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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Ex.1: Sample Entropy · EntropyHub.jl</title><meta name="title" content="Ex.1: Sample Entropy · EntropyHub.jl"/><meta property="og:title" content="Ex.1: Sample Entropy · EntropyHub.jl"/><meta property="twitter:title" content="Ex.1: Sample Entropy · EntropyHub.jl"/><meta name="description" content="Documentation for EntropyHub.jl."/><meta property="og:description" content="Documentation for EntropyHub.jl."/><meta property="twitter:description" content="Documentation for EntropyHub.jl."/><meta property="og:url" content="https://mattwillflood.github.io/EntropyHub.jl/Examples/Example1/"/><meta property="twitter:url" content="https://mattwillflood.github.io/EntropyHub.jl/Examples/Example1/"/><link rel="canonical" href="https://mattwillflood.github.io/EntropyHub.jl/Examples/Example1/"/><script data-outdated-warner src="../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../search_index.js"></script><script src="../../siteinfo.js"></script><script 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id="menuitem-3" type="checkbox" checked/><label class="tocitem" for="menuitem-3"><span class="docs-label">Examples</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../Examples/">Notes on Examples</a></li><li class="is-active"><a class="tocitem" href>Ex.1: Sample Entropy</a></li><li><a class="tocitem" href="../Example2/">Ex.2: Permutation Entropy</a></li><li><a class="tocitem" href="../Example3/">Ex.3: Phase Entropy</a></li><li><a class="tocitem" href="../Example4/">Ex.4: Cross-Distribution Entropy</a></li><li><a class="tocitem" href="../Example5/">Ex.5: Multiscale Entropy Object</a></li><li><a class="tocitem" href="../Example6/">Ex.6: Multiscale [Increment] Entropy</a></li><li><a class="tocitem" href="../Example7/">Ex.7: Refined Multiscale [Sample] Entropy</a></li><li><a class="tocitem" href="../Example8/">Ex.8: Composite Multiscale Cross-Approximate Entropy</a></li><li><a class="tocitem" href="../Example9/">Ex.9: Hierarchical Multiscale corrected Cross-Conditional Entropy</a></li><li><a class="tocitem" href="../Example10/">Ex.10: Bidimensional Fuzzy Entropy</a></li><li><a class="tocitem" href="../Example11/">Ex.11: Multivariate Dispersion Entropy</a></li><li><a class="tocitem" href="../Example12/">Ex.12: [Generalized] Refined-composite Multivariate Multiscale Fuzzy Entropy</a></li><li><a class="tocitem" href="../Example13/">Ex.13: Window Data Tool</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Ex.1: Sample Entropy</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Ex.1: Sample Entropy</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/MattWillFlood/EntropyHub.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/MattWillFlood/EntropyHub.jl/blob/master/docs/src/Examples/Example1.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Example-1:-Sample-Entropy"><a class="docs-heading-anchor" href="#Example-1:-Sample-Entropy">Example 1: Sample Entropy</a><a id="Example-1:-Sample-Entropy-1"></a><a class="docs-heading-anchor-permalink" href="#Example-1:-Sample-Entropy" title="Permalink"></a></h1><p>Import a signal of normally distributed random numbers [mean = 0; SD = 1], and calculate the sample entropy for each embedding dimension (m) from 0 to 4.</p><pre><code class="language-julia hljs">X = ExampleData(&quot;gaussian&quot;);
Samp, _ = SampEn(X, m = 4);</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">5-element Vector{Float64}:
2.178923612371957
2.175742327787873
2.181969567351662
2.2209839754321417
2.1755667174542923</code></pre><p>Select the last value to get the sample entropy for m = 4.</p><pre><code class="language-julia hljs">Samp[end]</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">2.1755667174542923</code></pre><p>Calculate the sample entropy for each embedding dimension (m) from 0 to 4 with a time delay (tau) of 2 samples.</p><pre><code class="language-julia hljs">Samp, Phi1, Phi2 = SampEn(X, m = 4, tau = 2)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">([2.178923612371957, 2.183323250654987, 2.188041075511569, 2.189184333017654, 2.1440802180581136], [1.414258e6, 159224.0, 17843.0, 1998.0, 234.0], [1.24975e7, 1.413233e6, 159119.0, 17838.0, 1997.0])</code></pre><p>Import a signal of uniformly distributed random numbers in the range [-1, 1] and calculate the sample entropy for an embedding dimension (m) of 5, a time delay of 2, and a threshold radius of 0.075. Return the conditional probability (Vcp) and the number of overlapping matching vector pairs of lengths m+1 (Ka) and m (Kb), respectively.</p><pre><code class="language-julia hljs">Samp, _, _, Vcp_Ka_Kb = SampEn(X, m = 5, tau = 2, r = 0.075, Vcp = true)
Vcp, Ka, Kb = Vcp_Ka_Kb</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Vcp = 0.00018629728228987074
Ka = 92
Kb = 3943</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Examples/">« Notes on Examples</a><a class="docs-footer-nextpage" href="../Example2/">Ex.2: Permutation Entropy »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 24 April 2024 20:07">Wednesday 24 April 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Ex.10: Bidimensional Fuzzy Entropy · EntropyHub.jl</title><meta name="title" content="Ex.10: Bidimensional Fuzzy Entropy · EntropyHub.jl"/><meta property="og:title" content="Ex.10: Bidimensional Fuzzy Entropy · EntropyHub.jl"/><meta property="twitter:title" content="Ex.10: Bidimensional Fuzzy Entropy · EntropyHub.jl"/><meta name="description" content="Documentation for EntropyHub.jl."/><meta property="og:description" content="Documentation for EntropyHub.jl."/><meta property="twitter:description" content="Documentation for EntropyHub.jl."/><meta property="og:url" content="https://mattwillflood.github.io/EntropyHub.jl/Examples/Example10/"/><meta property="twitter:url" content="https://mattwillflood.github.io/EntropyHub.jl/Examples/Example10/"/><link rel="canonical" href="https://mattwillflood.github.io/EntropyHub.jl/Examples/Example10/"/><script data-outdated-warner src="../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../search_index.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script><link href="../../assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="EntropyHub.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../">EntropyHub.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><input class="collapse-toggle" id="menuitem-2" type="checkbox"/><label class="tocitem" for="menuitem-2"><span class="docs-label">Guide</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../../Guide/Base_Entropies/">Base Entropies</a></li><li><a class="tocitem" href="../../Guide/Cross_Entropies/">Cross-Entropies</a></li><li><a class="tocitem" href="../../Guide/Multivariate_Entropies/">Multivariate Entropies</a></li><li><a class="tocitem" href="../../Guide/Bidimensional_Entropies/">Bidimensional Entropies</a></li><li><a class="tocitem" href="../../Guide/Multiscale_Entropies/">Multiscale Entropies</a></li><li><a class="tocitem" href="../../Guide/Multiscale_Cross_Entropies/">Multiscale Cross-Entropies</a></li><li><a class="tocitem" href="../../Guide/Multivariate_Multiscale_Entropies/">Multivariate Multiscale Entropies</a></li><li><a class="tocitem" href="../../Guide/Other/">Other Functions</a></li></ul></li><li><input class="collapse-toggle" id="menuitem-3" type="checkbox" checked/><label class="tocitem" for="menuitem-3"><span class="docs-label">Examples</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../Examples/">Notes on Examples</a></li><li><a class="tocitem" href="../Example1/">Ex.1: Sample Entropy</a></li><li><a class="tocitem" href="../Example2/">Ex.2: Permutation Entropy</a></li><li><a class="tocitem" href="../Example3/">Ex.3: Phase Entropy</a></li><li><a class="tocitem" href="../Example4/">Ex.4: Cross-Distribution Entropy</a></li><li><a class="tocitem" href="../Example5/">Ex.5: Multiscale Entropy Object</a></li><li><a class="tocitem" href="../Example6/">Ex.6: Multiscale [Increment] Entropy</a></li><li><a class="tocitem" href="../Example7/">Ex.7: Refined Multiscale [Sample] Entropy</a></li><li><a class="tocitem" href="../Example8/">Ex.8: Composite Multiscale Cross-Approximate Entropy</a></li><li><a class="tocitem" href="../Example9/">Ex.9: Hierarchical Multiscale corrected Cross-Conditional Entropy</a></li><li class="is-active"><a class="tocitem" href>Ex.10: Bidimensional Fuzzy Entropy</a></li><li><a class="tocitem" href="../Example11/">Ex.11: Multivariate Dispersion Entropy</a></li><li><a class="tocitem" href="../Example12/">Ex.12: [Generalized] Refined-composite Multivariate Multiscale Fuzzy Entropy</a></li><li><a class="tocitem" href="../Example13/">Ex.13: Window Data Tool</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Ex.10: Bidimensional Fuzzy Entropy</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Ex.10: Bidimensional Fuzzy Entropy</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/MattWillFlood/EntropyHub.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/MattWillFlood/EntropyHub.jl/blob/master/docs/src/Examples/Example10.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Example-10:-Bidimensional-Fuzzy-Entropy"><a class="docs-heading-anchor" href="#Example-10:-Bidimensional-Fuzzy-Entropy">Example 10: Bidimensional Fuzzy Entropy</a><a id="Example-10:-Bidimensional-Fuzzy-Entropy-1"></a><a class="docs-heading-anchor-permalink" href="#Example-10:-Bidimensional-Fuzzy-Entropy" title="Permalink"></a></h1><p>Import an image of a Mandelbrot fractal as a matrix.</p><pre><code class="nohighlight hljs">X = ExampleData(&quot;mandelbrot_Mat&quot;);

using Plots
heatmap(X, background_color=&quot;black&quot;)</code></pre><p><img src="../../assets/mandelbrotjl.png" alt="AlmondBread"/></p><p>Calculate the bidimensional fuzzy entropy in trits (logarithm base 3) with a template matrix of size [8 x 5], and a time delay (<code>tau</code>) of 2 using a <code>&#39;constgaussian&#39;</code> fuzzy membership function (r=24).</p><pre><code class="language-julia hljs">FE2D = FuzzEn2D(X, m = (8, 5), tau = 2, Fx = &quot;constgaussian&quot;, r = 24, Logx = 3)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">1.4885540777860427</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Example9/">« Ex.9: Hierarchical Multiscale corrected Cross-Conditional Entropy</a><a class="docs-footer-nextpage" href="../Example11/">Ex.11: Multivariate Dispersion Entropy »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 24 April 2024 20:07">Wednesday 24 April 2024</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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