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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2025-01-09T07:33:58","documenter_version":"1.8.0"}}
{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2025-01-09T10:24:05","documenter_version":"1.8.0"}}
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14 changes: 7 additions & 7 deletions dev/extrapolation_methods/index.html
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t_eval_left = range(-1, first(t), length = 25)
t_eval_right = range(last(t), 3.5, length = 25)
A = QuadraticSpline(u, t)
plot(A)</code></pre><img src="31fc52df.svg" alt="Example block output"/><p>Extrapolation behavior can be set left and right of the data simultaneously with the <code>extension</code> keyword, or left and right separately with the <code>extrapolation_left</code> and <code>extrapolation_right</code> keywords respectively.</p><h2 id="ExtrapolationType.None"><a class="docs-heading-anchor" href="#ExtrapolationType.None"><code>ExtrapolationType.None</code></a><a id="ExtrapolationType.None-1"></a><a class="docs-heading-anchor-permalink" href="#ExtrapolationType.None" title="Permalink"></a></h2><p>This extrapolation type will throw an error when the input <code>t</code> is beyond the data in the specified direction.</p><h2 id="ExtrapolationType.Constant"><a class="docs-heading-anchor" href="#ExtrapolationType.Constant"><code>ExtrapolationType.Constant</code></a><a id="ExtrapolationType.Constant-1"></a><a class="docs-heading-anchor-permalink" href="#ExtrapolationType.Constant" title="Permalink"></a></h2><p>This extrapolation type extends the interpolation with the boundary values of the data <code>u</code>.</p><pre><code class="language-julia hljs">A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Constant)
plot(A)</code></pre><img src="11883255.svg" alt="Example block output"/><p>Extrapolation behavior can be set left and right of the data simultaneously with the <code>extension</code> keyword, or left and right separately with the <code>extrapolation_left</code> and <code>extrapolation_right</code> keywords respectively.</p><h2 id="ExtrapolationType.None"><a class="docs-heading-anchor" href="#ExtrapolationType.None"><code>ExtrapolationType.None</code></a><a id="ExtrapolationType.None-1"></a><a class="docs-heading-anchor-permalink" href="#ExtrapolationType.None" title="Permalink"></a></h2><p>This extrapolation type will throw an error when the input <code>t</code> is beyond the data in the specified direction.</p><h2 id="ExtrapolationType.Constant"><a class="docs-heading-anchor" href="#ExtrapolationType.Constant"><code>ExtrapolationType.Constant</code></a><a id="ExtrapolationType.Constant-1"></a><a class="docs-heading-anchor-permalink" href="#ExtrapolationType.Constant" title="Permalink"></a></h2><p>This extrapolation type extends the interpolation with the boundary values of the data <code>u</code>.</p><pre><code class="language-julia hljs">A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Constant)
plot(A)
plot!(t_eval_left, A.(t_eval_left); label = &quot;extrapolation left&quot;)
plot!(t_eval_right, A.(t_eval_right); label = &quot;extrapolation right&quot;)</code></pre><img src="106b8a9c.svg" alt="Example block output"/><h2 id="ExtrapolationType.Linear"><a class="docs-heading-anchor" href="#ExtrapolationType.Linear"><code>ExtrapolationType.Linear</code></a><a id="ExtrapolationType.Linear-1"></a><a class="docs-heading-anchor-permalink" href="#ExtrapolationType.Linear" title="Permalink"></a></h2><p>This extrapolation type extends the interpolation with a linear continuation of the interpolation, making it <span>$C^1$</span> smooth at the data boundaries.</p><pre><code class="language-julia hljs">A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Linear)
plot!(t_eval_right, A.(t_eval_right); label = &quot;extrapolation right&quot;)</code></pre><img src="51d8bd40.svg" alt="Example block output"/><h2 id="ExtrapolationType.Linear"><a class="docs-heading-anchor" href="#ExtrapolationType.Linear"><code>ExtrapolationType.Linear</code></a><a id="ExtrapolationType.Linear-1"></a><a class="docs-heading-anchor-permalink" href="#ExtrapolationType.Linear" title="Permalink"></a></h2><p>This extrapolation type extends the interpolation with a linear continuation of the interpolation, making it <span>$C^1$</span> smooth at the data boundaries.</p><pre><code class="language-julia hljs">A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Linear)
plot(A)
plot!(t_eval_left, A.(t_eval_left); label = &quot;extrapolation left&quot;)
plot!(t_eval_right, A.(t_eval_right); label = &quot;extrapolation right&quot;)</code></pre><img src="9e44ce05.svg" alt="Example block output"/><h2 id="ExtrapolationType.Extension"><a class="docs-heading-anchor" href="#ExtrapolationType.Extension"><code>ExtrapolationType.Extension</code></a><a id="ExtrapolationType.Extension-1"></a><a class="docs-heading-anchor-permalink" href="#ExtrapolationType.Extension" title="Permalink"></a></h2><p>This extrapolation type extends the interpolation with a continuation of the expression for the interpolation at the boundary intervals for maximum smoothness.</p><pre><code class="language-julia hljs">A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Extension)
plot!(t_eval_right, A.(t_eval_right); label = &quot;extrapolation right&quot;)</code></pre><img src="58eed19e.svg" alt="Example block output"/><h2 id="ExtrapolationType.Extension"><a class="docs-heading-anchor" href="#ExtrapolationType.Extension"><code>ExtrapolationType.Extension</code></a><a id="ExtrapolationType.Extension-1"></a><a class="docs-heading-anchor-permalink" href="#ExtrapolationType.Extension" title="Permalink"></a></h2><p>This extrapolation type extends the interpolation with a continuation of the expression for the interpolation at the boundary intervals for maximum smoothness.</p><pre><code class="language-julia hljs">A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Extension)
plot(A)
plot!(t_eval_left, A.(t_eval_left); label = &quot;extrapolation down&quot;)
plot!(t_eval_right, A.(t_eval_right); label = &quot;extrapolation up&quot;)</code></pre><img src="9612dce4.svg" alt="Example block output"/><h2 id="ExtrapolationType.Periodic"><a class="docs-heading-anchor" href="#ExtrapolationType.Periodic"><code>ExtrapolationType.Periodic</code></a><a id="ExtrapolationType.Periodic-1"></a><a class="docs-heading-anchor-permalink" href="#ExtrapolationType.Periodic" title="Permalink"></a></h2><p>this extrapolation type extends the interpolation such that <code>A(t + T) == A(t)</code> for all <code>t</code>, where the period is given by <code>T = last(A.t) - first(A.t)</code>.</p><pre><code class="language-julia hljs">T = last(A.t) - first(A.t)
plot!(t_eval_right, A.(t_eval_right); label = &quot;extrapolation up&quot;)</code></pre><img src="2d8981eb.svg" alt="Example block output"/><h2 id="ExtrapolationType.Periodic"><a class="docs-heading-anchor" href="#ExtrapolationType.Periodic"><code>ExtrapolationType.Periodic</code></a><a id="ExtrapolationType.Periodic-1"></a><a class="docs-heading-anchor-permalink" href="#ExtrapolationType.Periodic" title="Permalink"></a></h2><p>this extrapolation type extends the interpolation such that <code>A(t + T) == A(t)</code> for all <code>t</code>, where the period is given by <code>T = last(A.t) - first(A.t)</code>.</p><pre><code class="language-julia hljs">T = last(A.t) - first(A.t)
t_eval_left = range(first(t) - 2T, first(t), length = 100)
t_eval_right = range(last(t), last(t) + 2T, length = 100)
A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Periodic)
plot(A)
plot!(t_eval_left, A.(t_eval_left); label = &quot;extrapolation down&quot;)
plot!(t_eval_right, A.(t_eval_right); label = &quot;extrapolation up&quot;)</code></pre><img src="4e85d9f1.svg" alt="Example block output"/><h2 id="ExtrapolationType.Reflective"><a class="docs-heading-anchor" href="#ExtrapolationType.Reflective"><code>ExtrapolationType.Reflective</code></a><a id="ExtrapolationType.Reflective-1"></a><a class="docs-heading-anchor-permalink" href="#ExtrapolationType.Reflective" title="Permalink"></a></h2><p>this extrapolation type extends the interpolation such that <code>A(t_ + t) == A(t_ - t)</code> for all <code>t_, t</code> such that <code>(t_ - first(A.t)) % T == 0</code> and <code>0 &lt; t &lt; T</code>, where <code>T = last(A.t) - first(A.t)</code>.</p><pre><code class="language-julia hljs">A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Reflective)
plot!(t_eval_right, A.(t_eval_right); label = &quot;extrapolation up&quot;)</code></pre><img src="dd921020.svg" alt="Example block output"/><h2 id="ExtrapolationType.Reflective"><a class="docs-heading-anchor" href="#ExtrapolationType.Reflective"><code>ExtrapolationType.Reflective</code></a><a id="ExtrapolationType.Reflective-1"></a><a class="docs-heading-anchor-permalink" href="#ExtrapolationType.Reflective" title="Permalink"></a></h2><p>this extrapolation type extends the interpolation such that <code>A(t_ + t) == A(t_ - t)</code> for all <code>t_, t</code> such that <code>(t_ - first(A.t)) % T == 0</code> and <code>0 &lt; t &lt; T</code>, where <code>T = last(A.t) - first(A.t)</code>.</p><pre><code class="language-julia hljs">A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Reflective)
plot(A)
plot!(t_eval_left, A.(t_eval_left); label = &quot;extrapolation down&quot;)
plot!(t_eval_right, A.(t_eval_right); label = &quot;extrapolation up&quot;)</code></pre><img src="3c84a473.svg" alt="Example block output"/><h2 id="Mixed-extrapolation"><a class="docs-heading-anchor" href="#Mixed-extrapolation">Mixed extrapolation</a><a id="Mixed-extrapolation-1"></a><a class="docs-heading-anchor-permalink" href="#Mixed-extrapolation" title="Permalink"></a></h2><p>You can also have different extrapolation types left and right of the data.</p><pre><code class="language-julia hljs">A = QuadraticSpline(u, t; extrapolation_left = ExtrapolationType.Reflective,
plot!(t_eval_right, A.(t_eval_right); label = &quot;extrapolation up&quot;)</code></pre><img src="7912df09.svg" alt="Example block output"/><h2 id="Mixed-extrapolation"><a class="docs-heading-anchor" href="#Mixed-extrapolation">Mixed extrapolation</a><a id="Mixed-extrapolation-1"></a><a class="docs-heading-anchor-permalink" href="#Mixed-extrapolation" title="Permalink"></a></h2><p>You can also have different extrapolation types left and right of the data.</p><pre><code class="language-julia hljs">A = QuadraticSpline(u, t; extrapolation_left = ExtrapolationType.Reflective,
extrapolation_right = ExtrapolationType.Periodic)
plot(A)
plot!(t_eval_left, A.(t_eval_left); label = &quot;extrapolation left&quot;)
plot!(t_eval_right, A.(t_eval_right); label = &quot;extrapolation right&quot;)</code></pre><img src="5b7de00d.svg" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../methods/">« Interpolation methods</a><a class="docs-footer-nextpage" href="../interface/">Interface »</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 1.8.0 on <span class="colophon-date" title="Thursday 9 January 2025 07:33">Thursday 9 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
plot!(t_eval_right, A.(t_eval_right); label = &quot;extrapolation right&quot;)</code></pre><img src="f7e2b489.svg" alt="Example block output"/></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../methods/">« Interpolation methods</a><a class="docs-footer-nextpage" href="../interface/">Interface »</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 1.8.0 on <span class="colophon-date" title="Thursday 9 January 2025 10:24">Thursday 9 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2 changes: 1 addition & 1 deletion dev/index.html
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[8e850b90] libblastrampoline_jll v5.11.0+0
[8e850ede] nghttp2_jll v1.59.0+0
[3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`</code></pre></details><p>You can also download the <a href="https://github.com/SciML/DataInterpolations.jl/tree/gh-pages/v7.0.0/assets/Manifest.toml">manifest</a> file and the <a href="https://github.com/SciML/DataInterpolations.jl/tree/gh-pages/v7.0.0/assets/Project.toml">project</a> file.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="methods/">Interpolation methods »</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 1.8.0 on <span class="colophon-date" title="Thursday 9 January 2025 07:33">Thursday 9 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`</code></pre></details><p>You can also download the <a href="https://github.com/SciML/DataInterpolations.jl/tree/gh-pages/v7.0.0/assets/Manifest.toml">manifest</a> file and the <a href="https://github.com/SciML/DataInterpolations.jl/tree/gh-pages/v7.0.0/assets/Project.toml">project</a> file.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="methods/">Interpolation methods »</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 1.8.0 on <span class="colophon-date" title="Thursday 9 January 2025 10:24">Thursday 9 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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