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Documenter.jl committed Jun 15, 2024
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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-06-14T15:19:54","documenter_version":"1.4.1"}}
{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-06-15T07:54:22","documenter_version":"1.4.1"}}
18 changes: 9 additions & 9 deletions dev/ad/index.html
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@assert ForwardDiff.partials(f_df, 1) ≈ D * v # the Jacobian of `f(u) = D * u` is `D`</code></pre><p>You can of course also use this with nonlinear functions, e.g.,</p><pre><code class="language-julia hljs">f(u, D) = u .* (D * (u.^2))

f_df = f(u_v, D)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">8-element StructArray(::Vector{Float64}, ::Vector{ForwardDiff.Partials{1, Float64}}) with eltype ForwardDiff.Dual{Nothing, Float64, 1}:
Dual{Nothing}(-1.0803574671683276,5.352332694973359)
Dual{Nothing}(0.9834603055010078,-0.52978595264932)
Dual{Nothing}(-0.9147808707906251,1.658525901851851)
Dual{Nothing}(0.3968332383135114,-11.836379590271717)
Dual{Nothing}(-2.3521922204436465,25.76026066601995)
Dual{Nothing}(-5.931592247894148,21.39488977054527)
Dual{Nothing}(1.0805319966370046,12.93213364958514)
Dual{Nothing}(0.9483238461186805,-0.008488662503189026)</code></pre><p>The Jacobian of this function is</p><pre><code class="language-julia hljs">using LinearAlgebra
Dual{Nothing}(-2.0174635835440364,22.78426994458202)
Dual{Nothing}(2.4364628987677626,-4.313615546965806)
Dual{Nothing}(0.22493882348332112,-0.13870945296816908)
Dual{Nothing}(1.3627368661763686,0.30298875025384164)
Dual{Nothing}(2.1354470671506967,3.441255173270508)
Dual{Nothing}(35.84303314872701,-39.936257549827154)
Dual{Nothing}(5.8326757290263105,-20.12437446575593)
Dual{Nothing}(26.336261611466,-20.694379426259594)</code></pre><p>The Jacobian of this function is</p><pre><code class="language-julia hljs">using LinearAlgebra

J = Diagonal(D * u.^2) + 2 .* u .* Matrix(D) * Diagonal(u)

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<span class="sgr32"><span class="sgr1"> Status</span></span> `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl/docs/Manifest.toml`
<span class="sgr90"> [f6369f11] </span>ForwardDiff v0.10.36
<span class="sgr90"> [09ab397b] </span>StructArrays v0.6.18
<span class="sgr90"> [9f78cca6] </span>SummationByPartsOperators v0.5.61 `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl`</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tutorials/kdv/">« Korteweg-de Vries equation</a><a class="docs-footer-nextpage" href="../applications/">Applications &amp; references »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Friday 14 June 2024 15:19">Friday 14 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<span class="sgr90"> [9f78cca6] </span>SummationByPartsOperators v0.5.62 `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl`</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tutorials/kdv/">« Korteweg-de Vries equation</a><a class="docs-footer-nextpage" href="../applications/">Applications &amp; references »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Saturday 15 June 2024 07:54">Saturday 15 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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