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</script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img alt="ModelingToolkit.jl logo" src="../../assets/logo.png"/></a><div class="docs-package-name"><span class="docs-autofit">ModelingToolkit.jl</span></div><form action="../../search/" class="docs-search"><input class="docs-search-query" id="documenter-search-query" name="q" placeholder="Search docs" type="text"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><span class="tocitem">Tutorials</span><ul><li><a class="tocitem" href="../../tutorials/symbolic_functions/">Symbolic Calculations and Building Fast Parallel Functions</a></li><li><a class="tocitem" href="../../tutorials/ode_modeling/">Component-Based Modeling with Ordinary Differential Equations</a></li><li><a class="tocitem" href="../../tutorials/higher_order/">Automatic Transformation of Nth Order ODEs to 1st Order ODEs</a></li><li><a class="tocitem" 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href="../../build_function/">Function Building and Compilation (build_function)</a></li><li><a class="tocitem" href="../../IR/">ModelingToolkit IR</a></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"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Systems</a></li><li class="is-active"><a href="">NonlinearSystem</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href="">NonlinearSystem</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/SciML/ModelingToolkit.jl/blob/master/docs/src/systems/NonlinearSystem.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" href="#" id="documenter-settings-button" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" href="#" id="documenter-sidebar-button"></a></div></header><article class="content" id="documenter-page"><h1 id="NonlinearSystem-1"><a class="docs-heading-anchor" href="#NonlinearSystem-1">NonlinearSystem</a><a class="docs-heading-anchor-permalink" href="#NonlinearSystem-1" title="Permalink"></a></h1><h2 id="System-Constructors-1"><a class="docs-heading-anchor" href="#System-Constructors-1">System Constructors</a><a class="docs-heading-anchor-permalink" href="#System-Constructors-1" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" href="#ModelingToolkit.NonlinearSystem" id="ModelingToolkit.NonlinearSystem"><code>ModelingToolkit.NonlinearSystem</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">struct NonlinearSystem <: ModelingToolkit.AbstractSystem</code></pre><p>A nonlinear system of equations.</p><p><strong>Fields</strong></p><ul><li><p><code>eqs</code></p><p>Vector of equations defining the system.</p></li><li><p><code>states</code></p><p>Unknown variables.</p></li><li><p><code>ps</code></p><p>Parameters.</p></li><li><p><code>pins</code></p></li><li><p><code>observed</code></p></li><li><p><code>name</code></p><p>Name: the name of the system</p></li></ul><ul><li><p><code>systems</code></p><p>systems: The internal systems</p></li></ul><p><strong>Examples</strong></p><pre><code class="language-none">@variables x y z
@parameters σ ρ β
eqs = [0 ~ σ*(y-x),
0 ~ x*(ρ-z)-y,
0 ~ x*y - β*z]
ns = NonlinearSystem(eqs, [x,y,z],[σ,ρ,β])</code></pre></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/914d34f911be2eb2ddcee5d5731c5b2877c15bb4/src/systems/nonlinear/nonlinearsystem.jl#L1" target="_blank">source</a></section></article><h2 id="Composition-and-Accessor-Functions-1"><a class="docs-heading-anchor" href="#Composition-and-Accessor-Functions-1">Composition and Accessor Functions</a><a class="docs-heading-anchor-permalink" href="#Composition-and-Accessor-Functions-1" title="Permalink"></a></h2><ul><li><code>sys.eqs</code> or <code>equations(sys)</code>: The equations that define the nonlinear system.</li><li><code>sys.states</code> or <code>states(sys)</code>: The set of states in the nonlinear system.</li><li><code>sys.parameters</code> or <code>parameters(sys)</code>: The parameters of the nonlinear system.</li></ul><h2 id="Transformations-1"><a class="docs-heading-anchor" href="#Transformations-1">Transformations</a><a class="docs-heading-anchor-permalink" href="#Transformations-1" title="Permalink"></a></h2><h2 id="Applicable-Calculation-and-Generation-Functions-1"><a class="docs-heading-anchor" href="#Applicable-Calculation-and-Generation-Functions-1">Applicable Calculation and Generation Functions</a><a class="docs-heading-anchor-permalink" href="#Applicable-Calculation-and-Generation-Functions-1" title="Permalink"></a></h2><pre><code class="language-julia">calculate_jacobian
generate_jacobian
jacobian_sparsity</code></pre><h2 id="Problem-Constructors-1"><a class="docs-heading-anchor" href="#Problem-Constructors-1">Problem Constructors</a><a class="docs-heading-anchor-permalink" href="#Problem-Constructors-1" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" href="#DiffEqBase.NonlinearProblem" id="DiffEqBase.NonlinearProblem"><code>DiffEqBase.NonlinearProblem</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">function DiffEqBase.NonlinearProblem{iip}(sys::NonlinearSystem,u0map,tspan,
parammap=DiffEqBase.NullParameters();
jac = false, sparse=false,
checkbounds = false,
linenumbers = true, parallel=SerialForm(),
kwargs...) where iip</code></pre><p>Generates an NonlinearProblem from a NonlinearSystem and allows for automatically symbolically calculating numerical enhancements.</p></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/914d34f911be2eb2ddcee5d5731c5b2877c15bb4/src/systems/nonlinear/nonlinearsystem.jl#L76-L88" target="_blank">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../JumpSystem/">« JumpSystem</a><a class="docs-footer-nextpage" href="../OptimizationSystem/">OptimizationSystem »</a></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></p><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div><p></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Monday 16 November 2020 20:42">Monday 16 November 2020</span>. Using Julia version 1.4.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></HTML>