build based on 1a9f51c

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-04T22:31:42","documenter_version":"1.7.0"}}
+{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-04T22:36:34","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/de127134f9ddb1219af6d93a84ff90e7ffe0ee1c/src/ad.jl#L101-L125">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/1a9f51ca50533dd42f790acbe77f09e4b89b7552/src/ad.jl#L101-L125">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/de127134f9ddb1219af6d93a84ff90e7ffe0ee1c/src/ad.jl#L138-L162">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 4 September 2024 22:31">Wednesday 4 September 2024</span>. Using Julia version 1.10.5.</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/1a9f51ca50533dd42f790acbe77f09e4b89b7552/src/ad.jl#L138-L162">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 4 September 2024 22:36">Wednesday 4 September 2024</span>. Using Julia version 1.10.5.</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">9.567 ns</td><td style="text-align: right">×3.4</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">62.577 ns</td><td style="text-align: right">×18.4</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">62.781 ns</td><td style="text-align: right">×16.9</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">11.132 ns</td><td style="text-align: right">×3.3</td></tr><tr><td style="text-align: left"><code>S ⊡ S</code></td><td style="text-align: right">3.406 ns</td><td style="text-align: right">11.131 ns</td><td style="text-align: right">×3.3</td></tr><tr><td style="text-align: left"><code>B ⊡ A</code></td><td style="text-align: right">5.419 ns</td><td style="text-align: right">131.552 ns</td><td style="text-align: right">×24.3</td></tr><tr><td style="text-align: left"><code>AA ⊡ A</code></td><td style="text-align: right">14.351 ns</td><td style="text-align: right">145.523 ns</td><td style="text-align: right">×10.1</td></tr><tr><td style="text-align: left"><code>SS ⊡ S</code></td><td style="text-align: right">4.207 ns</td><td style="text-align: right">145.524 ns</td><td style="text-align: right">×34.6</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">13.555 ns</td><td style="text-align: right">40.165 ns</td><td style="text-align: right">×3.0</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">13.555 ns</td><td style="text-align: right">40.165 ns</td><td style="text-align: right">×3.0</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">199.408 ns</td><td style="text-align: right">×58.5</td></tr><tr><td style="text-align: left"><code>det(S)</code></td><td style="text-align: right">3.095 ns</td><td style="text-align: right">196.807 ns</td><td style="text-align: right">×63.6</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">15.108 ns</td><td style="text-align: right">516.775 ns</td><td style="text-align: right">×34.2</td></tr><tr><td style="text-align: left"><code>inv(S)</code></td><td style="text-align: right">4.849 ns</td><td style="text-align: right">515.911 ns</td><td style="text-align: right">×106.4</td></tr><tr><td style="text-align: left"><code>inv(AA)</code></td><td style="text-align: right">930.962 ns</td><td style="text-align: right">1.560 μs</td><td style="text-align: right">×1.7</td></tr><tr><td style="text-align: left"><code>inv(SS)</code></td><td style="text-align: right">368.668 ns</td><td style="text-align: right">1.573 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">2.785 ns</td><td style="text-align: right">9.567 ns</td><td style="text-align: right">×3.4</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">64.010 ns</td><td style="text-align: right">×18.8</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">64.082 ns</td><td style="text-align: right">×17.3</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">3.416 ns</td><td style="text-align: right">11.121 ns</td><td style="text-align: right">×3.3</td></tr><tr><td style="text-align: left"><code>S ⊡ S</code></td><td style="text-align: right">3.406 ns</td><td style="text-align: right">18.523 ns</td><td style="text-align: right">×5.4</td></tr><tr><td style="text-align: left"><code>B ⊡ A</code></td><td style="text-align: right">5.430 ns</td><td style="text-align: right">130.503 ns</td><td style="text-align: right">×24.0</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">154.462 ns</td><td style="text-align: right">×20.0</td></tr><tr><td style="text-align: left"><code>SS ⊡ S</code></td><td style="text-align: right">4.278 ns</td><td style="text-align: right">145.739 ns</td><td style="text-align: right">×34.1</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">40.165 ns</td><td style="text-align: right">×11.8</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">40.165 ns</td><td style="text-align: right">×11.8</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">191.746 ns</td><td style="text-align: right">×56.3</td></tr><tr><td style="text-align: left"><code>det(S)</code></td><td style="text-align: right">3.095 ns</td><td style="text-align: right">187.368 ns</td><td style="text-align: right">×60.5</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">5.831 ns</td><td style="text-align: right">516.613 ns</td><td style="text-align: right">×88.6</td></tr><tr><td style="text-align: left"><code>inv(S)</code></td><td style="text-align: right">4.929 ns</td><td style="text-align: right">498.280 ns</td><td style="text-align: right">×101.1</td></tr><tr><td style="text-align: left"><code>inv(AA)</code></td><td style="text-align: right">929.606 ns</td><td style="text-align: right">1.588 μs</td><td style="text-align: right">×1.7</td></tr><tr><td style="text-align: left"><code>inv(SS)</code></td><td style="text-align: right">350.792 ns</td><td style="text-align: right">1.585 μs</td><td style="text-align: right">×4.5</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 1.10.5
 Commit 6f3fdf7b362 (2024-08-27 14:19 UTC)
 Build Info:
@@ -16,4 +16,4 @@
   LIBM: libopenlibm
   LLVM: libLLVM-15.0.7 (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 4 September 2024 22:31">Wednesday 4 September 2024</span>. Using Julia version 1.10.5.</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 4 September 2024 22:36">Wednesday 4 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>