⚠️ This repository is deprecated

Development has stopped, effective immediately.

The Nonlinear Analysis Core is now the Quantitative Analysis Research Core (QUARC), and this library has moved:

→ https://github.com/Quantitative-Analysis-Research-Core/quarc-nonlinear

The new repository carries the full commit history of this one, so nothing is lost. It also contains corrections to defects found in an audit of this code, including several that silently produced wrong numbers. See its README for the list.

This repository will be removed after 31 December 2026. Clone or fork anything you still need before then, and move to the new repository.

No further issues or pull requests will be accepted here.

NONANToolbox

INSTALLATION

To download this library, click on the green dropdown box that says "Code" and click on "Download ZIP". Once the ZIP file has downloaded, you will have to extract the files from that ZIP folder. Once the files are extracted, they will be available for your use.

MATLAB VERSION

There are no known incompatibilities using MATLAB version R2019a.

MATLAB Toolboxes Required:

Statistics and Machine Learning Toolbox

Signal Processing Toolbox

Image Processing Toolbox

Parallel Computing Toolbox

Application Compiler Toolbox

PYTHON VERSION

To install from the requirements.txt file, make sure you have the package installer for Python (pip) on your PATH, and use the following command:

pip install -r requirements.txt

If you are installing using pip3, then simply use the command:

pip3 install -r requirements.txt

After installing these libraries, the Python scripts are available for use.

DOCUMENTATION

For documentation related to this library, we have a GitHub page hosted here.

FILES

This is a list of the included functions and the full name of the methods.

All function and file names are lower_snake_case. The previous names still work through shims in matlab/deprecated/; add that folder to your path if you need them, and they will warn once per session.

function	description
ami	Average mutual information versus lag, for choosing an embedding delay. Wrapper over ami_histogram and ami_kde.
ami_histogram	AMI by equal-width joint histogram.
ami_kde	AMI by Gaussian kernel density estimate.
chaos_library	Systems of differential equations that produce chaotic attractors.
corr_dim	Correlation dimension.
crqa	Cross recurrence quantification analysis.
dfa	Detrended fluctuation analysis.
embed	Delay embedding of a time series.
ent_ap	Approximate entropy.
ent_ms_plus	Refined composite multiscale, composite multiscale, multiscale, multiscale fuzzy, and generalized multiscale entropy.
ent_permu	Permutation entropy, log base 2.
ent_samp	Sample entropy.
ent_symbolic	Symbolic entropy.
ent_weighted	Weighted entropy of a recurrence plot.
ent_xap	Cross approximate entropy between two series.
ent_xsamp	Cross sample entropy between two series.
fgn_sim	Simulate fractional Gaussian noise at a specified Hurst exponent.
fnn	Embedding dimension by false nearest neighbours.
jrqa	Joint recurrence quantification analysis.
line_hist	Diagonal and vertical line histograms of a recurrence plot.
lye_r	Largest Lyapunov exponent, Rosenstein's method. Returns the divergence curve.
lye_w	Largest Lyapunov exponent, Wolf's method. Returns bits per unit time.
mdrqa	Multidimensional recurrence quantification analysis.
psr	Phase space reconstruction.
rel_phase_cont	Continuous relative phase between two cyclic series.
rel_phase_disc	Discrete relative phase between two series.
rqa	Recurrence quantification analysis.
rqa_legacy	Previous combined RQA/cRQA/jRQA/mdRQA entry point, kept for reproducibility.
rqa_plot	Plot a recurrence plot and its statistics.
set_radius	Find the radius giving a target percent recurrence.
surr_find_rho	Optimal noise radius for a pseudo-periodic surrogate.
surr_pseudo_periodic	Pseudo-periodic surrogate, using the radius from surr_find_rho.
surr_theiler	Theiler surrogates: shuffle, Fourier transform, and amplitude-adjusted Fourier transform.

TESTS

matlab -batch "addpath('tests/matlab'); run_tests"
python3 tests/python/run_tests.py

Headless, base MATLAB only, exits nonzero on failure. See tests/README.md.

COPYRIGHT

Copyright 2021 Nonlinear Analysis Core, Center for Human Movement Variability, University of Nebraska at Omaha

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

CONTACT

Please contact bmchnonan@unomaha.edu regarding any questions or troubleshooting.