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ordpy: A Python Package for Data Analysis with Permutation Entropy and Ordinal Network Methods

ordpy is a pure Python module [#pessa2021]_ that implements data analysis methods based on Bandt and Pompe's [#bandt_pompe]_ symbolic encoding scheme.

If you have used ordpy in a scientific publication, we would appreciate citations to the following reference [#pessa2021]_:

A. A. B. Pessa, H. V. Ribeiro, ordpy: A Python package for data analysis with permutation entropy and ordinal network methods <https://doi.org/10.1063/5.0049901>, Chaos 31, 063110 (2021). arXiv:2102.06786 <https://arxiv.org/abs/2102.06786>

.. code-block:: bibtex

@article{pessa2021ordpy, title = {ordpy: A Python package for data analysis with permutation entropy and ordinal network methods}, author = {Arthur A. B. Pessa and Haroldo V. Ribeiro}, journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science}, volume = {31}, number = {6}, pages = {063110}, year = {2021}, doi = {10.1063/5.0049901}, }

ordpy implements the following data analysis methods:

Released on version 1.0 (February 2021):

Permutation entropy for time series [#bandt_pompe]_ and images [#ribeiro_2012]_;
Complexity-entropy plane for time series [#lopezruiz], [#rosso] and images [#ribeiro_2012]_;
Multiscale complexity-entropy plane for time series [#zunino2012]_ and images [#zunino2016]_;
Tsallis [#ribeiro2017]_ and Rényi [#jauregui]_ generalized complexity-entropy curves for time series and images;
Ordinal networks for time series [#small], [#pessa2019] and images [#pessa2020]_;
Global node entropy of ordinal networks for time series [#McCullough], [#pessa2019] and images [#pessa2020]_.
Missing ordinal patterns [#amigo]_ and missing transitions between ordinal patterns [#pessa2019]_ for time series and images.

Released on version 1.1.0 (January 2023):

Weighted permutation entropy for time series [#fadlallah]_ and images;
Fisher-Shannon plane for time series [#olivares]_ and images;
Permutation Jensen-Shannon distance for time series [#zunino2022]_ and images;
Four pattern permutation contrasts (up-down balance, persistence, rotational-asymmetry, and up-down scaling.) for time series [#bandt]_;
Smoothness-structure plane for images [#bandt_wittfeld]_.

Released on version 1.2.0 (April 2025):

Two-by-two ordinal patterns for images [#tarozo]_.

For more detailed information about the methods implemented in ordpy, please consult its documentation <https://arthurpessa.github.io/ordpy/_build/html/index.html>_.

Installing

Ordpy can be installed via the command line using

.. code-block:: console

pip install ordpy

or you can directly clone its git repository:

.. code-block:: console

git clone https://github.com/arthurpessa/ordpy.git cd ordpy pip install -e .

Basic usage

We provide a notebook <https://github.com/arthurpessa/ordpy/blob/master/examples/ordpy.ipynb>_ illustrating how to use ordpy. This notebook reproduces all figures of our article [#pessa2021]_. The code below shows simple applications of ordpy.

.. code-block:: python

#Complexity-entropy plane for logistic map and Gaussian noise.

import numpy as np
import ordpy
from matplotlib import pylab as plt

def logistic(a=4, n=100000, x0=0.4):
    x = np.zeros(n)
    x[0] = x0
    for i in range(n-1):
        x[i+1] = a*x[i]*(1-x[i])
    return(x)

time_series = [logistic(a) for a in [3.05, 3.55, 4]]
time_series += [np.random.normal(size=100000)]

HC = [ordpy.complexity_entropy(series, dx=4) for series in time_series]


f, ax = plt.subplots(figsize=(8.19, 6.3))

for HC_, label_ in zip(HC, ['Period-2 (a=3.05)', 
                            'Period-8 (a=3.55)', 
                            'Chaotic (a=4)', 
                            'Gaussian noise']):
    ax.scatter(*HC_, label=label_, s=100)
    
ax.set_xlabel('Permutation entropy, $H$')
ax.set_ylabel('Statistical complexity, $C$')

ax.legend()

.. figure:: https://raw.githubusercontent.com/arthurpessa/ordpy/master/examples/figs/sample_fig.png :height: 489px :width: 633px :scale: 80 % :align: center

.. code-block:: python

#Ordinal networks for logistic map and Gaussian noise.

import numpy as np
import igraph
import ordpy
from matplotlib import pylab as plt
from IPython.core.display import display, SVG

def logistic(a=4, n=100000, x0=0.4):
    x = np.zeros(n)
    x[0] = x0
    for i in range(n-1):
        x[i+1] = a*x[i]*(1-x[i])
    return(x)

time_series = [logistic(a=4), np.random.normal(size=100000)]

vertex_list, edge_list, edge_weight_list = list(), list(), list()
for series in time_series:
    v_, e_, w_   = ordpy.ordinal_network(series, dx=4)
    vertex_list += [v_]
    edge_list   += [e_]
    edge_weight_list += [w_]

def create_ig_graph(vertex_list, edge_list, edge_weight):
    
    G = igraph.Graph(directed=True)
    
    for v_ in vertex_list:
        G.add_vertex(v_)
    
    for [in_, out_], weight_ in zip(edge_list, edge_weight):
        G.add_edge(in_, out_, weight=weight_)
        
    return G

graphs = []

for v_, e_, w_ in zip(vertex_list, edge_list, edge_weight_list):
    graphs += [create_ig_graph(v_, e_, w_)]

def igplot(g):
    f = igraph.plot(g,
                    layout=g.layout_circle(),
                    bbox=(500,500),
                    margin=(40, 40, 40, 40),
                    vertex_label = [s.replace('|','') for s in g.vs['name']],
                    vertex_label_color='#202020',
                    vertex_color='#969696',
                    vertex_size=20,
                    vertex_font_size=6,
                    edge_width=(1 + 8*np.asarray(g.es['weight'])).tolist(),
                   )
    return f

for graph_, label_ in zip(graphs, ['Chaotic (a=4)', 
                                   'Gaussian noise']):
    print(label_)
    display(SVG(igplot(graph_)._repr_svg_()))

.. figure:: https://raw.githubusercontent.com/arthurpessa/ordpy/master/examples/figs/sample_net.png :height: 1648px :width: 795px :scale: 50 % :align: center

Contributing

Pull requests addressing errors or adding new functionalities are always welcome.

References

.. [#pessa2021] Pessa, A. A. B., & Ribeiro, H. V. (2021). ordpy: A Python package for data analysis with permutation entropy and ordinal networks methods. Chaos, 31, 063110.

.. [#bandt_pompe] Bandt, C., & Pompe, B. (2002). Permutation entropy: A Natural Complexity Measure for Time Series. Physical Review Letters, 88, 174102.

.. [#ribeiro_2012] Ribeiro, H. V., Zunino, L., Lenzi, E. K., Santoro, P. A., & Mendes, R. S. (2012). Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns. PLOS ONE, 7, e40689.

.. [#lopezruiz] Lopez-Ruiz, R., Mancini, H. L., & Calbet, X. (1995). A Statistical Measure of Complexity. Physics Letters A, 209, 321-326.

.. [#rosso] Rosso, O. A., Larrondo, H. A., Martin, M. T., Plastino, A., & Fuentes, M. A. (2007). Distinguishing Noise from Chaos. Physical Review Letters, 99, 154102.

.. [#zunino2012] Zunino, L., Soriano, M. C., & Rosso, O. A. (2012). Distinguishing Chaotic and Stochastic Dynamics from Time Series by Using a Multiscale Symbolic Approach. Physical Review E, 86, 046210.

.. [#zunino2016] Zunino, L., & Ribeiro, H. V. (2016). Discriminating Image Textures with the Multiscale Two-Dimensional Complexity-Entropy Causality Plane. Chaos, Solitons & Fractals, 91, 679-688.

.. [#ribeiro2017] Ribeiro, H. V., Jauregui, M., Zunino, L., & Lenzi, E. K. (2017). Characterizing Time Series Via Complexity-Entropy Curves. Physical Review E, 95, 062106.

.. [#jauregui] Jauregui, M., Zunino, L., Lenzi, E. K., Mendes, R. S., & Ribeiro, H. V. (2018). Characterization of Time Series via Rényi Complexity-Entropy Curves. Physica A, 498, 74-85.

.. [#small] Small, M. (2013). Complex Networks From Time Series: Capturing Dynamics. In 2013 IEEE International Symposium on Circuits and Systems (ISCAS2013) (pp. 2509-2512). IEEE.

.. [#pessa2019] Pessa, A. A. B., & Ribeiro, H. V. (2019). Characterizing Stochastic Time Series With Ordinal Networks. Physical Review E, 100, 042304.

.. [#pessa2020] Pessa, A. A. B., & Ribeiro, H. V. (2020). Mapping Images Into Ordinal Networks. Physical Review E, 102, 052312.

.. [#McCullough] McCullough, M., Small, M., Iu, H. H. C., & Stemler, T. (2017). Multiscale Ordinal Network Analysis of Human Cardiac Dynamics. Philosophical Transactions of the Royal Society A, 375, 20160292.

.. [#amigo] Amigó, J. M., Zambrano, S., & Sanjuán, M. A. F. (2007). True and False Forbidden Patterns in Deterministic and Random Dyna

Ordpy

Install / Use

README

ordpy: A Python Package for Data Analysis with Permutation Entropy and Ordinal Network Methods

Installing

Basic usage

Contributing

References