build based on b36a40a

Author: Documenter.jl

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.11.4","generation_timestamp":"2025-04-08T10:09:51","documenter_version":"1.10.1"}}
+{"documenter":{"julia_version":"1.11.4","generation_timestamp":"2025-04-11T04:56:44","documenter_version":"1.10.1"}}

dev/api/index.html

@@ -27,4 +27,4 @@
     backend=nothing,
     preparation=nothing,
 )
-</code></pre><p>What does this wrapper do? When we call it as a function, it just falls back on <code>implicit.forward</code>, so unsurprisingly we get the output <span>$y(x)$</span> and the byproduct <code>z</code>.</p><pre><code class="language-julia hljs">implicit(x)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">([2.0, 3.0], nothing)</code></pre><p>And when we try to compute its Jacobian, the <a href="https://en.wikipedia.org/wiki/Implicit_function_theorem">implicit function theorem</a> is applied in the background to circumvent the lack of differentiability of the forward mapping.</p><h2 id="Forward-and-reverse-mode-autodiff"><a class="docs-heading-anchor" href="#Forward-and-reverse-mode-autodiff">Forward and reverse mode autodiff</a><a id="Forward-and-reverse-mode-autodiff-1"></a><a class="docs-heading-anchor-permalink" href="#Forward-and-reverse-mode-autodiff" title="Permalink"></a></h2><p>Now ForwardDiff.jl works seamlessly.</p><pre><code class="language-julia hljs">ForwardDiff.jacobian(first ∘ implicit, x) ≈ J</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><p>And so does Zygote.jl. Hurray!</p><pre><code class="language-julia hljs">Zygote.jacobian(first ∘ implicit, x)[1] ≈ J</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../1_basic/">Basic use cases »</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 1.10.1 on <span class="colophon-date" title="Tuesday 8 April 2025 10:09">Tuesday 8 April 2025</span>. Using Julia version 1.11.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</code></pre><p>What does this wrapper do? When we call it as a function, it just falls back on <code>implicit.forward</code>, so unsurprisingly we get the output <span>$y(x)$</span> and the byproduct <code>z</code>.</p><pre><code class="language-julia hljs">implicit(x)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">([2.0, 3.0], nothing)</code></pre><p>And when we try to compute its Jacobian, the <a href="https://en.wikipedia.org/wiki/Implicit_function_theorem">implicit function theorem</a> is applied in the background to circumvent the lack of differentiability of the forward mapping.</p><h2 id="Forward-and-reverse-mode-autodiff"><a class="docs-heading-anchor" href="#Forward-and-reverse-mode-autodiff">Forward and reverse mode autodiff</a><a id="Forward-and-reverse-mode-autodiff-1"></a><a class="docs-heading-anchor-permalink" href="#Forward-and-reverse-mode-autodiff" title="Permalink"></a></h2><p>Now ForwardDiff.jl works seamlessly.</p><pre><code class="language-julia hljs">ForwardDiff.jacobian(first ∘ implicit, x) ≈ J</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><p>And so does Zygote.jl. Hurray!</p><pre><code class="language-julia hljs">Zygote.jacobian(first ∘ implicit, x)[1] ≈ J</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../1_basic/">Basic use cases »</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 1.10.1 on <span class="colophon-date" title="Friday 11 April 2025 04:56">Friday 11 April 2025</span>. Using Julia version 1.11.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/examples/0_intro/index.html

@@ -97,4 +97,4 @@
     Zygote.jacobian(_x -> first(forward_fixedpoint(_x, 10)), x)[1]
 catch e
     e
-end</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">ErrorException(&quot;Mutating arrays is not supported -- called copyto!(Vector{Float64}, ...)\nThis error occurs when you ask Zygote to differentiate operations that change\nthe elements of arrays in place (e.g. setting values with x .= ...)\n\nPossible fixes:\n- avoid mutating operations (preferred)\n- or read the documentation and solutions for this error\n  https://fluxml.ai/Zygote.jl/latest/limitations\n&quot;)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../0_intro/">« Introduction</a><a class="docs-footer-nextpage" href="../2_advanced/">Advanced use cases »</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 1.10.1 on <span class="colophon-date" title="Tuesday 8 April 2025 10:09">Tuesday 8 April 2025</span>. Using Julia version 1.11.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">ErrorException(&quot;Mutating arrays is not supported -- called copyto!(Vector{Float64}, ...)\nThis error occurs when you ask Zygote to differentiate operations that change\nthe elements of arrays in place (e.g. setting values with x .= ...)\n\nPossible fixes:\n- avoid mutating operations (preferred)\n- or read the documentation and solutions for this error\n  https://fluxml.ai/Zygote.jl/latest/limitations\n&quot;)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../0_intro/">« Introduction</a><a class="docs-footer-nextpage" href="../2_advanced/">Advanced use cases »</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 1.10.1 on <span class="colophon-date" title="Friday 11 April 2025 04:56">Friday 11 April 2025</span>. Using Julia version 1.11.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/examples/1_basic/index.html

@@ -35,11 +35,11 @@
   ⋅        0.0</code></pre><p>Forward mode autodiff</p><pre><code class="language-julia hljs">ForwardDiff.jacobian(first ∘ implicit_cstr_optim, x)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">2×2 Matrix{Float64}:
  0.912871  0.0
  0.0       0.0</code></pre><pre><code class="language-julia hljs">ForwardDiff.jacobian(first ∘ forward_cstr_optim, x)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">2×2 Matrix{Float64}:
- -0.827895    35.7151
- -3.15318e-5   0.000646931</code></pre><p>Reverse mode autodiff</p><pre><code class="language-julia hljs">Zygote.jacobian(first ∘ implicit_cstr_optim, x)[1]</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">2×2 Matrix{Float64}:
+  0.9128     0.00145278
+ -2.1666e-8  4.4167e-7</code></pre><p>Reverse mode autodiff</p><pre><code class="language-julia hljs">Zygote.jacobian(first ∘ implicit_cstr_optim, x)[1]</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">2×2 Matrix{Float64}:
   0.912871  -0.0
  -0.0        0.0</code></pre><pre><code class="language-julia hljs">try
     Zygote.jacobian(first ∘ forward_cstr_optim, x)[1]
 catch e
     e
-end</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">ErrorException(&quot;Can&#39;t differentiate foreigncall expression \$(Expr(:foreigncall, :(:jl_clock_now), Float64, svec(), 0, :(:ccall))).\nYou might want to check the Zygote limitations documentation.\nhttps://fluxml.ai/Zygote.jl/latest/limitations\n&quot;)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../1_basic/">« Basic use cases</a><a class="docs-footer-nextpage" href="../3_tricks/">Tricks »</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 1.10.1 on <span class="colophon-date" title="Tuesday 8 April 2025 10:09">Tuesday 8 April 2025</span>. Using Julia version 1.11.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">ErrorException(&quot;Can&#39;t differentiate foreigncall expression \$(Expr(:foreigncall, :(:jl_clock_now), Float64, svec(), 0, :(:ccall))).\nYou might want to check the Zygote limitations documentation.\nhttps://fluxml.ai/Zygote.jl/latest/limitations\n&quot;)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../1_basic/">« Basic use cases</a><a class="docs-footer-nextpage" href="../3_tricks/">Tricks »</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 1.10.1 on <span class="colophon-date" title="Friday 11 April 2025 04:56">Friday 11 April 2025</span>. Using Julia version 1.11.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/examples/2_advanced/index.html

@@ -41,4 +41,4 @@
     x = ComponentVector(; a=a, b=b, m=m)
     y, _ = implicit_components(x)
     return y.d, y.e
-end;</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../2_advanced/">« Advanced use cases</a><a class="docs-footer-nextpage" href="../../api/">API reference »</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 1.10.1 on <span class="colophon-date" title="Tuesday 8 April 2025 10:09">Tuesday 8 April 2025</span>. Using Julia version 1.11.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end;</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../2_advanced/">« Advanced use cases</a><a class="docs-footer-nextpage" href="../../api/">API reference »</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 1.10.1 on <span class="colophon-date" title="Friday 11 April 2025 04:56">Friday 11 April 2025</span>. Using Julia version 1.11.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>