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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Contextual Variable Types · ModelingToolkit.jl</title><script data-outdated-warner src="../../assets/warner.js"></script><link rel="canonical" href="https://mtk.sciml.ai/stable/basics/ContextualVariables/"/><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/0.039/juliamono-regular.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.3/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.3/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.3/css/brands.min.css" rel="stylesheet" type="text/css"/><link 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class="is-active"><a href>Contextual Variable Types</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/SciML/ModelingToolkit.jl/blob/master/docs/src/basics/ContextualVariables.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Contextual-Variable-Types"><a class="docs-heading-anchor" href="#Contextual-Variable-Types">Contextual Variable Types</a><a id="Contextual-Variable-Types-1"></a><a class="docs-heading-anchor-permalink" href="#Contextual-Variable-Types" title="Permalink"></a></h1><p>ModelingToolkit.jl has a system of contextual variable types which allows for helping the system transformation machinery do complex manipulations and automatic detection. The standard variable definition in ModelingToolkit.jl is the <code>@variable</code> which is defined by <a href="https://github.com/JuliaSymbolics/Symbolics.jl">Symbolics.jl</a>. For example:</p><pre><code class="language-julia hljs">@variables x y(x)</code></pre><p>This is used for the "normal" variable of a given system, like the states of a differential equation or objective function. All of the macros below support the same syntax as <code>@variables</code>.</p><h2 id="Parameters"><a class="docs-heading-anchor" href="#Parameters">Parameters</a><a id="Parameters-1"></a><a class="docs-heading-anchor-permalink" href="#Parameters" title="Permalink"></a></h2><p>All modeling projects have some form of parameters. <code>@parameters</code> marks a variable as being the parameter of some system, which allows automatic detection algorithms to ignore such variables when attempting to find the states of a system.</p><h2 id="Variable-metadata-[Experimental/TODO]"><a class="docs-heading-anchor" href="#Variable-metadata-[Experimental/TODO]">Variable metadata [Experimental/TODO]</a><a id="Variable-metadata-[Experimental/TODO]-1"></a><a class="docs-heading-anchor-permalink" href="#Variable-metadata-[Experimental/TODO]" title="Permalink"></a></h2><p>In many engineering systems some variables act like "flows" while others do not. For example, in circuit models you have current which flows, and the related voltage which does not. Or in thermal models you have heat flows. In these cases, the <code>connect</code> statement enforces conservation of flow between all of the connected components.</p><p>For example, the following specifies that <code>x</code> is a 2x2 matrix of flow variables with the unit m^3/s:</p><pre><code class="language-julia hljs">@variables x[1:2,1:2] [connect = Flow; unit = u"m^3/s"]</code></pre><p>ModelingToolkit defines <code>connect</code>, <code>unit</code>, <code>noise</code>, and <code>description</code> keys for the metadata. One can get and set metadata by</p><pre><code class="language-julia hljs">julia> @variables x [unit = u"m^3/s"];
julia> hasmetadata(x, Symbolics.option_to_metadata_type(Val(:unit)))
true
julia> getmetadata(x, Symbolics.option_to_metadata_type(Val(:unit)))
m³ s⁻¹
julia> x = setmetadata(x, Symbolics.option_to_metadata_type(Val(:unit)), u"m/s")
x
julia> getmetadata(x, Symbolics.option_to_metadata_type(Val(:unit)))
m s⁻¹</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../AbstractSystem/">« The AbstractSystem Interface</a><a class="docs-footer-nextpage" href="../Composition/">Composing Models and Building Reusable Components »</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="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 0.27.6 on <span class="colophon-date" title="Tuesday 14 September 2021 16:27">Tuesday 14 September 2021</span>. Using Julia version 1.6.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>