svd module

Singular value decomposition (SVD) of the TR-WAXS data.

class analysis.svd.SVD(data)[source]

Compute the SVD and store results for analysis and plotting.

Parameters:

data (np.ndarray) – Assumes an array where lines correspond to q-values and columns correspond to measured delays.

Examples

Assuming res is the result dict from txs.datared.datared:

>>> svd = SVD(res['diff_av']).run()
autocorr()[source]

Returns the autocorrelation of U and V singular vectors.

fit(f, xdata, vectors='v', rank=None, **kwargs)[source]

Fit the selected vectors up to given rank.

The scipy.optimize.curve_fit function is used with the provided function. This can be used to exctract a time evolution of the sample during an experiment.

Parameters:

  • f (callable) – A fit function to be used (typically a decaying exponential).

  • xdata (array-like) – An array containing the values for the x-axis (typically either q-values or experimental time).

  • vectors ({'u', 'v'}, optional) – Which vectors to use. Should be either ‘u’ for left-singular vectors or ‘v’ for right-singular vectors. (default, ‘v’)

  • rank (int, optional) – The maximum rank, or number of vectors, to fit. (default, None, all are used)

  • kwargs (dict-like) – Additional arguments to be passed to the scipy.optimize.curve_fit method.

Returns:

result – A list of outputs from scipy.optimize.curve_fit as tuples of the form (popt, perr) for each vector in vectors. The covariance matrix is directly converted to errors using perr = np.sqrt(np.diag(pcov)).

Return type:

list of tuples (popt, perr)

get_distance(other, rank=None)[source]

Computes the distance from vector dot product with another SVD.

For the matrices Ua and Va of this SVD, the dot products with the corresponding singular vectors in matrices Ub and Vb of other are computed. Then averages are computed for dot products obtained from U and V singular vectors separately.

Parameters:

  • other (SVD) – Another instance of SVD.

  • rank (int, optional) – The maximum rank of singular vector to be used. (default, None, all are used)

Returns:

  • dU (float) – The average inner product value for the U singular vectors.

  • dV (float) – The average inner product value for the V singular vectors.

maximize_autocorrelations(rank=(2, 10), side='left')[source]

Rotation of the SVD left or right matrix to maximize autocorrelation.

Parameters:

  • rank ({int, list, slice}, optional) – Selection of singular vectors to include in the rotation procedure. If an integer, it will select all vectors up to rank. If a 2-tuple, it will select vectors in the range defined by the tuple of the form (min, max). If a list or slice, it will select the ranks given. (default, (2, 10))

  • side ({'left', 'right'}, optional) – Which singular vectors to use, should be either “left” or “right”. (default, “left”)

patterns(rank=None)[source]

Returns the left and right basis patterns obtained from the SVD.

recompose(rank=None)[source]

Recomposes the signal by computing the matrix product USV.

result(rank=None)[source]

Returns the singular values and vectors up to rank.

Returns:

  • u (2D array) – The left-singular vectors (column-wise)

  • s (1D array) – The computed singular values arranged on the diagonal

  • v (2D array) – The right-singular vectors (row-wise)

run()[source]

Run the SVD calculation and stores result.

The result can be obtained using the result() method.

Left and right singular vectors can be obtained using the autocorr() method.

The basis patterns can be obtained using the patterns() method.

The recomposed signal can be obtained by using the recompose() method.

analysis.svd.reconstruct_corrected_signal(data, threshold=0.6, max_rank_rescale=1, maximize_autocorrelations=None, exclude=None)[source]

Use SVD to apply corrections on data and recontruct them.

Parameters:

  • data (dict-like or list of dict) – A data set or a list of data set obtained from txs datared routine.

  • threshold (float in [0, 1], optional) – Value of autocorrelation below which singular vectors are discarded. After a first crossing of the threshold, all subsequent vectors are discarded, whatever the value of their autocorrelation. (default, 0.6)

  • max_rank_rescale (int, optional) – The maximum rank of singular vectors for which a rescaling will be done. The time evolution of the right-singular vectors is fitted. The fitted model is then normalized and the corresponding patterns are divided by the normalized model. (default, 1)

  • maximize_autocorrelation (2-tuple, optional) – If not None, a 2-tuple giving the range of singular vector rank to be rotated such that the autocorrelation is maximized in increaing order. (default, None)

  • exclude (list of int) – If data is a list, exclude should contains the indices of data that should not be corrected for the kinetics.

Returns:

corr_data – The corrected data in the same format as the input data.

Return type:

dict or list of dict