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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><a class="tocitem" href="../../highlevel/">High Level API</a></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><a class="tocitem" href="../SDESystem/">SDESystem</a></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 class="is-active"><a class="tocitem" href="">Dependency Graphs</a><ul class="internal"><li class="toplevel"><a class="tocitem" href="#Types-1"><span>Types</span></a></li><li class="toplevel"><a class="tocitem" href="#Utility-functions-for-BiPartiteGraphs-1"><span>Utility functions for <code>BiPartiteGraph</code>s</span></a></li><li class="toplevel"><a class="tocitem" href="#Functions-for-calculating-dependency-graphs-1"><span>Functions for calculating dependency graphs</span></a></li></ul></li></ul></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="">Dependency Graphs</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href="">Dependency Graphs</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/DependencyGraphs.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="Dependency-Graphs-1"><a class="docs-heading-anchor" href="#Dependency-Graphs-1">Dependency Graphs</a><a class="docs-heading-anchor-permalink" href="#Dependency-Graphs-1" title="Permalink"></a></h1><h1 id="Types-1"><a class="docs-heading-anchor" href="#Types-1">Types</a><a class="docs-heading-anchor-permalink" href="#Types-1" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-binding" href="#ModelingToolkit.BipartiteGraph" id="ModelingToolkit.BipartiteGraph"><code>ModelingToolkit.BipartiteGraph</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">mutable struct BipartiteGraph{T<:Integer}</code></pre><p>A bipartite graph representation between two, possibly distinct, sets of vertices (source and dependencies). Maps source vertices, labelled <code>1:N₁</code>, to vertices on which they depend (labelled <code>1:N₂</code>).</p><p><strong>Fields</strong></p><ul><li><p><code>ne</code></p><p>Number of edges from source vertices to vertices they depend on.</p></li><li><p><code>fadjlist</code></p><p>Forward adjacency list mapping index of source vertices to the vertices they depend on.</p></li><li><p><code>badjlist</code></p><p>Backward adjacency list mapping index of vertices that are dependencies to the source vertices that depend on them.</p></li></ul><p><strong>Example</strong></p><pre><code class="language-julia">using ModelingToolkit
ne = 4
srcverts = 1:4
depverts = 1:2
# six source vertices
fadjlist = [[1],[1],[2],[2],[1],[1,2]]
# two vertices they depend on
badjlist = [[1,2,5,6],[3,4,6]]
bg = BipartiteGraph(7, fadjlist, badjlist)</code></pre></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/5ca00a77599dab91f70e52959d0495713a42413c/src/systems/dependency_graphs.jl#L58" target="_blank">source</a></section></article><h1 id="Utility-functions-for-BiPartiteGraphs-1"><a class="docs-heading-anchor" href="#Utility-functions-for-BiPartiteGraphs-1">Utility functions for <code>BiPartiteGraph</code>s</a><a class="docs-heading-anchor-permalink" href="#Utility-functions-for-BiPartiteGraphs-1" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-binding" href="#Base.isequal" id="Base.isequal"><code>Base.isequal</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">Base.isequal(bg1::BipartiteGraph{T}, bg2::BipartiteGraph{T}) where {T<:Integer} </code></pre><p>Test whether two <a href="#ModelingToolkit.BipartiteGraph"><code>BipartiteGraph</code></a>s are equal.</p></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/5ca00a77599dab91f70e52959d0495713a42413c/src/systems/dependency_graphs.jl#L94-L100" target="_blank">source</a></section></article><h1 id="Functions-for-calculating-dependency-graphs-1"><a class="docs-heading-anchor" href="#Functions-for-calculating-dependency-graphs-1">Functions for calculating dependency graphs</a><a class="docs-heading-anchor-permalink" href="#Functions-for-calculating-dependency-graphs-1" title="Permalink"></a></h1><article class="docstring"><header><a class="docstring-binding" href="#ModelingToolkit.equation_dependencies" id="ModelingToolkit.equation_dependencies"><code>ModelingToolkit.equation_dependencies</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">equation_dependencies(sys::AbstractSystem; variables=states(sys))</code></pre><p>Given an <code>AbstractSystem</code> calculate for each equation the variables it depends on. </p><p>Notes:</p><ul><li>Variables that are not in <code>variables</code> are filtered out.</li><li><code>get_variables!</code> is used to determine the variables within a given equation. </li><li>returns a <code>Vector{Vector{Variable}}()</code> mapping the index of an equation to the <code>variables</code> it depends on.</li></ul><p>Example:</p><pre><code class="language-julia">using ModelingToolkit
@parameters β γ κ η t
@variables S(t) I(t) R(t)
# use a reaction system to easily generate ODE and jump systems
rxs = [Reaction(β, [S,I], [I], [1,1], [2]),
Reaction(γ, [I], [R]),
Reaction(κ+η, [R], [S])]
rs = ReactionSystem(rxs, t, [S,I,R], [β,γ,κ,η])
# ODEs:
odesys = convert(ODESystem, rs)
# dependency of each ODE on state variables
equation_dependencies(odesys)
# dependency of each ODE on parameters
equation_dependencies(odesys, variables=parameters(odesys))
# Jumps
jumpsys = convert(JumpSystem, rs)
# dependency of each jump rate function on state variables
equation_dependencies(jumpsys)
# dependency of each jump rate function on parameters
equation_dependencies(jumpsys, variables=parameters(jumpsys)) </code></pre></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/5ca00a77599dab91f70e52959d0495713a42413c/src/systems/dependency_graphs.jl#L1-L43" target="_blank">source</a></section></article><article class="docstring"><header><a class="docstring-binding" href="#ModelingToolkit.asgraph" id="ModelingToolkit.asgraph"><code>ModelingToolkit.asgraph</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">asgraph(eqdeps, vtois) </code></pre><p>Convert a collection of equation dependencies, for example as returned by <code>equation_dependencies</code>, to a <a href="#ModelingToolkit.BipartiteGraph"><code>BipartiteGraph</code></a>.</p><p>Notes:</p><ul><li><code>vtois</code> should provide a <code>Dict</code> like mapping from each <code>Variable</code> dependency in <code>eqdeps</code> to the integer idx of the variable to use in the graph.</li></ul><p>Example: Continuing the example started in <a href="#ModelingToolkit.equation_dependencies"><code>equation_dependencies</code></a></p><pre><code class="language-julia">digr = asgraph(equation_dependencies(odesys), Dict(s => i for (i,s) in enumerate(states(odesys))))</code></pre></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/5ca00a77599dab91f70e52959d0495713a42413c/src/systems/dependency_graphs.jl#L108-L125" target="_blank">source</a></section><section><div><pre><code class="language-julia">asgraph(sys::AbstractSystem; variables=states(sys),
variablestoids=Dict(convert(Variable, v) => i for (i,v) in enumerate(variables)))</code></pre><p>Convert an <code>AbstractSystem</code> to a <a href="#ModelingToolkit.BipartiteGraph"><code>BipartiteGraph</code></a> mapping the index of equations to the indices of variables they depend on.</p><p>Notes:</p><ul><li>Defaults for kwargs creating a mapping from <code>equations(sys)</code> to <code>states(sys)</code> they depend on.</li><li><code>variables</code> should provide the list of variables to use for generating the dependency graph.</li><li><code>variablestoids</code> should provide <code>Dict</code> like mapping from a <code>Variable</code> to its <code>Int</code> index within <code>variables</code>.</li></ul><p>Example: Continuing the example started in <a href="#ModelingToolkit.equation_dependencies"><code>equation_dependencies</code></a></p><pre><code class="language-julia">digr = asgraph(odesys)</code></pre></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/5ca00a77599dab91f70e52959d0495713a42413c/src/systems/dependency_graphs.jl#L144-L166" target="_blank">source</a></section></article><article class="docstring"><header><a class="docstring-binding" href="#ModelingToolkit.variable_dependencies" id="ModelingToolkit.variable_dependencies"><code>ModelingToolkit.variable_dependencies</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">variable_dependencies(sys::AbstractSystem; variables=states(sys), variablestoids=nothing)</code></pre><p>For each variable determine the equations that modify it and return as a <a href="#ModelingToolkit.BipartiteGraph"><code>BipartiteGraph</code></a>.</p><p>Notes:</p><ul><li>Dependencies are returned as a <a href="#ModelingToolkit.BipartiteGraph"><code>BipartiteGraph</code></a> mapping variable indices to the indices of equations that modify them.</li><li><code>variables</code> denotes the list of variables to determine dependencies for.</li><li><code>variablestoids</code> denotes a <code>Dict</code> mapping <code>Variable</code>s to their <code>Int</code> index in <code>variables</code>.</li></ul><p>Example: Continuing the example of <a href="#ModelingToolkit.equation_dependencies"><code>equation_dependencies</code></a></p><pre><code class="language-julia">variable_dependencies(odesys)</code></pre></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/5ca00a77599dab91f70e52959d0495713a42413c/src/systems/dependency_graphs.jl#L172-L190" target="_blank">source</a></section></article><article class="docstring"><header><a class="docstring-binding" href="#ModelingToolkit.asdigraph" id="ModelingToolkit.asdigraph"><code>ModelingToolkit.asdigraph</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">asdigraph(g::BipartiteGraph, sys::AbstractSystem; variables = states(sys), equationsfirst = true)</code></pre><p>Convert a <a href="#ModelingToolkit.BipartiteGraph"><code>BipartiteGraph</code></a> to a <code>LightGraph.SimpleDiGraph</code>.</p><p>Notes:</p><ul><li>The resulting <code>SimpleDiGraph</code> unifies the two sets of vertices (equations and then states in the case it comes from <a href="#ModelingToolkit.asgraph"><code>asgraph</code></a>), producing one ordered set of integer vertices (<code>SimpleDiGraph</code> does not support two distinct collections of vertices so they must be merged).</li><li><code>variables</code> gives the variables that <code>g</code> is associated with (usually the <code>states</code> of a system).</li><li><code>equationsfirst</code> (default is <code>true</code>) gives whether the <a href="#ModelingToolkit.BipartiteGraph"><code>BipartiteGraph</code></a> gives a mapping from equations to variables they depend on (<code>true</code>), as calculated by <a href="#ModelingToolkit.asgraph"><code>asgraph</code></a>, or whether it gives a mapping from variables to the equations that modify them, as calculated by <a href="#ModelingToolkit.variable_dependencies"><code>variable_dependencies</code></a>.</li></ul><p>Example: Continuing the example in <a href="#ModelingToolkit.asgraph"><code>asgraph</code></a></p><pre><code class="language-julia">dg = asdigraph(digr)</code></pre></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/5ca00a77599dab91f70e52959d0495713a42413c/src/systems/dependency_graphs.jl#L213-L237" target="_blank">source</a></section></article><article class="docstring"><header><a class="docstring-binding" href="#ModelingToolkit.eqeq_dependencies" id="ModelingToolkit.eqeq_dependencies"><code>ModelingToolkit.eqeq_dependencies</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">eqeq_dependencies(eqdeps::BipartiteGraph{T}, vardeps::BipartiteGraph{T}) where {T <: Integer}</code></pre><p>Calculate a <code>LightGraph.SimpleDiGraph</code> that maps each equation to equations they depend on.</p><p>Notes:</p><ul><li>The <code>fadjlist</code> of the <code>SimpleDiGraph</code> maps from an equation to the equations that modify variables it depends on.</li><li>The <code>badjlist</code> of the <code>SimpleDiGraph</code> maps from an equation to equations that depend on variables it modifies.</li></ul><p>Example: Continuing the example of <code>equation_dependencies</code></p><pre><code class="language-julia">eqeqdep = eqeq_dependencies(asgraph(odesys), variable_dependencies(odesys))</code></pre></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/5ca00a77599dab91f70e52959d0495713a42413c/src/systems/dependency_graphs.jl#L257-L275" target="_blank">source</a></section></article><article class="docstring"><header><a class="docstring-binding" href="#ModelingToolkit.varvar_dependencies" id="ModelingToolkit.varvar_dependencies"><code>ModelingToolkit.varvar_dependencies</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">varvar_dependencies(eqdeps::BipartiteGraph{T}, vardeps::BipartiteGraph{T}) where {T <: Integer} = eqeq_dependencies(vardeps, eqdeps)</code></pre><p>Calculate a <code>LightGraph.SimpleDiGraph</code> that maps each variable to variables they depend on.</p><p>Notes:</p><ul><li>The <code>fadjlist</code> of the <code>SimpleDiGraph</code> maps from a variable to the variables that depend on it.</li><li>The <code>badjlist</code> of the <code>SimpleDiGraph</code> maps from a variable to variables on which it depends.</li></ul><p>Example: Continuing the example of <code>equation_dependencies</code></p><pre><code class="language-julia">varvardep = varvar_dependencies(asgraph(odesys), variable_dependencies(odesys))</code></pre></div><a class="docs-sourcelink" href="https://github.com/SciML/ModelingToolkit.jl/blob/5ca00a77599dab91f70e52959d0495713a42413c/src/systems/dependency_graphs.jl#L290-L308" target="_blank">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../PDESystem/">« PDESystem</a><a class="docs-footer-nextpage" href="../../IR/">ModelingToolkit IR »</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 14 June 2020 19:17">Sunday 14 June 2020</span>. 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