MFSpectrum#

class pymultifracs.scalingfunction.MFSpectrum#

Bases: ScalingFunction

Estimates the Multifractal Spectrum

Based on equations 2.74 - 2.78 of Herwig Wendt’s thesis [1]

Note

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

Attributes:

formalismstr

Formalism used. Can be any of ‘wavelet coefs’, ‘wavelet leaders’, or ‘wavelet p-leaders’.

jndarray, shape (n_scales,)

List of the j values (scales), in order presented in the value arrays.

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-leadParameters ———-

figsize: (int, int) | None: If not None, indicates the size of the figure.
nrowint: Number of rows of the figure.
j1int: Constrains the plot to scales \(j \geq j_1\).
filenamestr | None: If not None, saves the figure to filename.
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.
**kwargsdict: Optional arguments sent to pymultifracs.viz.plot_cumulants().[Tuple[int]]

List of pairs of (j1, j2) ranges of scales for the analysis

Dqndarray, shape (n_exponents, n_rep)

Fractal dimensions : \(D(q)\), y-axis of the multifractal spectrum

hqndarray, shape (n_exponents, n_rep)

Hölder exponents : \(h(q)\), x-axis of the multifractal spectrum

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_objMFSpectrum | None

Storing the bootstrapped version of the structure function if bootstraping has been used.

References

[1]

H. Wendt (2008). Contributions of Wavelet Leaders and Bootstrap to Multifractal Analysis: Images, Estimation Performance, Dependence Structure and Vanishing Moments. Confidence Intervals and Hypothesis Tests. Ph.D thesis, Laboratoire de Physique, Ecole Normale Superieure de Lyon. https://www.irit.fr/~Herwig.Wendt/data/ThesisWendt.pdf

D_q()#: Returns \(\mathcal{L}(q)\).

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

V_q(q)#: Returns \(V_q(j)\) 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.

h_q()#: Returns \(h(q)\).

plot(filename=None, ax=None, fmt='ko-', range_idx=0, signal_idx=0, shift_gamint=False, **plot_kwargs)#

Plot the multifractal spectrum.

Parameters:

filenamestr | None: If not None, saves the figure to filename.
axAxes | None: Axes where to plot the spectrum. Defaults to None, which creates a new figure.
fmtstr: Format string for the plot.
range_idxint: If multiple scaling ranges were used in fitting, indicates the index to use.
signal_idxint: If using a multivariate signal, index of the signal to plot.
shift_gamintbool: If fractional integration was used, shifts the spectrum on the x-axis by \(-\gamma\).
**plot_kwargsdict: Optional arguments sent to the plotting function plt.plot().