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dev/basics/AbstractSystem/index.html

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dev/basics/DependencyGraphs/index.html

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dev/systems/ControlSystem/index.html

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D(v) ~ u^3
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]
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sys = ControlSystem(loss,eqs,t,[x,v],[u],[])</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/ModelingToolkit.jl/blob/9524fc408911411c307bc518015afd6e35be903e/src/systems/control/controlsystem.jl#L21">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>get_eqs(sys)</code> or <code>equations(sys)</code>: The equations that define the system.</li><li><code>get_states(sys)</code> or <code>states(sys)</code>: The set of states in the system.</li><li><code>get_ps(sys)</code> or <code>parameters(sys)</code>: The parameters of the system.</li><li><code>get_controls(sys)</code> or <code>controls(sys)</code>: The control variables of the 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><article class="docstring"><header><a class="docstring-binding" id="ModelingToolkit.runge_kutta_discretize" href="#ModelingToolkit.runge_kutta_discretize"><code>ModelingToolkit.runge_kutta_discretize</code></a><span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">runge_kutta_discretize(sys::ControlSystem,dt,tspan;
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tab = ModelingToolkit.constructRadauIIA5())</code></pre><p>Transforms a nonlinear optimal control problem into a constrained <code>OptimizationProblem</code> according to a Runge-Kutta tableau that describes a collocation method. Requires a fixed <code>dt</code> over a given <code>timespan</code>. Defaults to using the 5th order RadauIIA tableau, and altnerative tableaus can be specified using the SciML tableau style.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/ModelingToolkit.jl/blob/9524fc408911411c307bc518015afd6e35be903e/src/systems/control/controlsystem.jl#L129-L140">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="ModelingToolkit.structural_simplify" href="#ModelingToolkit.structural_simplify"><code>ModelingToolkit.structural_simplify</code></a><span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">structural_simplify(sys)
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</code></pre><p>Structurally simplify algebraic equations in a system and compute the topological sort of the observed equations.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/ModelingToolkit.jl/blob/9524fc408911411c307bc518015afd6e35be903e/src/systems/abstractsystem.jl#L538">source</a></section></article><h2 id="Analyses-1"><a class="docs-heading-anchor" href="#Analyses-1">Analyses</a><a class="docs-heading-anchor-permalink" href="#Analyses-1" title="Permalink"></a></h2></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../OptimizationSystem/">« OptimizationSystem</a><a class="docs-footer-nextpage" href="../ReactionSystem/">ReactionSystem »</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><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> on <span class="colophon-date" title="Wednesday 21 April 2021 22:29">Wednesday 21 April 2021</span>. Using Julia version 1.6.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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sys = ControlSystem(loss,eqs,t,[x,v],[u],[])</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/ModelingToolkit.jl/blob/d6bb4b65fae7c288e462daa66b47bc2311a2c639/src/systems/control/controlsystem.jl#L21">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>get_eqs(sys)</code> or <code>equations(sys)</code>: The equations that define the system.</li><li><code>get_states(sys)</code> or <code>states(sys)</code>: The set of states in the system.</li><li><code>get_ps(sys)</code> or <code>parameters(sys)</code>: The parameters of the system.</li><li><code>get_controls(sys)</code> or <code>controls(sys)</code>: The control variables of the 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><article class="docstring"><header><a class="docstring-binding" id="ModelingToolkit.runge_kutta_discretize" href="#ModelingToolkit.runge_kutta_discretize"><code>ModelingToolkit.runge_kutta_discretize</code></a><span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">runge_kutta_discretize(sys::ControlSystem,dt,tspan;
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tab = ModelingToolkit.constructRadauIIA5())</code></pre><p>Transforms a nonlinear optimal control problem into a constrained <code>OptimizationProblem</code> according to a Runge-Kutta tableau that describes a collocation method. Requires a fixed <code>dt</code> over a given <code>timespan</code>. Defaults to using the 5th order RadauIIA tableau, and altnerative tableaus can be specified using the SciML tableau style.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/ModelingToolkit.jl/blob/d6bb4b65fae7c288e462daa66b47bc2311a2c639/src/systems/control/controlsystem.jl#L129-L140">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="ModelingToolkit.structural_simplify" href="#ModelingToolkit.structural_simplify"><code>ModelingToolkit.structural_simplify</code></a><span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">structural_simplify(sys)
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</code></pre><p>Structurally simplify algebraic equations in a system and compute the topological sort of the observed equations.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/ModelingToolkit.jl/blob/d6bb4b65fae7c288e462daa66b47bc2311a2c639/src/systems/abstractsystem.jl#L538">source</a></section></article><h2 id="Analyses-1"><a class="docs-heading-anchor" href="#Analyses-1">Analyses</a><a class="docs-heading-anchor-permalink" href="#Analyses-1" title="Permalink"></a></h2></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../OptimizationSystem/">« OptimizationSystem</a><a class="docs-footer-nextpage" href="../ReactionSystem/">ReactionSystem »</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><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> on <span class="colophon-date" title="Wednesday 21 April 2021 22:29">Wednesday 21 April 2021</span>. Using Julia version 1.6.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/systems/JumpSystem/index.html

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j₁ = ConstantRateJump(rate₁,affect₁)
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j₂ = ConstantRateJump(rate₂,affect₂)
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j₃ = MassActionJump(2*β+γ, [R =&gt; 1], [S =&gt; 1, R =&gt; -1])
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js = JumpSystem([j₁,j₂,j₃], t, [S,I,R], [β,γ])</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/ModelingToolkit.jl/blob/9524fc408911411c307bc518015afd6e35be903e/src/systems/jumps/jumpsystem.jl#L3">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>get_eqs(sys)</code> or <code>equations(sys)</code>: The equations that define the jump system.</li><li><code>get_states(sys)</code> or <code>states(sys)</code>: The set of states in the jump system.</li><li><code>get_ps(sys)</code> or <code>parameters(sys)</code>: The parameters of the jump system.</li><li><code>independent_variable(sys)</code>: The independent variable of the jump 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><div class="admonition is-warning"><header class="admonition-header">Missing docstring.</header><div class="admonition-body"><p>Missing docstring for <code>structural_simplify</code>. Check Documenter&#39;s build log for details.</p></div></div><h2 id="Analyses-1"><a class="docs-heading-anchor" href="#Analyses-1">Analyses</a><a class="docs-heading-anchor-permalink" href="#Analyses-1" title="Permalink"></a></h2><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" id="SciMLBase.DiscreteProblem" href="#SciMLBase.DiscreteProblem"><code>SciMLBase.DiscreteProblem</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">function DiffEqBase.DiscreteProblem(sys::JumpSystem, u0map, tspan,
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js = JumpSystem([j₁,j₂,j₃], t, [S,I,R], [β,γ])</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/ModelingToolkit.jl/blob/d6bb4b65fae7c288e462daa66b47bc2311a2c639/src/systems/jumps/jumpsystem.jl#L3">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>get_eqs(sys)</code> or <code>equations(sys)</code>: The equations that define the jump system.</li><li><code>get_states(sys)</code> or <code>states(sys)</code>: The set of states in the jump system.</li><li><code>get_ps(sys)</code> or <code>parameters(sys)</code>: The parameters of the jump system.</li><li><code>independent_variable(sys)</code>: The independent variable of the jump 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><div class="admonition is-warning"><header class="admonition-header">Missing docstring.</header><div class="admonition-body"><p>Missing docstring for <code>structural_simplify</code>. Check Documenter&#39;s build log for details.</p></div></div><h2 id="Analyses-1"><a class="docs-heading-anchor" href="#Analyses-1">Analyses</a><a class="docs-heading-anchor-permalink" href="#Analyses-1" title="Permalink"></a></h2><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" id="SciMLBase.DiscreteProblem" href="#SciMLBase.DiscreteProblem"><code>SciMLBase.DiscreteProblem</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">function DiffEqBase.DiscreteProblem(sys::JumpSystem, u0map, tspan,
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parammap=DiffEqBase.NullParameters; kwargs...)</code></pre><p>Generates a blank DiscreteProblem for a pure jump JumpSystem to utilize as its <code>prob.prob</code>. This is used in the case where there are no ODEs and no SDEs associated with the system.</p><p>Continuing the example from the <a href="#ModelingToolkit.JumpSystem"><code>JumpSystem</code></a> definition:</p><pre><code class="language-julia">using DiffEqBase, DiffEqJump
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u₀map = [S =&gt; 999, I =&gt; 1, R =&gt; 0]
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parammap = [β =&gt; .1/1000, γ =&gt; .01]
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tspan = (0.0, 250.0)
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dprob = DiscreteProblem(js, u₀map, tspan, parammap)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/ModelingToolkit.jl/blob/9524fc408911411c307bc518015afd6e35be903e/src/systems/jumps/jumpsystem.jl#L189-L207">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="DiffEqJump.JumpProblem" href="#DiffEqJump.JumpProblem"><code>DiffEqJump.JumpProblem</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">function DiffEqBase.JumpProblem(js::JumpSystem, prob, aggregator; kwargs...)</code></pre><p>Generates a JumpProblem from a JumpSystem.</p><p>Continuing the example from the <a href="#SciMLBase.DiscreteProblem"><code>DiscreteProblem</code></a> definition:</p><pre><code class="language-julia">jprob = JumpProblem(js, dprob, Direct())
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sol = solve(jprob, SSAStepper())</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/ModelingToolkit.jl/blob/9524fc408911411c307bc518015afd6e35be903e/src/systems/jumps/jumpsystem.jl#L253-L265">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../SDESystem/">« SDESystem</a><a class="docs-footer-nextpage" href="../NonlinearSystem/">NonlinearSystem »</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><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> on <span class="colophon-date" title="Wednesday 21 April 2021 22:29">Wednesday 21 April 2021</span>. Using Julia version 1.6.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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dprob = DiscreteProblem(js, u₀map, tspan, parammap)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/ModelingToolkit.jl/blob/d6bb4b65fae7c288e462daa66b47bc2311a2c639/src/systems/jumps/jumpsystem.jl#L189-L207">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="DiffEqJump.JumpProblem" href="#DiffEqJump.JumpProblem"><code>DiffEqJump.JumpProblem</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">function DiffEqBase.JumpProblem(js::JumpSystem, prob, aggregator; kwargs...)</code></pre><p>Generates a JumpProblem from a JumpSystem.</p><p>Continuing the example from the <a href="#SciMLBase.DiscreteProblem"><code>DiscreteProblem</code></a> definition:</p><pre><code class="language-julia">jprob = JumpProblem(js, dprob, Direct())
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sol = solve(jprob, SSAStepper())</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/SciML/ModelingToolkit.jl/blob/d6bb4b65fae7c288e462daa66b47bc2311a2c639/src/systems/jumps/jumpsystem.jl#L253-L265">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../SDESystem/">« SDESystem</a><a class="docs-footer-nextpage" href="../NonlinearSystem/">NonlinearSystem »</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><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> on <span class="colophon-date" title="Wednesday 21 April 2021 22:29">Wednesday 21 April 2021</span>. Using Julia version 1.6.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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