build based on beb7d80

dev/getting_started/find_root/index.html

@@ -73,4 +73,4 @@
  0.0
  0.0
  0.0</code></pre><h3 id="Step-5:-Analyze-the-Solution"><a class="docs-heading-anchor" href="#Step-5:-Analyze-the-Solution">Step 5: Analyze the Solution</a><a id="Step-5:-Analyze-the-Solution-1"></a><a class="docs-heading-anchor-permalink" href="#Step-5:-Analyze-the-Solution" title="Permalink"></a></h3><p>Now let&#39;s check out the solution. First of all, what kind of thing is the <code>sol</code>? We can see that by asking for its type:</p><pre><code class="language-julia hljs">typeof(sol)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">SciMLBase.NonlinearSolution{Float64, 1, Vector{Float64}, Vector{Float64}, SciMLBase.NonlinearProblem{Vector{Float64}, true, Vector{Float64}, SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, ModelingToolkit.var&quot;#f#725&quot;{RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋arg1, :ˍ₋arg2), ModelingToolkit.var&quot;#_RGF_ModTag&quot;, ModelingToolkit.var&quot;#_RGF_ModTag&quot;, (0x5f262905, 0x6044fdaf, 0x31be506b, 0x8fdff074, 0xa598b4b2), Nothing}, RuntimeGeneratedFunctions.RuntimeGeneratedFunction{(:ˍ₋out, :ˍ₋arg1, :ˍ₋arg2), ModelingToolkit.var&quot;#_RGF_ModTag&quot;, ModelingToolkit.var&quot;#_RGF_ModTag&quot;, (0xe94c9773, 0x427c8b16, 0x6db1219f, 0x162087b8, 0x6836ee13), Nothing}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Vector{Symbol}, Vector{Symbol}, ModelingToolkit.var&quot;#generated_observed#728&quot;{ModelingToolkit.NonlinearSystem, Dict{Any, Any}}, Nothing, ModelingToolkit.NonlinearSystem}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardNonlinearProblem}, NonlinearSolve.NewtonRaphson{0, true, Val{:forward}, Nothing, typeof(NonlinearSolve.DEFAULT_PRECS), true, nothing}, Nothing, Nothing, SciMLBase.NLStats}</code></pre><p>From this, we can see that it is an <code>NonlinearSolution</code>. We can see the documentation for how to use the <code>NonlinearSolution</code> by checking the <a href="https://docs.sciml.ai/NonlinearSolve/stable/basics/NonlinearSolution/">NonlinearSolve.jl solution type page.</a> For example, the solution is stored as <code>.u</code>. What is the solution to our nonlinear system, and what is the final residual value? We can check it as follows:</p><pre><code class="language-julia hljs"># Analyze the solution
-@show sol.u, sol.resid</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">([0.0, 0.0, 0.0], [0.0, 0.0, 0.0])</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../fit_simulation/">« Fit a simulation to a dataset</a><a class="docs-footer-nextpage" href="../../comparisons/python/">Getting Started with Julia&#39;s SciML for the Python User »</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="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> version 0.27.25 on <span class="colophon-date" title="Wednesday 16 August 2023 22:41">Wednesday 16 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+@show sol.u, sol.resid</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">([0.0, 0.0, 0.0], [0.0, 0.0, 0.0])</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../fit_simulation/">« Fit a simulation to a dataset</a><a class="docs-footer-nextpage" href="../../comparisons/python/">Getting Started with Julia&#39;s SciML for the Python User »</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="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> version 0.27.25 on <span class="colophon-date" title="Thursday 17 August 2023 01:40">Thursday 17 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/getting_started/first_optimization/index.html

@@ -32,4 +32,4 @@
 sol = solve(prob, NLopt.LD_LBFGS())</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">u: 2-element Vector{Float64}:
  1.0
  1.0</code></pre><h3 id="Step-4:-Analyze-the-Solution"><a class="docs-heading-anchor" href="#Step-4:-Analyze-the-Solution">Step 4: Analyze the Solution</a><a id="Step-4:-Analyze-the-Solution-1"></a><a class="docs-heading-anchor-permalink" href="#Step-4:-Analyze-the-Solution" title="Permalink"></a></h3><p>Now let&#39;s check out the solution. First of all, what kind of thing is the <code>sol</code>? We can see that by asking for its type:</p><pre><code class="language-julia hljs">typeof(sol)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">SciMLBase.OptimizationSolution{Float64, 1, Vector{Float64}, OptimizationNLopt.NLoptOptimizationCache{SciMLBase.OptimizationFunction{true, Optimization.AutoForwardDiff{nothing}, typeof(Main.L), Optimization.var&quot;#176#193&quot;{ForwardDiff.GradientConfig{ForwardDiff.Tag{Optimization.var&quot;#175#192&quot;{SciMLBase.OptimizationFunction{true, Optimization.AutoForwardDiff{nothing}, typeof(Main.L), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}, Optimization.ReInitCache{Vector{Float64}, Vector{Float64}}}, Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Optimization.var&quot;#175#192&quot;{SciMLBase.OptimizationFunction{true, Optimization.AutoForwardDiff{nothing}, typeof(Main.L), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}, Optimization.ReInitCache{Vector{Float64}, Vector{Float64}}}, Float64}, Float64, 2}}}, Optimization.var&quot;#175#192&quot;{SciMLBase.OptimizationFunction{true, Optimization.AutoForwardDiff{nothing}, typeof(Main.L), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}, Optimization.ReInitCache{Vector{Float64}, Vector{Float64}}}}, Optimization.var&quot;#179#196&quot;{ForwardDiff.HessianConfig{ForwardDiff.Tag{Optimization.var&quot;#175#192&quot;{SciMLBase.OptimizationFunction{true, Optimization.AutoForwardDiff{nothing}, typeof(Main.L), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}, Optimization.ReInitCache{Vector{Float64}, Vector{Float64}}}, Float64}, Float64, 2, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Optimization.var&quot;#175#192&quot;{SciMLBase.OptimizationFunction{true, Optimization.AutoForwardDiff{nothing}, typeof(Main.L), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}, Optimization.ReInitCache{Vector{Float64}, Vector{Float64}}}, Float64}, ForwardDiff.Dual{ForwardDiff.Tag{Optimization.var&quot;#175#192&quot;{SciMLBase.OptimizationFunction{true, Optimization.AutoForwardDiff{nothing}, typeof(Main.L), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}, Optimization.ReInitCache{Vector{Float64}, Vector{Float64}}}, Float64}, Float64, 2}, 2}}, Vector{ForwardDiff.Dual{ForwardDiff.Tag{Optimization.var&quot;#175#192&quot;{SciMLBase.OptimizationFunction{true, Optimization.AutoForwardDiff{nothing}, typeof(Main.L), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}, Optimization.ReInitCache{Vector{Float64}, Vector{Float64}}}, Float64}, Float64, 2}}}, Optimization.var&quot;#175#192&quot;{SciMLBase.OptimizationFunction{true, Optimization.AutoForwardDiff{nothing}, typeof(Main.L), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}, Optimization.ReInitCache{Vector{Float64}, Vector{Float64}}}}, Optimization.var&quot;#182#199&quot;, Nothing, Optimization.var&quot;#186#203&quot;{SciMLBase.OptimizationFunction{true, Optimization.AutoForwardDiff{nothing}, typeof(Main.L), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}, Optimization.ReInitCache{Vector{Float64}, Vector{Float64}}}, Optimization.var&quot;#191#208&quot;{SciMLBase.OptimizationFunction{true, Optimization.AutoForwardDiff{nothing}, typeof(Main.L), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}, Optimization.ReInitCache{Vector{Float64}, Vector{Float64}}}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing}, Optimization.ReInitCache{Vector{Float64}, Vector{Float64}}, Vector{Float64}, Vector{Float64}, Nothing, NLopt.Algorithm, Bool}, NLopt.Algorithm, Float64, NLopt.Opt, Float64, Nothing}</code></pre><p>From this, we can see that it is an <code>OptimizationSolution</code>. We can see the documentation for how to use the <code>OptimizationSolution</code> by checking the <a href="https://docs.sciml.ai/Optimization/stable/API/optimization_solution/">Optimization.jl solution type page</a>. For example, the solution is stored as <code>.u</code>. What is the solution to our optimization, and what is the final loss value? We can check it as follows:</p><pre><code class="language-julia hljs"># Analyze the solution
-@show sol.u, L(sol.u, p)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">([1.0, 1.0], 0.0)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../first_simulation/">« Build and run your first simulation with Julia&#39;s SciML</a><a class="docs-footer-nextpage" href="../fit_simulation/">Fit a simulation to a dataset »</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="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> version 0.27.25 on <span class="colophon-date" title="Wednesday 16 August 2023 22:41">Wednesday 16 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+@show sol.u, L(sol.u, p)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">([1.0, 1.0], 0.0)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../first_simulation/">« Build and run your first simulation with Julia&#39;s SciML</a><a class="docs-footer-nextpage" href="../fit_simulation/">Fit a simulation to a dataset »</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="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> version 0.27.25 on <span class="colophon-date" title="Thursday 17 August 2023 01:40">Thursday 17 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>