v3.12.0/systems/SDESystem/index.html

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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/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" href="../../tutorials/nonlinear/">Solving Nonlinear Systems with NLsolve</a></li><li><a class="tocitem" href="../../tutorials/modelingtoolkitize/">Symbolic Extensions to ODEProblem via Modelingtoolkize</a></li><li><a class="tocitem" href="../../tutorials/auto_parallel/">Automated Sparse Parallelism of ODEs via Tracing</a></li></ul></li><li><span class="tocitem">Systems</span><ul><li><a class="tocitem" href="../AbstractSystem/">The AbstractSystem Interface</a></li><li><a class="tocitem" href="../ODESystem/">ODESystem</a></li><li class="is-active"><a class="tocitem" href="">SDESystem</a><ul class="internal"><li><a class="tocitem" href="#System-Constructors-1"><span>System Constructors</span></a></li><li><a class="tocitem" href="#Composition-and-Accessor-Functions-1"><span>Composition and Accessor Functions</span></a></li><li><a class="tocitem" href="#Transformations-1"><span>Transformations</span></a></li><li><a class="tocitem" href="#Applicable-Calculation-and-Generation-Functions-1"><span>Applicable Calculation and Generation Functions</span></a></li><li><a class="tocitem" href="#Problem-Constructors-1"><span>Problem Constructors</span></a></li></ul></li><li><a class="tocitem" href="../JumpSystem/">JumpSystem</a></li><li><a class="tocitem" href="../NonlinearSystem/">NonlinearSystem</a></li><li><a class="tocitem" href="../OptimizationSystem/">OptimizationSystem</a></li><li><a class="tocitem" href="../ReactionSystem/">ReactionSystem</a></li><li><a class="tocitem" href="../PDESystem/">PDESystem</a></li><li><a class="tocitem" href="../DependencyGraphs/">Dependency Graphs</a></li></ul></li><li><a class="tocitem" href="../../highlevel/">High Level API</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="">SDESystem</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href="">SDESystem</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/SDESystem.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="SDESystem-1"><a class="docs-heading-anchor" href="#SDESystem-1">SDESystem</a><a class="docs-heading-anchor-permalink" href="#SDESystem-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.SDESystem" id="ModelingToolkit.SDESystem"><code>ModelingToolkit.SDESystem</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">struct SDESystem &lt;: ModelingToolkit.AbstractODESystem</code></pre><p>A system of stochastic differential equations.</p><p><strong>Fields</strong></p><ul><li><p><code>eqs</code></p><p>The expressions defining the drift term.</p></li><li><p><code>noiseeqs</code></p><p>The expressions defining the diffusion term.</p></li><li><p><code>iv</code></p><p>Independent variable.</p></li><li><p><code>states</code></p><p>Dependent (state) variables.</p></li><li><p><code>ps</code></p><p>Parameter variables.</p></li><li><p><code>tgrad</code></p><p>Time-derivative matrix. Note: this field will not be defined until <a href="../AbstractSystem/#ModelingToolkit.calculate_tgrad"><code>calculate_tgrad</code></a> is called on the system.</p></li></ul><ul><li><p><code>jac</code></p><p>Jacobian matrix. Note: this field will not be defined until <a href="../AbstractSystem/#ModelingToolkit.calculate_jacobian"><code>calculate_jacobian</code></a> is called on the system.</p></li></ul><ul><li><p><code>Wfact</code></p><p><code>Wfact</code> matrix. Note: this field will not be defined until <a href="../AbstractSystem/#ModelingToolkit.generate_factorized_W"><code>generate_factorized_W</code></a> is called on the system.</p></li></ul><ul><li><p><code>Wfact_t</code></p><p><code>Wfact_t</code> matrix. Note: this field will not be defined until <a href="../AbstractSystem/#ModelingToolkit.generate_factorized_W"><code>generate_factorized_W</code></a> is called on the system.</p></li></ul><ul><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>Example</strong></p><pre><code class="language-none">using ModelingToolkit

@parameters t σ ρ β
@variables x(t) y(t) z(t)
@derivatives D'~t

eqs = [D(x) ~ σ*(y-x),
       D(y) ~ x*(ρ-z)-y,
       D(z) ~ x*y - β*z]

noiseeqs = [0.1*x,
            0.1*y,
            0.1*z]

de = SDESystem(eqs,noiseeqs,t,[x,y,z],[σ,ρ,β])</code></pre></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/419e6c27c9f42e62a0126acac641dd3edf4b7656/src/systems/diffeqs/sdesystem.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 SDE.</li><li><code>sys.states</code> or <code>states(sys)</code>: The set of states in the SDE.</li><li><code>sys.parameters</code> or <code>parameters(sys)</code>: The parameters of the SDE.</li><li><code>sys.iv</code> or <code>independent_variable(sys)</code>: The independent variable of the SDE.</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
calculate_tgrad
calculate_factorized_W
generate_jacobian
generate_tgrad
generate_factorized_W</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.SDEFunction" id="DiffEqBase.SDEFunction"><code>DiffEqBase.SDEFunction</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">function DiffEqBase.SDEFunction{iip}(sys::SDESystem, dvs = sys.states, ps = sys.ps;
                                     version = nothing, tgrad=false, sparse = false,
                                     jac = false, Wfact = false, kwargs...) where {iip}</code></pre><p>Create an <code>SDEFunction</code> from the <a href="#ModelingToolkit.SDESystem"><code>SDESystem</code></a>. The arguments <code>dvs</code> and <code>ps</code> are used to set the order of the dependent variable and parameter vectors, respectively.</p></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/419e6c27c9f42e62a0126acac641dd3edf4b7656/src/systems/diffeqs/sdesystem.jl#L90-L100" target="_blank">source</a></section></article><article class="docstring"><header><a class="docstring-binding" href="#DiffEqBase.SDEProblem" id="DiffEqBase.SDEProblem"><code>DiffEqBase.SDEProblem</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">function DiffEqBase.SDEProblem{iip}(sys::SDESystem,u0map,tspan,p=parammap;
                                    version = nothing, tgrad=false,
                                    jac = false, Wfact = false,
                                    checkbounds = false, sparse = false,
                                    sparsenoise = sparse,
                                    linenumbers = true, parallel=SerialForm(),
                                    kwargs...)</code></pre><p>Generates an SDEProblem from an SDESystem and allows for automatically symbolically calculating numerical enhancements.</p></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/419e6c27c9f42e62a0126acac641dd3edf4b7656/src/systems/diffeqs/sdesystem.jl#L240-L253" target="_blank">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../ODESystem/">« ODESystem</a><a class="docs-footer-nextpage" href="../JumpSystem/">JumpSystem »</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="Sunday 5 July 2020 20:14">Sunday 5 July 2020</span>. Using Julia version 1.4.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></HTML>