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Documenter.jl committed May 29, 2024
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{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-04-08T07:56:53","documenter_version":"1.3.0"}}
{"documenter":{"julia_version":"1.10.3","generation_timestamp":"2024-05-29T04:49:02","documenter_version":"1.4.1"}}
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x_4 + \epsilon_2
\end{bmatrix}
\to
f(\vec{x}_{\epsilon}) = f(\vec{x}) + \frac{\delta f(\vec{x})}{\delta x_3} \epsilon_1 + \frac{\delta f(\vec{x})}{\delta x_4} \epsilon_2\]</p><p>This seeding process is similar for Jacobians, so we won&#39;t rehash it here.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../user/upgrade/">« Upgrading from Older Versions</a><a class="docs-footer-nextpage" href="../contributing/">How to Contribute »</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 1.3.0 on <span class="colophon-date" title="Monday 8 April 2024 07:56">Monday 8 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
f(\vec{x}_{\epsilon}) = f(\vec{x}) + \frac{\delta f(\vec{x})}{\delta x_3} \epsilon_1 + \frac{\delta f(\vec{x})}{\delta x_4} \epsilon_2\]</p><p>This seeding process is similar for Jacobians, so we won&#39;t rehash it here.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../user/upgrade/">« Upgrading from Older Versions</a><a class="docs-footer-nextpage" href="../contributing/">How to Contribute »</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="Wednesday 29 May 2024 04:49">Wednesday 29 May 2024</span>. Using Julia version 1.10.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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end
2×4 Matrix{Float64}:
0.707107 0.0 0.0 0.0
0.0 12.0 8.0 6.0</code></pre><p>If you find ForwardDiff useful in your work, we kindly request that you cite <a href="https://arxiv.org/abs/1607.07892">our paper</a>. The relevant <a href="https://github.com/JuliaDiff/ForwardDiff.jl#publications">BibLaTex is available in ForwardDiff&#39;s README</a> (not included here because BibLaTex doesn&#39;t play nice with Documenter/Jekyll).</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="user/limitations/">Limitations of ForwardDiff »</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 1.3.0 on <span class="colophon-date" title="Monday 8 April 2024 07:56">Monday 8 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
0.0 12.0 8.0 6.0</code></pre><p>If you find ForwardDiff useful in your work, we kindly request that you cite <a href="https://arxiv.org/abs/1607.07892">our paper</a>. The relevant <a href="https://github.com/JuliaDiff/ForwardDiff.jl#publications">BibLaTex is available in ForwardDiff&#39;s README</a> (not included here because BibLaTex doesn&#39;t play nice with Documenter/Jekyll).</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="user/limitations/">Limitations of ForwardDiff »</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="Wednesday 29 May 2024 04:49">Wednesday 29 May 2024</span>. Using Julia version 1.10.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2 changes: 1 addition & 1 deletion dev/user/advanced/index.html
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0 0 0
2 1 0</code></pre><p>Likewise, you could write a version of <code>vector_hessian</code> which supports functions of the form <code>f!(y, x)</code>, or perhaps an in-place Jacobian with <code>ForwardDiff.jacobian!</code>.</p><h2 id="Custom-tags-and-tag-checking"><a class="docs-heading-anchor" href="#Custom-tags-and-tag-checking">Custom tags and tag checking</a><a id="Custom-tags-and-tag-checking-1"></a><a class="docs-heading-anchor-permalink" href="#Custom-tags-and-tag-checking" title="Permalink"></a></h2><p>The <code>Dual</code> type includes a &quot;tag&quot; parameter indicating the particular function call to which it belongs. This is to avoid a problem known as <a href="https://github.com/JuliaDiff/ForwardDiff.jl/issues/83"><em>perturbation confusion</em></a> which can arise when there are nested differentiation calls. Tags are automatically generated as part of the appropriate config object, and the tag is checked when the config is used as part of a differentiation call (<code>derivative</code>, <code>gradient</code>, etc.): an <code>InvalidTagException</code> will be thrown if the incorrect config object is used.</p><p>This checking can sometimes be inconvenient, and there are certain cases where you may want to disable this checking.</p><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p>Disabling tag checking should only be done with caution, especially if the code itself could be used inside another differentiation call.</p></div></div><ol><li><p>(preferred) Provide an extra <code>Val{false}()</code> argument to the differentiation function, e.g.</p><pre><code class="language-julia hljs">cfg = ForwardDiff.GradientConfig(g, x)
ForwardDiff.gradient(f, x, cfg, Val{false}())</code></pre><p>If using as part of a library, the tag can be checked manually via</p><pre><code class="language-julia hljs">ForwardDiff.checktag(cfg, g, x)</code></pre></li><li><p>(discouraged) Construct the config object with <code>nothing</code> instead of a function argument, e.g.</p><pre><code class="language-julia hljs">cfg = GradientConfig(nothing, x)
gradient(f, x, cfg)</code></pre></li></ol></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../api/">« Differentiation API</a><a class="docs-footer-nextpage" href="../upgrade/">Upgrading from Older Versions »</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 1.3.0 on <span class="colophon-date" title="Monday 8 April 2024 07:56">Monday 8 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
gradient(f, x, cfg)</code></pre></li></ol></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../api/">« Differentiation API</a><a class="docs-footer-nextpage" href="../upgrade/">Upgrading from Older Versions »</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="Wednesday 29 May 2024 04:49">Wednesday 29 May 2024</span>. Using Julia version 1.10.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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jf! = ForwardDiff.jacobian(f!, mutates = true, output_length = length(y))

# ForwardDiff v0.2 &amp; above
jf! = (out, y, x) -&gt; ForwardDiff.jacobian!(out, f!, y, x)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../advanced/">« Advanced Usage Guide</a><a class="docs-footer-nextpage" href="../../dev/how_it_works/">How ForwardDiff Works »</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 1.3.0 on <span class="colophon-date" title="Monday 8 April 2024 07:56">Monday 8 April 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
jf! = (out, y, x) -&gt; ForwardDiff.jacobian!(out, f!, y, x)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../advanced/">« Advanced Usage Guide</a><a class="docs-footer-nextpage" href="../../dev/how_it_works/">How ForwardDiff Works »</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="Wednesday 29 May 2024 04:49">Wednesday 29 May 2024</span>. Using Julia version 1.10.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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