build based on fe5e478

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.11.0","generation_timestamp":"2024-10-16T03:31:39","documenter_version":"1.7.0"}}
+{"documenter":{"julia_version":"1.11.0","generation_timestamp":"2024-10-16T04:56:58","documenter_version":"1.7.0"}}

dev/Automatic differentiation/index.html

@@ -13,7 +13,7 @@
  0.0  0.0  1.0
 
 julia> ∇f, f = gradient(tr, x, :all)
-([1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0], 1.1733382401532275)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/KeitaNakamura/Tensorial.jl/blob/d955d967ee89ddadfd671e54069233e522e63f42/src/ad.jl#L154-L178">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Tensorial.hessian-Tuple{Any, Union{Number, AbstractTensor}}" href="#Tensorial.hessian-Tuple{Any, Union{Number, AbstractTensor}}"><code>Tensorial.hessian</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">hessian(f, x)
+([1.0 0.0 0.0; 0.0 1.0 0.0; 0.0 0.0 1.0], 1.1733382401532275)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/KeitaNakamura/Tensorial.jl/blob/fe5e478db9ce52cc6061a611c06f53f4f9314046/src/ad.jl#L154-L178">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Tensorial.hessian-Tuple{Any, Union{Number, AbstractTensor}}" href="#Tensorial.hessian-Tuple{Any, Union{Number, AbstractTensor}}"><code>Tensorial.hessian</code></a> — <span class="docstring-category">Method</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">hessian(f, x)
 hessian(f, x, :all)</code></pre><p>Compute the hessian of <code>f</code> with respect to <code>x</code> by the automatic differentiation. If pseudo keyword <code>:all</code> is given, the value of <code>f(x)</code> is also returned.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; x = rand(Vec{3})
 3-element Vec{3, Float64}:
  0.32597672886359486
@@ -27,4 +27,4 @@
  -0.231782  -0.390397   1.32626
 
 julia&gt; ∇∇f, ∇f, f = hessian(norm, x, :all)
-([1.1360324375454411 -0.5821964220304534 -0.23178236037013888; -0.5821964220304533 0.5010791569244991 -0.39039709608344814; -0.23178236037013886 -0.39039709608344814 1.3262640626479867], [0.4829957515506539, 0.8135223859352438, 0.3238771859304809], 0.6749059962060727)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/KeitaNakamura/Tensorial.jl/blob/d955d967ee89ddadfd671e54069233e522e63f42/src/ad.jl#L182-L206">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Broadcast/">« Broadcast</a><a class="docs-footer-nextpage" href="../Einstein summation/">Einstein summation »</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 1.7.0 on <span class="colophon-date" title="Wednesday 16 October 2024 03:31">Wednesday 16 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+([1.1360324375454411 -0.5821964220304534 -0.23178236037013888; -0.5821964220304533 0.5010791569244991 -0.39039709608344814; -0.23178236037013886 -0.39039709608344814 1.3262640626479867], [0.4829957515506539, 0.8135223859352438, 0.3238771859304809], 0.6749059962060727)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/KeitaNakamura/Tensorial.jl/blob/fe5e478db9ce52cc6061a611c06f53f4f9314046/src/ad.jl#L182-L206">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Broadcast/">« Broadcast</a><a class="docs-footer-nextpage" href="../Einstein summation/">Einstein summation »</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 1.7.0 on <span class="colophon-date" title="Wednesday 16 October 2024 04:56">Wednesday 16 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/Benchmarks/index.html

@@ -4,7 +4,7 @@
 S = rand(SymmetricSecondOrderTensor{3})
 B = rand(Tensor{Tuple{3,3,3}})
 AA = rand(FourthOrderTensor{3})
-SS = rand(SymmetricFourthOrderTensor{3})</code></pre><table><tr><th style="text-align: left">Operation</th><th style="text-align: right"><code>Tensor</code></th><th style="text-align: right"><code>Array</code></th><th style="text-align: right">speed-up</th></tr><tr><td style="text-align: left"><strong>Single contraction</strong></td><td style="text-align: right"></td><td style="text-align: right"></td><td style="text-align: right"></td></tr><tr><td style="text-align: left"><code>a ⋅ a</code></td><td style="text-align: right">2.785 ns</td><td style="text-align: right">9.256 ns</td><td style="text-align: right">×3.3</td></tr><tr><td style="text-align: left"><code>A ⋅ a</code></td><td style="text-align: right">3.095 ns</td><td style="text-align: right">53.999 ns</td><td style="text-align: right">×17.4</td></tr><tr><td style="text-align: left"><code>S ⋅ a</code></td><td style="text-align: right">3.396 ns</td><td style="text-align: right">53.775 ns</td><td style="text-align: right">×15.8</td></tr><tr><td style="text-align: left"><strong>Double contraction</strong></td><td style="text-align: right"></td><td style="text-align: right"></td><td style="text-align: right"></td></tr><tr><td style="text-align: left"><code>A ⊡ A</code></td><td style="text-align: right">3.406 ns</td><td style="text-align: right">11.422 ns</td><td style="text-align: right">×3.4</td></tr><tr><td style="text-align: left"><code>S ⊡ S</code></td><td style="text-align: right">3.095 ns</td><td style="text-align: right">11.422 ns</td><td style="text-align: right">×3.7</td></tr><tr><td style="text-align: left"><code>B ⊡ A</code></td><td style="text-align: right">5.410 ns</td><td style="text-align: right">128.613 ns</td><td style="text-align: right">×23.8</td></tr><tr><td style="text-align: left"><code>AA ⊡ A</code></td><td style="text-align: right">7.732 ns</td><td style="text-align: right">144.599 ns</td><td style="text-align: right">×18.7</td></tr><tr><td style="text-align: left"><code>SS ⊡ S</code></td><td style="text-align: right">15.719 ns</td><td style="text-align: right">152.234 ns</td><td style="text-align: right">×9.7</td></tr><tr><td style="text-align: left"><strong>Tensor product</strong></td><td style="text-align: right"></td><td style="text-align: right"></td><td style="text-align: right"></td></tr><tr><td style="text-align: left"><code>a ⊗ a</code></td><td style="text-align: right">3.716 ns</td><td style="text-align: right">33.597 ns</td><td style="text-align: right">×9.0</td></tr><tr><td style="text-align: left"><strong>Cross product</strong></td><td style="text-align: right"></td><td style="text-align: right"></td><td style="text-align: right"></td></tr><tr><td style="text-align: left"><code>a × a</code></td><td style="text-align: right">3.716 ns</td><td style="text-align: right">33.597 ns</td><td style="text-align: right">×9.0</td></tr><tr><td style="text-align: left"><strong>Determinant</strong></td><td style="text-align: right"></td><td style="text-align: right"></td><td style="text-align: right"></td></tr><tr><td style="text-align: left"><code>det(A)</code></td><td style="text-align: right">3.406 ns</td><td style="text-align: right">170.710 ns</td><td style="text-align: right">×50.1</td></tr><tr><td style="text-align: left"><code>det(S)</code></td><td style="text-align: right">3.406 ns</td><td style="text-align: right">169.943 ns</td><td style="text-align: right">×49.9</td></tr><tr><td style="text-align: left"><strong>Inverse</strong></td><td style="text-align: right"></td><td style="text-align: right"></td><td style="text-align: right"></td></tr><tr><td style="text-align: left"><code>inv(A)</code></td><td style="text-align: right">5.931 ns</td><td style="text-align: right">478.118 ns</td><td style="text-align: right">×80.6</td></tr><tr><td style="text-align: left"><code>inv(S)</code></td><td style="text-align: right">12.032 ns</td><td style="text-align: right">472.719 ns</td><td style="text-align: right">×39.3</td></tr><tr><td style="text-align: left"><code>inv(AA)</code></td><td style="text-align: right">964.143 ns</td><td style="text-align: right">1.531 μs</td><td style="text-align: right">×1.6</td></tr><tr><td style="text-align: left"><code>inv(SS)</code></td><td style="text-align: right">357.154 ns</td><td style="text-align: right">1.529 μs</td><td style="text-align: right">×4.3</td></tr></table><p>The benchmarks are generated by <a href="https://github.com/KeitaNakamura/Tensorial.jl/blob/master/benchmark/runbenchmarks.jl"><code>runbenchmarks.jl</code></a> on the following system:</p><pre><code class="language-julia hljs">julia&gt; versioninfo()
+SS = rand(SymmetricFourthOrderTensor{3})</code></pre><table><tr><th style="text-align: left">Operation</th><th style="text-align: right"><code>Tensor</code></th><th style="text-align: right"><code>Array</code></th><th style="text-align: right">speed-up</th></tr><tr><td style="text-align: left"><strong>Single contraction</strong></td><td style="text-align: right"></td><td style="text-align: right"></td><td style="text-align: right"></td></tr><tr><td style="text-align: left"><code>a ⋅ a</code></td><td style="text-align: right">3.095 ns</td><td style="text-align: right">9.256 ns</td><td style="text-align: right">×3.0</td></tr><tr><td style="text-align: left"><code>A ⋅ a</code></td><td style="text-align: right">3.396 ns</td><td style="text-align: right">53.634 ns</td><td style="text-align: right">×15.8</td></tr><tr><td style="text-align: left"><code>S ⋅ a</code></td><td style="text-align: right">3.706 ns</td><td style="text-align: right">53.512 ns</td><td style="text-align: right">×14.4</td></tr><tr><td style="text-align: left"><strong>Double contraction</strong></td><td style="text-align: right"></td><td style="text-align: right"></td><td style="text-align: right"></td></tr><tr><td style="text-align: left"><code>A ⊡ A</code></td><td style="text-align: right">3.706 ns</td><td style="text-align: right">11.422 ns</td><td style="text-align: right">×3.1</td></tr><tr><td style="text-align: left"><code>S ⊡ S</code></td><td style="text-align: right">3.396 ns</td><td style="text-align: right">11.422 ns</td><td style="text-align: right">×3.4</td></tr><tr><td style="text-align: left"><code>B ⊡ A</code></td><td style="text-align: right">5.420 ns</td><td style="text-align: right">122.123 ns</td><td style="text-align: right">×22.5</td></tr><tr><td style="text-align: left"><code>AA ⊡ A</code></td><td style="text-align: right">7.732 ns</td><td style="text-align: right">143.526 ns</td><td style="text-align: right">×18.6</td></tr><tr><td style="text-align: left"><code>SS ⊡ S</code></td><td style="text-align: right">4.197 ns</td><td style="text-align: right">146.164 ns</td><td style="text-align: right">×34.8</td></tr><tr><td style="text-align: left"><strong>Tensor product</strong></td><td style="text-align: right"></td><td style="text-align: right"></td><td style="text-align: right"></td></tr><tr><td style="text-align: left"><code>a ⊗ a</code></td><td style="text-align: right">3.406 ns</td><td style="text-align: right">33.150 ns</td><td style="text-align: right">×9.7</td></tr><tr><td style="text-align: left"><strong>Cross product</strong></td><td style="text-align: right"></td><td style="text-align: right"></td><td style="text-align: right"></td></tr><tr><td style="text-align: left"><code>a × a</code></td><td style="text-align: right">3.406 ns</td><td style="text-align: right">33.150 ns</td><td style="text-align: right">×9.7</td></tr><tr><td style="text-align: left"><strong>Determinant</strong></td><td style="text-align: right"></td><td style="text-align: right"></td><td style="text-align: right"></td></tr><tr><td style="text-align: left"><code>det(A)</code></td><td style="text-align: right">3.406 ns</td><td style="text-align: right">175.817 ns</td><td style="text-align: right">×51.6</td></tr><tr><td style="text-align: left"><code>det(S)</code></td><td style="text-align: right">3.406 ns</td><td style="text-align: right">180.956 ns</td><td style="text-align: right">×53.1</td></tr><tr><td style="text-align: left"><strong>Inverse</strong></td><td style="text-align: right"></td><td style="text-align: right"></td><td style="text-align: right"></td></tr><tr><td style="text-align: left"><code>inv(A)</code></td><td style="text-align: right">6.001 ns</td><td style="text-align: right">479.621 ns</td><td style="text-align: right">×79.9</td></tr><tr><td style="text-align: left"><code>inv(S)</code></td><td style="text-align: right">5.250 ns</td><td style="text-align: right">484.469 ns</td><td style="text-align: right">×92.3</td></tr><tr><td style="text-align: left"><code>inv(AA)</code></td><td style="text-align: right">958.182 ns</td><td style="text-align: right">1.521 μs</td><td style="text-align: right">×1.6</td></tr><tr><td style="text-align: left"><code>inv(SS)</code></td><td style="text-align: right">363.676 ns</td><td style="text-align: right">1.530 μs</td><td style="text-align: right">×4.2</td></tr></table><p>The benchmarks are generated by <a href="https://github.com/KeitaNakamura/Tensorial.jl/blob/master/benchmark/runbenchmarks.jl"><code>runbenchmarks.jl</code></a> on the following system:</p><pre><code class="language-julia hljs">julia&gt; versioninfo()
 Julia Version 1.11.0
 Commit 501a4f25c2b (2024-10-07 11:40 UTC)
 Build Info:
@@ -15,4 +15,4 @@
   WORD_SIZE: 64
   LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
 Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
-</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Quaternion/">« Quaternion</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 1.7.0 on <span class="colophon-date" title="Wednesday 16 October 2024 03:31">Wednesday 16 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Quaternion/">« Quaternion</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 1.7.0 on <span class="colophon-date" title="Wednesday 16 October 2024 04:56">Wednesday 16 October 2024</span>. Using Julia version 1.11.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>