ordpy 1.0.3

A Python package for data analysis with permutation entropy and ordinal networks methods.

.. |logo1| image:: https://img.shields.io/pypi/v/ordpy?style=plastic :alt: PyPI
:target: https://pypi.org/project/ordpy/
:scale: 100%
.. |logo2| image:: https://img.shields.io/github/license/arthurpessa/ordpy?style=plastic :alt: GitHub
:target: https://github.com/arthurpessa/ordpy/blob/master/LICENSE
:scale: 100%
.. |logo3| image:: https://img.shields.io/pypi/dm/ordpy?style=plastic :alt: PyPI - Downloads
:target: https://pypi.org/project/ordpy/
:scale: 100%

|logo1| |logo2| |logo3|

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://arxiv.org/abs/2102.06786>`_, arXiv: 2102.06786 (2021).

.. code-block:: bibtex

@misc{pessa2021ordpy,
title = {ordpy: A Python module implementing permutation entropy and ordinal network methods for data analysis},
author = {Arthur A. B. Pessa and Haroldo V. Ribeiro},
year = {2021},
eprint = {2102.06786},
archivePrefix = {arXiv},
}

``ordpy`` implements the following data analysis methods:

- 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.

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



References
==========

.. [#pessa2021] Pessa, A. A., & Ribeiro, H. V. (2021). ordpy: A Python package
for data analysis with permutation entropy and ordinal networks methods.
arXiv: 2102.06786.

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

.. [#pessa2020] Pessa, A. A., & 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.

.. [#rosso_curvas] Martin, M. T., Plastino, A., & Rosso, O. A. (2006).
Generalized Statistical Complexity Measures: Geometrical and
Analytical Properties, Physica A, 369, 439–462.