Examples:

The following sections provide some basic examples of EntropyHub functions. These examples are merely a snippet of the full range of EntropyHub functionality.

In the following examples, signals / data are imported into Julia using the ExampleData() function. To use this function as shown in the examples below, an internet connection is required.

EntropyHub._ExampleData.ExampleData — Function

Data = ExampleData(SigName::String)

Imports sample data time series with specific properties that are commonly used as benchmarks for assessing the performance of various entropy methods. The datasets returned by ExampleData() are used in the examples provided in documentation on www.EntropyHub.xyz and elsewhere. ***Note*** ExampleData() requires an internet connection to download and import the required datasets!

Datais the sample dataset imported corresponding to the string input SigName which can be one of the following string:

Arguments:

SigName -

        `uniform`          - uniformly distributed random number sequence in range [0 1], N = 5000
        `randintegers`     - randomly distributed integer sequence in range [1 8], N = 4096
        `gaussian`         - normally distributed number sequence [mean: 0, SD: 1], N = 5000
        `henon`            - X and Y components of the Henon attractor [alpha: 1.4, beta: .3, Xo = 0, Yo = 0], N = 4500
        `lorenz`           - X, Y, and Z components of the Lorenz attractor [sigma: 10, beta: 8/3, rho: 28, Xo = 10, Yo = 20, Zo = 10], N = 5917
        `chirp`            - chirp signal (f0 = .01, t1 = 4000, f1 = .025), N = 5000
        `uniform2`         - two uniformly distributed random number sequences in range [0,1], N = 4096
        `gaussian2`        - two normally distributed number sequences [mean: 0, SD: 1], N = 3000
        `randintegers2`    - two uniformly distributed pseudorandom integer sequences in range [1 8], N = 3000
        `uniform_Mat`      - matrix of uniformly distributed random numbers in range [0 1], N = 50 x 50
        `gaussian_Mat`     - matrix of normally distributed numbers [mean: 0, SD: 1], N = 60 x 120
        `randintegers_Mat` - matrix of randomly distributed integers in range [1 8], N = 88 x 88
        `mandelbrot_Mat`   - matrix representing a Mandelbrot fractal image with values in range [0 255], N = 92 x 115
        `entropyhub_Mat`   - matrix representing the EntropyHub logo with values in range [0 255], N = 127 x 95
                     
For further info on these graining procedures see the `EntropyHub guide <https://github.com/MattWillFlood/EntropyHub/blob/main/EntropyHub%20Guide.pdf>`_.

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IMPORTANT TO NOTE

Parameters of the base or cross- entropy methods are passed to multiscale and multiscale cross- functions using the multiscale entropy object using MSobject. Base and cross- entropy methods are declared with MSobject() using any Base or Cross- entropy function. See the MSobject example in the following sections for more info.

Hierarchical Multiscale Entropy (+ Multiscale Cross-Entropy)

In hierarchical multiscale entropy (hMSEn) and hierarchical multiscale cross-entropy (hXMSEn) functions, the length of the time series signal(s) is halved at each scale. Thus, hMSEn and hXMSEn only use the first 2^N data points where 2^N <= the length of the original time series signal. i.e. For a signal of 5000 points, only the first 4096 are used. For a signal of 1500 points, only the first 1024 are used.

BIDIMENSIONAL ENTROPIES

Each bidimensional entropy function (SampEn2D, FuzzEn2D, DistEn2D) has an important keyword argument - Lock. Bidimensional entropy functions are "locked" by default (Lock == true) to only permit matrices with a maximum size of 128 x 128.