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AntroPy is a Python 3 package providing several time-efficient algorithms for computing the complexity of time-series. It can be used for example to extract features from EEG signals.

Installation

pip install antropy

Dependencies

Functions

Entropy

import numpy as np
import antropy as ant
np.random.seed(1234567)
x = np.random.normal(size=3000)
# Permutation entropy
print(ant.perm_entropy(x, normalize=True))
# Spectral entropy
print(ant.spectral_entropy(x, sf=100, method='welch', normalize=True))
# Singular value decomposition entropy
print(ant.svd_entropy(x, normalize=True))
# Approximate entropy
print(ant.app_entropy(x))
# Sample entropy
print(ant.sample_entropy(x))
# Hjorth mobility and complexity
print(ant.hjorth_params(x))
# Number of zero-crossings
print(ant.num_zerocross(x))
# Lempel-Ziv complexity
print(ant.lziv_complexity('01111000011001', normalize=True))
0.9995371694290871
0.9940882825422431
0.9999110978316078
2.015221318528564
2.198595813245399
(1.4313385010057378, 1.215335712274099)
1531
1.3597696150205727

Fractal dimension

# Petrosian fractal dimension
print(ant.petrosian_fd(x))
# Katz fractal dimension
print(ant.katz_fd(x))
# Higuchi fractal dimension
print(ant.higuchi_fd(x))
# Detrended fluctuation analysis
print(ant.detrended_fluctuation(x))
1.0310643385753608
5.954272156665926
2.005040632258251
0.47903505674073327

Execution time

Here are some benchmarks computed on a MacBook Pro (2020).

import numpy as np
import antropy as ant
np.random.seed(1234567)
x = np.random.rand(1000)
# Entropy
%timeit ant.perm_entropy(x)
%timeit ant.spectral_entropy(x, sf=100)
%timeit ant.svd_entropy(x)
%timeit ant.app_entropy(x)  # Slow
%timeit ant.sample_entropy(x)  # Numba
# Fractal dimension
%timeit ant.petrosian_fd(x)
%timeit ant.katz_fd(x)
%timeit ant.higuchi_fd(x) # Numba
%timeit ant.detrended_fluctuation(x) # Numba
106 µs ± 5.49 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)
138 µs ± 3.53 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)
40.7 µs ± 303 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
2.44 ms ± 134 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
2.21 ms ± 35.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
23.5 µs ± 695 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
40.1 µs ± 2.09 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)
13.7 µs ± 251 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
315 µs ± 10.7 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

Development

AntroPy was created and is maintained by Raphael Vallat. Contributions are more than welcome so feel free to contact me, open an issue or submit a pull request!

To see the code or report a bug, please visit the GitHub repository.

Note that this program is provided with NO WARRANTY OF ANY KIND. Always double check the results.

Acknowledgement

Several functions of AntroPy were adapted from:

All the credit goes to the author of these excellent packages.