build based on 172e956

previews/PR144/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-19T07:41:17","documenter_version":"1.7.0"}}
+{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-19T15:01:44","documenter_version":"1.7.0"}}

previews/PR144/generated/StochasticSystem/index.html

@@ -48,10 +48,10 @@
 ode_prob = ODEProblem(nd, uflat(u0), (0.0, 500.0), pflat(p))
 ode_sol = solve(ode_prob, Tsit5())
 
-plot(ode_sol; idxs=vidxs(nd,:,:ω), ylims=(-1.0, 1.0), ylabel=L&quot;\omega&quot;, legend=false, fmt=:png)</code></pre><img src="0665ba92.svg" alt="Example block output"/><p>We see that this is in fact a fixpoint solution. We will later use this as an initial condition for the numerical integration of the SDE system.</p><h2 id="Adding-a-Stochastic-Layer"><a class="docs-heading-anchor" href="#Adding-a-Stochastic-Layer">Adding a Stochastic Layer</a><a id="Adding-a-Stochastic-Layer-1"></a><a class="docs-heading-anchor-permalink" href="#Adding-a-Stochastic-Layer" title="Permalink"></a></h2><p>For adding the stochastic part of the dynamics we have to define a second graph layer. In our example, the fluctuations at different nodes are independent of each other. Therefore, we define a second graph with the same number of vertices but without any edges.</p><pre><code class="language-julia hljs">h = SimpleGraph(4, 0)</code></pre><p>The dynamics at the nodes has to have the same dimension as in the deterministic case. In our example we only have fluctuations in the second variable.</p><pre><code class="language-julia hljs">function fluctuation!(dx, x, edges, p, t)
+plot(ode_sol; idxs=vidxs(nd,:,:ω), ylims=(-1.0, 1.0), ylabel=L&quot;\omega&quot;, legend=false, fmt=:png)</code></pre><img src="aa24c923.svg" alt="Example block output"/><p>We see that this is in fact a fixpoint solution. We will later use this as an initial condition for the numerical integration of the SDE system.</p><h2 id="Adding-a-Stochastic-Layer"><a class="docs-heading-anchor" href="#Adding-a-Stochastic-Layer">Adding a Stochastic Layer</a><a id="Adding-a-Stochastic-Layer-1"></a><a class="docs-heading-anchor-permalink" href="#Adding-a-Stochastic-Layer" title="Permalink"></a></h2><p>For adding the stochastic part of the dynamics we have to define a second graph layer. In our example, the fluctuations at different nodes are independent of each other. Therefore, we define a second graph with the same number of vertices but without any edges.</p><pre><code class="language-julia hljs">h = SimpleGraph(4, 0)</code></pre><p>The dynamics at the nodes has to have the same dimension as in the deterministic case. In our example we only have fluctuations in the second variable.</p><pre><code class="language-julia hljs">function fluctuation!(dx, x, edges, p, t)
     dx[1] = 0.0
     dx[2] = 0.05
 end</code></pre><p>Now we can construct the dynamics of the second layer by using <code>network_dynamics()</code>. Since the graph structure of the stochastic layer has no edges we can take the edge function of the deterministic case as a placeholder.</p><pre><code class="language-julia hljs">fluctuation_vertex = ODEVertex(fluctuation!; dim=2)
 nd_noise = Network(h, fluctuation_vertex, NetworkDynamics.EdgeFunction[])</code></pre><h2 id="Simulating-the-SDE"><a class="docs-heading-anchor" href="#Simulating-the-SDE">Simulating the SDE</a><a id="Simulating-the-SDE-1"></a><a class="docs-heading-anchor-permalink" href="#Simulating-the-SDE" title="Permalink"></a></h2><p>Finally, we can create an <code>SDEProblem</code> and solve it with <code>DifferentialEquations</code>.</p><pre><code class="language-julia hljs">sde_prob = SDEProblem(nd, nd_noise, uflat(u0), (0.0, 500.0), pflat(p))
 sde_sol = solve(sde_prob, SOSRA())
-plot(sde_sol; idxs=vidxs(nd,:,:ω), ylims=(-1.0, 1.0), ylabel=L&quot;\omega&quot;, legend=false, fmt=:png)</code></pre><img src="c3cd3b7b.svg" alt="Example block output"/><p>More details on SDE problems, e.g. how to include correlations or how to define an <code>EnsembleProblem</code>, can be found in the <a href="https://diffeq.sciml.ai/stable/types/sde_types/">documentation</a> of <code>DifferentialEquations</code>.</p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../heterogeneous_system/">« Heterogeneous systems</a><a class="docs-footer-nextpage" href="../cascading_failure/">Cascading failure »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Thursday 19 September 2024 07:41">Thursday 19 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+plot(sde_sol; idxs=vidxs(nd,:,:ω), ylims=(-1.0, 1.0), ylabel=L&quot;\omega&quot;, legend=false, fmt=:png)</code></pre><img src="db4f9e02.svg" alt="Example block output"/><p>More details on SDE problems, e.g. how to include correlations or how to define an <code>EnsembleProblem</code>, can be found in the <a href="https://diffeq.sciml.ai/stable/types/sde_types/">documentation</a> of <code>DifferentialEquations</code>.</p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../heterogeneous_system/">« Heterogeneous systems</a><a class="docs-footer-nextpage" href="../cascading_failure/">Cascading failure »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Thursday 19 September 2024 15:01">Thursday 19 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR144/generated/cascading_failure/index.html

@@ -70,4 +70,4 @@
 Line 4 tripped at t=2.5025231922343427
 Line 1 tripped at t=3.1947647115091087
 Line 3 tripped at t=3.3380530127480017
-Line 2 tripped at t=3.4042696241611816</code></pre><p>Through the magic of symbolic indexing we can plot the power flows on all lines:</p><pre><code class="language-julia hljs">plot(sol; idxs=eidxs(sol,:,:P))</code></pre><img src="8e884ba6.svg" alt="Example block output"/><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../StochasticSystem/">« Stochastic differential equations</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Thursday 19 September 2024 07:40">Thursday 19 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+Line 2 tripped at t=3.4042696241611816</code></pre><p>Through the magic of symbolic indexing we can plot the power flows on all lines:</p><pre><code class="language-julia hljs">plot(sol; idxs=eidxs(sol,:,:P))</code></pre><img src="c5a9ca2f.svg" alt="Example block output"/><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../StochasticSystem/">« Stochastic differential equations</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Thursday 19 September 2024 15:00">Thursday 19 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>