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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="../symbolic_functions/">Symbolic Calculations and Building Fast Parallel Functions</a></li><li><a class="tocitem" href="../ode_modeling/">Component-Based Modeling with Ordinary Differential Equations</a></li><li><a class="tocitem" href="../higher_order/">Automatic Transformation of Nth Order ODEs to 1st Order ODEs</a></li><li><a class="tocitem" href="../nonlinear/">Solving Nonlinear Systems with NLsolve</a></li><li class="is-active"><a class="tocitem" href="">Symbolic Extensions to ODEProblem via Modelingtoolkize</a></li><li><a class="tocitem" href="../auto_parallel/">Automated Sparse Parallelism of ODEs via Tracing</a></li><li><a class="tocitem" href="../converting_to_C/">Automatic Conversion of Julia Code to C Functions</a></li></ul></li><li><span class="tocitem">Systems</span><ul><li><a class="tocitem" href="../../systems/AbstractSystem/">The AbstractSystem Interface</a></li><li><a class="tocitem" href="../../systems/ODESystem/">ODESystem</a></li><li><a class="tocitem" href="../../systems/SDESystem/">SDESystem</a></li><li><a class="tocitem" href="../../systems/JumpSystem/">JumpSystem</a></li><li><a class="tocitem" href="../../systems/NonlinearSystem/">NonlinearSystem</a></li><li><a class="tocitem" href="../../systems/OptimizationSystem/">OptimizationSystem</a></li><li><a class="tocitem" href="../../systems/ControlSystem/">ControlSystem</a></li><li><a class="tocitem" href="../../systems/ReactionSystem/">ReactionSystem</a></li><li><a class="tocitem" href="../../systems/PDESystem/">PDESystem</a></li><li><a class="tocitem" href="../../systems/DependencyGraphs/">Dependency Graphs</a></li></ul></li><li><a class="tocitem" href="../../comparison/">Comparison Against SymPy</a></li><li><a class="tocitem" href="../../highlevel/">High Level API</a></li><li><a class="tocitem" 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">Tutorials</a></li><li class="is-active"><a href="">Symbolic Extensions to ODEProblem via Modelingtoolkize</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href="">Symbolic Extensions to ODEProblem via Modelingtoolkize</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/SciML/ModelingToolkit.jl/blob/master/docs/src/tutorials/modelingtoolkitize.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="Symbolic-Extensions-to-ODEProblem-via-Modelingtoolkize-1"><a class="docs-heading-anchor" href="#Symbolic-Extensions-to-ODEProblem-via-Modelingtoolkize-1">Symbolic Extensions to ODEProblem via Modelingtoolkize</a><a class="docs-heading-anchor-permalink" href="#Symbolic-Extensions-to-ODEProblem-via-Modelingtoolkize-1" title="Permalink"></a></h1><p>For some <code>DEProblem</code> types, automatic tracing functionality is already included via the <code>modelingtoolkitize</code> function. Take, for example, the Robertson ODE defined as an <code>ODEProblem</code> for DifferentialEquations.jl:</p><pre><code class="language-julia">using DifferentialEquations
function rober(du,u,p,t)
y₁,y₂,y₃ = u
k₁,k₂,k₃ = p
du[1] = -k₁*y₁+k₃*y₂*y₃
du[2] = k₁*y₁-k₂*y₂^2-k₃*y₂*y₃
du[3] = k₂*y₂^2
nothing
end
prob = ODEProblem(rober,[1.0,0.0,0.0],(0.0,1e5),(0.04,3e7,1e4))</code></pre><p>If we want to get a symbolic representation, we can simply call <code>modelingtoolkitize</code> on the <code>prob</code>, which will return an <code>ODESystem</code>:</p><pre><code class="language-julia">sys = modelingtoolkitize(prob)</code></pre><p>Using this, we can symbolically build the Jacobian and then rebuild the ODEProblem:</p><pre><code class="language-julia">jac = eval(ModelingToolkit.generate_jacobian(sys)[2])
f = ODEFunction(rober, jac=jac)
prob_jac = ODEProblem(f,[1.0,0.0,0.0],(0.0,1e5),(0.04,3e7,1e4))</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../nonlinear/">« Solving Nonlinear Systems with NLsolve</a><a class="docs-footer-nextpage" href="../auto_parallel/">Automated Sparse Parallelism of ODEs via Tracing »</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="Tuesday 1 September 2020 00:37">Tuesday 1 September 2020</span>. Using Julia version 1.4.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></HTML>