The OPA (ordinal-patterns-analysis) toolbox is intended for nonlinear analysis of multivariate time series with becoming more and more popular ordinal-patterns-based measures [1-5] which are efficiently computed [6,7] and visualized:
- permutation entropy (cfg.method = 'PE') 
- permutation entropy for ordinal patterns with tied ranks (cfg.method = 'eqPE') [4,8]
- permutation entropy and ordinal patterns distributions (cfg.method = 'opdPE') 
- conditional entropy of ordinal patterns (cfg.method = 'cePE') 
- robust permutation entropy (cfg.method = 'rePE') [4,7]
- new ordinal-patterns-based measures are to be added (your suggestions and feedback are welcome!)
The interface of OPA toolbox is provided by a function outdata = OPanalysis( cfg, indata ), where
- cfg is a configuration structure with method's parameters;
- indata is data to be analyzed.
- outdata - computed values of ordinal-patterns-based complexity measure
CITING THE CODE
[a] Unakafova, Valentina (2017). Ordinal-patterns-based analysis (beta-version) (www.mathworks.com/matlabcentral/fileexchange/63782-ordinal-patterns-based-analysis--beta-version-), MATLAB Central File Exchange. Retrieved Month Day, Year.
[b] Unakafova, V.A., Keller, K., 2013. Efficiently measuring complexity on the basis of real-world data. Entropy, 15(10), 4392-4415.
EXAMPLE OF USE (see more examples for different methods and parameters in examples.m and OPanalysis.m help):
cfg = ;
cfg.method = 'opdPE'; % try also 'PE', 'CE', 'rePE' and 'all' here
cfg.order = 3; % for ordinal pattens of order 3 (4-points ordinal patterns)
cfg.delay = 1; % for delay 1 between points in ordinal patterns (successive points)
cfg.windowSize = 512; % for window size 512 in time points
indata = rand( 1, 7777 );
for i = 4000:7000 % change of data complexity
indata( i ) = 4*indata( i - 1 )*( 1 - indata( i - 1 ) );
outdata = OPanalysis( cfg, indata );
examples.m script contains examples of using OPA toolbox for different ordinal-patterns-based measures with different parameters
The Code folder contains functions for computing the aforementioned ordinal-patterns-based measures.
The Data folder contains example epileptic EEG datasets from https://vis.caltech.edu/~rodri/data.htm
(dataset 5, 130-2_c4.asc) used for illustrating in examples.m.
The Tables folder contain precomputed tables as *.mat-files for efficient computing of ordinal-patterns-based methods.
Please, see www.mathworks.com/matlabcentral/fileexchange/44161-permutation-entropy--fast-algorithm- for some discussion of parameters choice. Values of ordinal-patterns-based measures are computed in maximally overlapping sliding windows in a fast way [6,7]. This is a beta-version of OPA-toolbox, new ordinal-patterns-based measures are to be added (your feedback and comments are welcome)!
 Amigo, J.M., Keller, K. and Unakafova, V.A., 2015. On entropy, entropy-like quantities, and applications. Discrete & Continuous Dynamical Systems-Series B, 20(10).
 Bandt C., Pompe B., Permutation entropy: a natural complexity measure for time series. Physical review letters, 2002, APS
 Keller, K., and M. Sinn. Ordinal analysis of time series. Physica A: Statistical Mechanics and its Applications 356.1 (2005): 114--120
 Keller, K., Unakafov, A.M. and Unakafova, V.A., 2014. Ordinal patterns, entropy, and EEG. Entropy, 16(12), pp.6212-6239.
 Zanin, M., Zunino, L., Rosso, O.A. and Papo, D., 2012.
Permutation entropy and its main biomedical and econophysics applications: a review. Entropy, 14(8), pp.1553-1577.
 Unakafova, V.A., Keller, K., 2013. Efficiently measuring complexity on the basis of real-world Data. Entropy, 15(10), 4392-4415.
 Unakafova, V.A., 2015. Investigating measures of complexity for dynamical systems and for time series (Doctoral dissertation, University of Luebeck).
 Bian, C., Qin, C., Ma, Q.D. and Shen, Q., 2012. Modified permutation-entropy analysis of heartbeat dynamics. Physical Review E, 85(2), p.021906.
 Amigo, J.M., Zambrano, S. and Sanjuan, M.A., 2008. Combinatorial detection of determinism in noisy time series. EPL (Europhysics Letters), 83(6), p.60005.
 Cao, Y., Tung, W.W., Gao, J.B. et al., 2004. Detecting dynamical changes in time series using the permutation entropy. Physical Review E, 70(4), p.046217.
 Riedl, M., Muller, A. and Wessel, N., 2013. Practical considerations of permutation entropy. The European Physical Journal Special Topics, 222(2), pp.249-262.
Valentina Unakafova (2020). Ordinal-patterns-based analysis (beta-version) (https://www.mathworks.com/matlabcentral/fileexchange/63782-ordinal-patterns-based-analysis-beta-version), MATLAB Central File Exchange. Retrieved .
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