WaveletDec#

class pymultifracs.multiresquantity.WaveletDec#

Bases: MultiResolutionQuantityBase

Wavelet Coefficient Decomposition.

It represents the wavelet coefficients of a signal \(d_X(j, k)\)

Note

Should not be instantiated directly but instead created using the wavelet_analysis function.

Attributes:

valuesdict[int, ndarray]: values[j] contains the coefficients at the scale j. Arrays are of the shape (nj, n_rep)
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.
gamintfloat: Fractional integration used in the computation of the MRQ.
wt_namestr: Name of the wavelet used for the decomposition.
interval_sizeint: Width of the coef interval over which the MRQ was computed.
origin_mrqWaveletDec | None: If MRQ is derived from another mrq, refers to the original MRQ.
bootstrapped_objWaveletDec | None: Storing the bootstrapped version of the MRQ if bootstraping has been used.

auto_integrate(scaling_ranges, weighted=None, idx_reject=None)#

Automatically integrates the signal to match the requirements of the multifractal formalism associated to the multi-resolution quantity.

Parameters:

scaling_rangeslist[tuple[int, int]]: List of pairs of \((j_1, j_2)\) ranges of scales for the analysis.
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.
idx_rejectdict[int, ndarray of bool]: Dictionary associating each scale to a boolean array indicating whether certain coefficients should be removed.

bootstrap(R, min_scale=1, idx_reject=None)#

Bootstrap the multi-resolution quantity by repeating.

Parameters:

Rint: Number of repetitions of the bootstrap.
min_scaleint: Minimum scale that will be kept in the bootstrapped MRQ, used to save memory space when analyzing the coarse scales of long time series.
idx_rejectdict[str, np.ndarray] | None: Dictionary of rejected values, by default None which means no rejected values.

Returns:

WaveletDec: MRQ containing the bootstrapped values.

classmethod bootstrap_multiple(R, min_scale, mrq_list)#: Bootstrap multiple MRQs at once

check_regularity(scaling_ranges, weighted=None, idx_reject=None, min_j=1)#

Verify that the MRQ has enough regularity for analysis.

Parameters:

scaling_rangeslist[tuple[int, int]]: List of pairs of (j1, j2) ranges of scales for the analysis.
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.
idx_rejectDict[int, ndarray]: Dictionary associating each scale to a boolean array indicating whether certain coefficients should be removed.

Returns:

ndarray: Estimate of the minimal Hölder exponent in the MRQ.

freq2scale(freq, sfreq)#

Get the scales associated to frequencies.

Parameters:

freqfloat | ndarray: Frequencies to convert to scales.
sfreqfloat: Sampling frequency of the signal.

Returns:

scalesfloat | ndarray: Scales associated to freq.

get_formalism()#

Obtains the fomalism of the multi-resolution quantity

Returns:

formalismstr

get_leaders(p_exp, interval_size=3, gamint=None)#

Compute (p-)leaders from the wavelet coefficients

Parameters:

p_expfloat | numpy.inf: np.inf means wavelet leaders will also be computed, and a float sets the value of the p exponent implying a wavelet p-leader formalism.
interval_sizeint: Width of the time shift interval over which the leaders are computed, by default the usual value of 3.
gamintint | None: Fractional integration coefficient, by default None which means that current integration will be conserved.

Returns:

WaveletLeader: Wavelet (p-)leader derived from the coefficients.

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

get_nj_interv(j1=None, j2=None, idx_reject=None)#: Returns nj as an array, for j in [j1,j2]

get_values(j, idx_reject=None)#: Get the values of the MRQ, applying any finite size effects corrections if necessary (Wavelet p-leaders).

get_wse(theta=0.5, omega=1, gamint=None)#

Compute weak scaling exponents from the wavelet coefficients

Parameters:

thetafloat, optional: Parameter controlling to which extent the cone reaches in the lower scales. Practically, \((\theta, \omega)\)-leaders computed at scale \(j\) reach down to \(j-j^{\theta}\).
omegafloat, optional: Parameter controlling the angle of the cone over which the weak scaling exponents are computed: practically, for computing the \((\theta, \omega)\)-leaders at scale \(j\), the width of the cone at scale \(j\prime\) is \((j-j\prime)^{omega} + 1\).
gamintfloat, optional: Fractional integration coefficient, defaults to 0 (no integration).

Returns:

WaveletWSE: Weak scaling exponent derived from the coefficients.

integrate(gamint)#

Fractionally integrate the wavelet coefficients.

Parameters:

gamintfloat: Fractional integration coefficient

Returns:

integratedWaveletDec

j2_eff()#: Returns the effective maximal scale

max_scale_bootstrap(idx_reject=None)#

Maximum scale at which bootstrapping can be done

Parameters:

idx_rejectdict[str, np.ndarray] | None: Dictionary of rejected values, by default None which means no rejected values.

Returns:

Scaleint

plot(j1, j2, ax=None, vmin=None, vmax=None, cbar=True, figsize=(4.5, 1.5), gamma=1, nan_idx=None, signal_idx=0, cbar_kw=None, cmap='magma')#

Plot the multi-resolution quantity.

Parameters:

j1int: Initial scale from which to display the values.
j2int: Maximal scale from which to display the values.
axmatplotlib.pyplot.axes | None: pyplot axes, defaults to None which creates a new figure.
vminfloat | None: Minimal value of the colorbar, by default None which uses the minimal value in the data.
vmaxfloat | None: Maximal value of the colorbar, by default None which uses the maximal value in the data.
cbarbool: Whether to display a colorbar.
figsizetuple, optional: Size of the figure, used if ax is None.
gammafloat, optional: Exponent of the power-law color normalization, set to 1 for no normalization.
nan_idxdict[str, ndarray] | None: Index of values to highlight (smart indexing), or boolean mask index of values to highlight as output by robust.get_outliers.
signal_idxint, optional: Index of the signal to plot, defaults to the first signal.
cbar_kwdict | None: Arguments to pass to the colorbar function call
cmapstr: Colormap for the plot.

scale2freq(scale, sfreq)#

Get the frequencies associated to scales.

Parameters:

scaleint | float | ndarray: Scales to convert to frequency.
sfreqfloat: Sampling frequency of the signal.

Returns:

freqfloat | ndarray: Frequencies associated to scales.