antropy.petrosian_fd¶

antropy.petrosian_fd(x, axis=-1)[source]¶

Petrosian fractal dimension.

Parameters:

xlist or np.array: 1D or N-D data.
axisint: The axis along which the FD is calculated. Default is -1 (last).

Returns:

pfdfloat: Petrosian fractal dimension.

Notes

The Petrosian fractal dimension of a time-series \(x\) is defined by:

\[P = \frac{\log_{10}(N)}{\log_{10}(N) + \log_{10}(\frac{N}{N+0.4N_{\delta}})}\]

where \(N\) is the length of the time series, and \(N_{\delta}\) is the number of sign changes in the signal derivative.

Original code from the pyrem package by Quentin Geissmann.

References

A. Petrosian, Kolmogorov complexity of finite sequences and recognition of different preictal EEG patterns, in , Proceedings of the Eighth IEEE Symposium on Computer-Based Medical Systems, 1995, pp. 212-217.
Goh, Cindy, et al. “Comparison of fractal dimension algorithms for the computation of EEG biomarkers for dementia.” 2nd International Conference on Computational Intelligence in Medicine and Healthcare (CIMED2005). 2005.

Examples

>>> import numpy as np
>>> import antropy as ant
>>> import stochastic.processes.noise as sn
>>> rng = np.random.default_rng(seed=42)
>>> x = sn.FractionalGaussianNoise(hurst=0.5, rng=rng).sample(10000)
>>> print(f"{ant.petrosian_fd(x):.4f}")
1.0264

Fractional Gaussian noise with H = 0.9

>>> rng = np.random.default_rng(seed=42)
>>> x = sn.FractionalGaussianNoise(hurst=0.9, rng=rng).sample(10000)
>>> print(f"{ant.petrosian_fd(x):.4f}")
1.0235

Fractional Gaussian noise with H = 0.1

>>> rng = np.random.default_rng(seed=42)
>>> x = sn.FractionalGaussianNoise(hurst=0.1, rng=rng).sample(10000)
>>> print(f"{ant.petrosian_fd(x):.4f}")
1.0283

Random

>>> rng = np.random.default_rng(seed=42)
>>> print(f"{ant.petrosian_fd(rng.random(1000)):.4f}")
1.0350

Pure sine wave

>>> x = np.sin(2 * np.pi * 1 * np.arange(3000) / 100)
>>> print(f"{ant.petrosian_fd(x):.4f}")
1.0010

Linearly-increasing time-series (should be 1)

>>> x = np.arange(1000)
>>> print(f"{ant.petrosian_fd(x):.4f}")
1.0000