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dev/.documenter-siteinfo.json

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{"documenter":{"julia_version":"1.11.6","generation_timestamp":"2025-08-18T02:54:44","documenter_version":"1.14.1"}}
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{"documenter":{"julia_version":"1.11.6","generation_timestamp":"2025-08-18T15:41:53","documenter_version":"1.14.1"}}

dev/dev/contributing/index.html

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dev/dev/how_it_works/index.html

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x_4 + \epsilon_2
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\end{bmatrix}
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\to
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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><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 1.14.1 on <span class="colophon-date" title="Monday 18 August 2025 02:54">Monday 18 August 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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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><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 1.14.1 on <span class="colophon-date" title="Monday 18 August 2025 15:41">Monday 18 August 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/index.html

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end
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2×4 Matrix{Float64}:
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0.707107 0.0 0.0 0.0
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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><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 1.14.1 on <span class="colophon-date" title="Monday 18 August 2025 02:54">Monday 18 August 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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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><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 1.14.1 on <span class="colophon-date" title="Monday 18 August 2025 15:41">Monday 18 August 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/search_index.js

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dev/user/advanced/index.html

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julia&gt; cfg = ForwardDiff.GradientConfig(rosenbrock, x);
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julia&gt; @time ForwardDiff.gradient!(out, rosenbrock, x, cfg);
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0.281853 seconds (4 allocations: 160 bytes)</code></pre><p>The underlying heuristic will compute a suitable chunk size smaller or equal to the <code>ForwardDiff.DEFAULT_CHUNK_THRESHOLD</code> constant. As of ForwardDiff v0.10.32 and Julia 1.6, this constant can be configured at load time via <a href="https://github.com/JuliaPackaging/Preferences.jl">Preferences.jl</a> by setting the <code>default_chunk_threshold</code> value.</p><p>If your input dimension is constant across calls, you should explicitly select a chunk size rather than relying on ForwardDiff&#39;s heuristic. There are two reasons for this. The first is that ForwardDiff&#39;s heuristic depends only on the input dimension, whereas in reality the optimal chunk size will also depend on the target function. The second is that ForwardDiff&#39;s heuristic is inherently type-unstable, which can cause the entire call to be type-unstable.</p><p>If your input dimension is a runtime variable, you can rely on ForwardDiff&#39;s heuristic without sacrificing type stability by manually asserting the output type, or - even better - by using the in-place API functions:</p><pre><code class="language-julia hljs"># will be type-stable since you&#39;re asserting the output type
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0.281853 seconds (4 allocations: 160 bytes)</code></pre><p>The underlying heuristic will compute a suitable chunk size smaller or equal to the <code>ForwardDiff.DEFAULT_CHUNK_THRESHOLD</code> constant. This constant can be configured at load time via <a href="https://github.com/JuliaPackaging/Preferences.jl">Preferences.jl</a> by setting the <code>default_chunk_threshold</code> value.</p><p>If your input dimension is constant across calls, you should explicitly select a chunk size rather than relying on ForwardDiff&#39;s heuristic. There are two reasons for this. The first is that ForwardDiff&#39;s heuristic depends only on the input dimension, whereas in reality the optimal chunk size will also depend on the target function. The second is that ForwardDiff&#39;s heuristic is inherently type-unstable, which can cause the entire call to be type-unstable.</p><p>If your input dimension is a runtime variable, you can rely on ForwardDiff&#39;s heuristic without sacrificing type stability by manually asserting the output type, or - even better - by using the in-place API functions:</p><pre><code class="language-julia hljs"># will be type-stable since you&#39;re asserting the output type
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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" id="Warning-3eb05abadd191f82"><header class="admonition-header">Warning<a class="admonition-anchor" href="#Warning-3eb05abadd191f82" title="Permalink"></a></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)
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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)
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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><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 1.14.1 on <span class="colophon-date" title="Monday 18 August 2025 02:54">Monday 18 August 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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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><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 1.14.1 on <span class="colophon-date" title="Monday 18 August 2025 15:41">Monday 18 August 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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