build based on cd515b3

Author: Documenter.jl

DifferentiationInterface/dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.12.4","generation_timestamp":"2026-01-09T22:26:39","documenter_version":"1.16.1"}}
+{"documenter":{"julia_version":"1.12.4","generation_timestamp":"2026-01-13T15:52:53","documenter_version":"1.16.1"}}

DifferentiationInterface/dev/api/index.html

@@ -6,4 +6,4 @@
 seed = 3
 coloring_algorithm = GreedyColoringAlgorithm(
     RandomOrder(StableRNG(seed), seed); postprocessing=true
-)</code></pre><h2 id="Batch-mode"><a class="docs-heading-anchor" href="#Batch-mode">Batch mode</a><a id="Batch-mode-1"></a><a class="docs-heading-anchor-permalink" href="#Batch-mode" title="Permalink"></a></h2><h3 id="Multiple-tangents"><a class="docs-heading-anchor" href="#Multiple-tangents">Multiple tangents</a><a id="Multiple-tangents-1"></a><a class="docs-heading-anchor-permalink" href="#Multiple-tangents" title="Permalink"></a></h3><p>The <a href="../../api/#DifferentiationInterface.jacobian"><code>jacobian</code></a> and <a href="../../api/#DifferentiationInterface.hessian"><code>hessian</code></a> operators compute matrices by repeatedly applying lower-level operators (<a href="../../api/#DifferentiationInterface.pushforward"><code>pushforward</code></a>, <a href="../../api/#DifferentiationInterface.pullback"><code>pullback</code></a> or <a href="../../api/#DifferentiationInterface.hvp"><code>hvp</code></a>) to a set of tangents. The tangents usually correspond to basis elements of the appropriate vector space. We could call the lower-level operator on each tangent separately, but some packages (<a href="https://github.com/JuliaDiff/ForwardDiff.jl">ForwardDiff.jl</a> and <a href="https://github.com/EnzymeAD/Enzyme.jl">Enzyme.jl</a>) have optimized implementations to handle multiple tangents at once.</p><p>This behavior is often called &quot;vector mode&quot; AD, but we call it &quot;batch mode&quot; to avoid confusion with Julia&#39;s <code>Vector</code> type. As a matter of fact, the optimal batch size <span>$B$</span> (number of simultaneous tangents) is usually very small, so tangents are passed within an <code>NTuple</code> and not a <code>Vector</code>. When the underlying vector space has dimension <span>$N$</span>, the operators <code>jacobian</code> and <code>hessian</code> process <span>$\lceil N / B \rceil$</span> batches of size <span>$B$</span> each.</p><h3 id="Optimal-batch-size"><a class="docs-heading-anchor" href="#Optimal-batch-size">Optimal batch size</a><a id="Optimal-batch-size-1"></a><a class="docs-heading-anchor-permalink" href="#Optimal-batch-size" title="Permalink"></a></h3><p>For every backend which does not support batch mode, the batch size is set to <span>$B = 1$</span>. But for <a href="https://sciml.github.io/ADTypes.jl/stable/#ADTypes.AutoForwardDiff"><code>AutoForwardDiff</code></a> and <a href="https://sciml.github.io/ADTypes.jl/stable/#ADTypes.AutoEnzyme"><code>AutoEnzyme</code></a>, more complicated rules apply. If the backend object has a pre-determined batch size <span>$B_0$</span>, then we always set <span>$B = B_0$</span>. In particular, this will throw errors when <span>$N &lt; B_0$</span>. On the other hand, without a pre-determined batch size, we apply backend-specific heuristics to pick <span>$B$</span> based on <span>$N$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../backends/">« Backends</a><a class="docs-footer-nextpage" href="../../faq/limitations/">Limitations »</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 1.16.1 on <span class="colophon-date" title="Friday 9 January 2026 22:26">Friday 9 January 2026</span>. Using Julia version 1.12.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+)</code></pre><h2 id="Batch-mode"><a class="docs-heading-anchor" href="#Batch-mode">Batch mode</a><a id="Batch-mode-1"></a><a class="docs-heading-anchor-permalink" href="#Batch-mode" title="Permalink"></a></h2><h3 id="Multiple-tangents"><a class="docs-heading-anchor" href="#Multiple-tangents">Multiple tangents</a><a id="Multiple-tangents-1"></a><a class="docs-heading-anchor-permalink" href="#Multiple-tangents" title="Permalink"></a></h3><p>The <a href="../../api/#DifferentiationInterface.jacobian"><code>jacobian</code></a> and <a href="../../api/#DifferentiationInterface.hessian"><code>hessian</code></a> operators compute matrices by repeatedly applying lower-level operators (<a href="../../api/#DifferentiationInterface.pushforward"><code>pushforward</code></a>, <a href="../../api/#DifferentiationInterface.pullback"><code>pullback</code></a> or <a href="../../api/#DifferentiationInterface.hvp"><code>hvp</code></a>) to a set of tangents. The tangents usually correspond to basis elements of the appropriate vector space. We could call the lower-level operator on each tangent separately, but some packages (<a href="https://github.com/JuliaDiff/ForwardDiff.jl">ForwardDiff.jl</a> and <a href="https://github.com/EnzymeAD/Enzyme.jl">Enzyme.jl</a>) have optimized implementations to handle multiple tangents at once.</p><p>This behavior is often called &quot;vector mode&quot; AD, but we call it &quot;batch mode&quot; to avoid confusion with Julia&#39;s <code>Vector</code> type. As a matter of fact, the optimal batch size <span>$B$</span> (number of simultaneous tangents) is usually very small, so tangents are passed within an <code>NTuple</code> and not a <code>Vector</code>. When the underlying vector space has dimension <span>$N$</span>, the operators <code>jacobian</code> and <code>hessian</code> process <span>$\lceil N / B \rceil$</span> batches of size <span>$B$</span> each.</p><h3 id="Optimal-batch-size"><a class="docs-heading-anchor" href="#Optimal-batch-size">Optimal batch size</a><a id="Optimal-batch-size-1"></a><a class="docs-heading-anchor-permalink" href="#Optimal-batch-size" title="Permalink"></a></h3><p>For every backend which does not support batch mode, the batch size is set to <span>$B = 1$</span>. But for <a href="https://sciml.github.io/ADTypes.jl/stable/#ADTypes.AutoForwardDiff"><code>AutoForwardDiff</code></a> and <a href="https://sciml.github.io/ADTypes.jl/stable/#ADTypes.AutoEnzyme"><code>AutoEnzyme</code></a>, more complicated rules apply. If the backend object has a pre-determined batch size <span>$B_0$</span>, then we always set <span>$B = B_0$</span>. In particular, this will throw errors when <span>$N &lt; B_0$</span>. On the other hand, without a pre-determined batch size, we apply backend-specific heuristics to pick <span>$B$</span> based on <span>$N$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../backends/">« Backends</a><a class="docs-footer-nextpage" href="../../faq/limitations/">Limitations »</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 1.16.1 on <span class="colophon-date" title="Tuesday 13 January 2026 15:52">Tuesday 13 January 2026</span>. Using Julia version 1.12.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>