- Example 1: Sample Entropy
- Example 2: (Fine-grained) Permutation Entropy
- Example 3: Phase Entropy w/ Second Order Difference Plot
- Example 4: Cross-Distribution Entropy w/ Different Binning Methods
- Example 5: Multiscale Entropy Object - MSobject()
- Example 6: Multiscale Increment Entropy
- Example 7: Refined Multiscale Sample Entropy
- Example 8: Composite Multiscale Cross-Approximate Entropy
- Example 9: Hierarchical Multiscale corrected Cross-Conditional Entropy
- Example 10: Bidimensional Fuzzy Entropy

# 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**.

ExampleData() accepts any of the following strings:

`"uniform"`

- vector of uniformly distributed random numbers in range [0 1]`"gaussian"`

- vector of normally distributed random numbers with mean = 0, SD = 1`"randintegers"`

- vector of uniformly distributed pseudorandom integers in range [1 8]`"chirp"`

- vector of chirp signal with the following parameters: f0 = .01; t1 = 4000; f1 = .025`"lorenz"`

- 3-column matrix: X, Y, Z components of the Lorenz system (alpha: 10; beta: 8/3 ; rho: 28); [Xo = 10; Yo = 20; Zo = 10]`"henon"`

- 2-column matrix: X, Y components of the Henon attractor (alpha: 1.4; beta: 0.3); [Xo = 0; Yo = 0]`"uniform2"`

- 2-column matrix: uniformly distributed random numbers in range [0 1]`"gaussian2"`

- 2-column matrix: normally distributed random numbers with mean = 0, SD = 1`"randintegers2"`

- 2-column matrix: uniformly distributed pseudorandom integers in range [1 8]`"uniform_Mat"`

- Matrix of uniformly distributed random numbers in range [0 1]`"gaussian_Mat"`

- Matrix of normally distributed random numbers with mean = 0; SD = 1`"randintegers_Mat"`

- Matrix of uniformly distributed pseudorandom integers in range [1 8]`"mandelbrot_Mat"`

- Matrix of image of fractal generated from the mandelbrot set`"entropyhub_Mat"`

- Matrix of image of the entropyhub logo

For cross-entropy and multiscale cross-entropy functions, the two time series signals are passed as a two-column or two-row matrix. At present, it is not possible to pass signals of different lengths separately.

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.

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.

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.