n_iter=3, ea_gridsize=10, distances=None, auto_run=True, verbose=2)[source]

Bases: object

GraphBuilder class.

This class computes the necessary quantities for RCA’s graph constraint.

Parameters:

  • obs_data (numpy.ndarray) – Observed data.

  • obs_pos (numpy.ndarray) – Corresponding positions.

  • obs_weights (numpy.ndarray) – Corresponding per-pixel weights.

  • n_comp (int) – Number of RCA components.

  • n_eigenvects (int) – Maximum number of eigenvectors to consider per \((e,a)\) couple. Default is None; if not provided, all eigenvectors will be considered, which can lead to a poor selection of graphs, especially when data is undersampled. Ignored if VT and alpha are provided.

  • n_iter (int) – How many alternations should there be when optimizing over \(e\) and \(a\). Default is 3.

  • ea_gridsize (int) – How fine should the logscale grid of \((e,a)\) values be. Default is 10.

  • distances (numpy.ndarray) – Pairwise distances for all positions. Default is None; if not provided, will be computed from given positions.

  • auto_run (bool) – Whether to immediately build the graph quantities. Default is True.

Methods

gen_eigenvects(mat)

Compute input matrix's eigenvectors.

pick_emax([epsilon])

Pick maximum value for e parameter.

select_params(R, e_range, a_range)

Select best graph parameters.
gen_eigenvects(mat)[source]

Compute input matrix’s eigenvectors.

Keep only the n_eigenvects associated with the smallest eigenvalues.

pick_emax(epsilon=1e-15)[source]

Pick maximum value for e parameter.

From now, we fix the maximum \(e\) to 1 and ignore the old procedure that was giving values that were too big.

Old procedure: Select maximum value of \(e\) for the greedy search over set of \((e,a)\) couples, so that the graph is still fully connected.

select_params(R, e_range, a_range)[source]

Select best graph parameters.

Select \((e,a)\) parameters and best eigenvector for current \(R_i\) matrix.

Parameters:

  • R (numpy.ndarray) – Current \(R_i\) matrix (as defined in RCA paper (Ngole et al.), sect. 5.5.3.)

  • e_range (numpy.ndarray) – List of \(e\) values to be tested.

  • a_range (numpy.ndarray) – List of \(a\) values to be tested.

wf_psf.utils.graph_utils.gen_Pea(distances, e, a)[source]

Compute the graph Laplacian for a given set of parameters.

Parameters:

  • distances (numpy.ndarray) – Array of pairwise distances

  • e (float) – Exponent to which the pairwise distances should be raised.

  • a (float) – Constant multiplier along Laplacian’s diagonal.

Returns:

Pea – Graph laplacian.

Return type:

numpy.ndarray

Notes

Computes \(P_{e,a}\) matrix for given e, a couple. See Equations (16-17) in RCA paper (Ngole et al.). Watch out with the e parameter as it plays a vital role in the graph definition as it is a parameter of the distance that defines the graph’s weights.

wf_psf.utils.graph_utils.pairwise_distances(obs_pos)[source]

Compute pairwise distances.

wf_psf.utils.graph_utils.select_vstar(eigenvects, R, weights)[source]

Pick best eigenvector from a set of \((e,a)\).

i.e., solve (35) from RCA paper (Ngole et al.).

Parameters: