StructureFunction#

class pymultifracs.scalingfunction.StructureFunction#

Bases: ScalingFunction

Contains the structre functions and their linear fit.

Note

Should not be instanciated but instead obtained from calling pymultifracs.mfa()

Attributes:

jndarray, shape (n_j): Values of j covered by the analysis.
njdict[int, ndarray]: Dictionnary giving the number of non-NaN values at every scale. Array are of shape (n_rep)
gamintfloat: Value of gamint used in the computation of the underlying MRQ.
formalismstr: Formalism used. Can be any of ‘wavelet coefs’, ‘wavelet leaders’, or ‘wavelet p-leaders’.
n_channelint: Number of underlying signals in the wavelet decomposition. May not match the dimensionality of the values arrays in case there are multiple repetitions associated to a single signal.
qndarray, shape (n_moments): \(q\) values for which the structure functions are computed.
valuesndarray, shape (n_moments, n_j, n_scaling_ranges, n_rep): \(S_q(j, k)\).
scaling_rangeslist[tuple[int, int]]: List of pairs of scales \((j_1, j_2)\) delimiting the temporal scale support over which the estimates are regressed.
slopendarray, shape (n_moments, n_scaling_ranges, n_rep): \(s_q\).
Hndarray: \(H = s_2 / 2\).
interceptndarray, shape (n_moments, n_scaling_ranges, n_rep): Intercept of the linear regression.
weightedstr | None: Weighting mode for the linear regressions. Defaults to None, which is no weighting. Possible values are ‘Nj’ which weighs by number of coefficients, and ‘bootstrap’ which weights by bootstrap-derived estimates of variance.
weightsndarray: Weights of the linear regression.
bootstrapped_objStructureFunction | None: Storing the bootstrapped version of the structure function if bootstraping has been used.

S_q(q)#: Returns \(S_q(j)\) for given q.

compute_Lambda()#

Computes \(\Lambda\) for bootstrap-based automated range selection. [1]

References

[1]

https://doi.org/10.1016/j.sigpro.2014.06.002

compute_R()#: Computes \(R\) for bootstrap-based automated range selection.

compute_R2()#: Computes \(R^2\) for the estimated linear regressions.

compute_RMSE()#: Computes root mean square error for the estimated linear regressions.

find_best_range(per_moment=False)#

Find the best range among those computed, given bootstrap was already performed

Parameters:

per_momentbool: If True, returns the best range for each moment. Otherwise, by default returns the overall best range for all moments.

References

[1]

https://doi.org/10.1016/j.sigpro.2014.06.002

get_jrange(j1=None, j2=None, bootstrap=False)#: Sanitize the scaling range \([j_1, j_2]\) and find the associated indices in the mrq.j array.

get_n_bootstrap()#: Returns the number of bootstrapping repetition, or 0 if no bootstrapping

get_nj_interv(j_min, j_max)#: Returns the number of coefficients on an interval of temporal scales.

plot(nrow=4, filename=None, ignore_q0=True, figsize=None, scaling_range=0, plot_scales=None, plot_CI=True, signal_idx=0)#

Plots the structure functions.

Parameters:

nrowint: Number of rows in the plot.
filenamestr | None: If not None, the file is saved to filename
ignore_q0bool: Whether to include the structure function for \(q=0\), which is always going to be a constant function valued 1. Defaults to True.
figsizetuple[int, int] | None: Size of the figure, in inches.
scaling_rangeint: If multiple scaling ranges were used in fitting, indicates the index to use.
plot_scalestuple[int, int] | None: Takes a tuple of the form \((j_1, j_2)\): Constrains the x-axis to the interval \([j_1, j_2]\).
plot_CIbool: If using bootstrap, plot bootstrap-derived confidence interval on the structure function.
signal_idxint: If using a multivariate signal, index of the signal to plot.

plot_scaling(filename=None, ax=None, signal_idx=0, range_idx=0, **plot_kw)#

Plots the scaling function \(\zeta(q)\).

Parameters:

filenamestr | None: If not None, saves the figure to filename.
axAxes | None: Provides the axes on which to draw the function. Defaults to None, which creates a new figure.
signal_idxint: If using a multivariate signal, index of the signal to plot.
range_idxint: If multiple scaling ranges were used in fitting, indicates the index to use.
**plot_kwdict: Extra arguments forwarded to the plot function call.

s_q(q)#: Returns \(s_q\) for given q.