API Reference#

Multifractal Analysis#

pymultifracs:

wavelet_analysis(signal[, wt_name, j2, ...])

Compute wavelet coefficient and wavelet leaders.

mfa(mrq, scaling_ranges[, weighted, ...])

Perform multifractal analysis, given wavelet coefficients.

Benchmark(signal_gen_grid, ...[, folder])

Compute and plot benchmarks, varying the models and analysis parameters.

Dataclasses#

Used to compute and store intermediary results. Not meant to be created outside of the analysis functions.

multiresquantity.WaveletDec(*[, ...])

Wavelet Coefficient Decomposition.

multiresquantity.WaveletLeader(*[, ...])

Wavelet Leader Representation.

multiresquantity.WaveletWSE(*[, ...])

Wavelet Weak Scaling Exponent.

scalingfunction.StructureFunction([...])

Contains the structre functions and their linear fit.

scalingfunction.Cumulants([...])

Computes and analyzes cumulant.

scalingfunction.MFSpectrum([...])

Estimates the Multifractal Spectrum

Storing the multifractal analysis output

utils.MFractalVar(structure, cumulants, spectrum)

Aggregates the output of multifractal analysis

utils.MFractalBiVar(structure, cumulants)

Aggregates the output of bivariate multifractal analysis

Visualization#

pymultifracs.viz:

viz.plot_psd(signal, fs[, wt_name, log_base, ax])

Plot the superposition of Fourier-based Welch estimation and Wavelet-based estimation of PSD on a log-log graphic.

viz.plot_cm(cm, ind_m, j1, j2, range_idx, ax)

Helper function to plot individual \(C_m(j)\) functions along with their associated \(c_m\) fit.

Bivariate Analysis#

pymultifracs.bivariate:

bivariate.bimfa(mrq1, mrq2, scaling_ranges)

Bivariate multifractal analysis.

bivariate.BiStructureFunction([...])

Bivariate structure function.

bivariate.BiCumulants([bootstrapped_obj, ...])

Bivariate cumulants.

Simulation#

pymultifracs.simul:

simul.mrw(shape, H, lam[, L, sigma, method, z0])

Create a realization of fractional Brownian motion using circulant matrix embedding.

simul.fbm(*args, **kwargs)

Simulate fBm.

Utility functions#

pymultifracs.utils:

utils.build_q_log(q_min, q_max, n)

Build a convenient vector of q values for multifractal analysis

Outlier detection#

pymultifracs.robust:

robust.get_outliers(wt_coefs, ...[, ...])

Detect outliers in a signal.