ordpy 1.2.2
A Python package for data analysis with permutation entropy and ordinal network methods
Requires Python: >=3.6

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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 Dynamics.
   Europhysics Letters, 79, 50001.

.. [#fadlallah] Fadlallah B., Chen, B., Keil A. & Príncipe, J. (2013). 
   Weighted-permutation entropy: a complexity measure for time series 
   incorporating amplitude information. Physical Review E, 97, 022911.

.. [#olivares] Olivares, F., Plastino, A., & Rosso, O. A. (2012). 
   Contrasting chaos with noise via local versus global 
   information quantifiers. Physics Letters A, 376, 1577–1583.

.. [#zunino2022] Zunino L., Olivares, F., Ribeiro H. V. & Rosso, O. A. (2022). 
   Permutation Jensen-Shannon distance: A versatile and fast symbolic tool
   for complex time-series analysis. Physical Review E, 105, 045310.

.. [#bandt] Bandt, C. (2023). Statistics and contrasts of order patterns in
   univariate time series, Chaos, 33, 033124.

.. [#bandt_wittfeld] Bandt, C., & Wittfeld, K. (2022). Two new parameters for 
   the ordinal analysis of images. arXiv:2212.14643.

.. [#tarozo] Tarozo, M. M., Pessa, A. A., Zunino, L., Rosso, O. A., Perc, M. 
   & Ribeiro, H. V. (2025). Two-by-two ordinal patterns in art paintings. 
   PNAS Nexus, 4, pgaf092.