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{"documenter":{"julia_version":"1.10.7","generation_timestamp":"2024-12-27T13:32:12","documenter_version":"1.8.0"}}
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{"documenter":{"julia_version":"1.10.7","generation_timestamp":"2024-12-27T13:36:21","documenter_version":"1.8.0"}}

previews/PR109/changelog/index.html

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previews/PR109/development/index.html

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mkdir run
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cd run
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julia --project=. -e 'using Pkg; Pkg.develop(PackageSpec(path=".."))' # Install local KernelInterpolation.jl clone
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julia --project=. -e &#39;using Pkg; Pkg.add([&quot;Plots&quot;, &quot;QuasiMonteCarlo&quot;, &quot;Meshes&quot;, &quot;OrdinaryDiffEqRosenbrock&quot;, &quot;OrdinaryDiffEqNonlinearSolve&quot;])&#39; # Install additional packages</code></pre><p>If you use other packages for executing KernelInterpolation.jl, you can add them to the project in the <code>run</code> directory in an analogous way as above. To use the Julia project within <code>run</code>, be sure to start the Julia REPL by</p><pre><code class="language-sh hljs">julia --project=.</code></pre><p>if already inside the the <code>run</code> directory or <code>julia --project=run</code> if in the main directory of the repo.</p><h2 id="Preview-of-the-documentation"><a class="docs-heading-anchor" href="#Preview-of-the-documentation">Preview of the documentation</a><a id="Preview-of-the-documentation-1"></a><a class="docs-heading-anchor-permalink" href="#Preview-of-the-documentation" title="Permalink"></a></h2><p>If you want to build the documentation locally, you can run</p><pre><code class="language-sh hljs">julia --project=docs -e &#39;using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()&#39;</code></pre><p>once from the KernelInterpolation.jl main directory to tell <a href="https://documenter.juliadocs.org/stable/man/guide/">Documenter.jl</a> to build the documentation of your local clone. To build the documentation, run</p><pre><code class="language-sh hljs">julia --project=docs --color=yes docs/make.jl</code></pre><p>The resulting <code>.html</code> files can then be found in <code>docs/build/</code> and you can look at them by opening them in a browser. For pull requests from the main repository (i.e. not from a fork), the documentation is automatically built and can be previewed under <code>https://joshualampert.github.io/KernelInterpolation.jl/previews/PRXXX/</code> where <code>XXX</code> is the number of the pull request.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tutorial_noisy_data/">« Dealing with noisy data</a><a class="docs-footer-nextpage" href="../ref/">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 1.8.0 on <span class="colophon-date" title="Friday 27 December 2024 13:32">Friday 27 December 2024</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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julia --project=. -e &#39;using Pkg; Pkg.add([&quot;Plots&quot;, &quot;QuasiMonteCarlo&quot;, &quot;Meshes&quot;, &quot;OrdinaryDiffEqRosenbrock&quot;, &quot;OrdinaryDiffEqNonlinearSolve&quot;])&#39; # Install additional packages</code></pre><p>If you use other packages for executing KernelInterpolation.jl, you can add them to the project in the <code>run</code> directory in an analogous way as above. To use the Julia project within <code>run</code>, be sure to start the Julia REPL by</p><pre><code class="language-sh hljs">julia --project=.</code></pre><p>if already inside the the <code>run</code> directory or <code>julia --project=run</code> if in the main directory of the repo.</p><h2 id="Preview-of-the-documentation"><a class="docs-heading-anchor" href="#Preview-of-the-documentation">Preview of the documentation</a><a id="Preview-of-the-documentation-1"></a><a class="docs-heading-anchor-permalink" href="#Preview-of-the-documentation" title="Permalink"></a></h2><p>If you want to build the documentation locally, you can run</p><pre><code class="language-sh hljs">julia --project=docs -e &#39;using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()&#39;</code></pre><p>once from the KernelInterpolation.jl main directory to tell <a href="https://documenter.juliadocs.org/stable/man/guide/">Documenter.jl</a> to build the documentation of your local clone. To build the documentation, run</p><pre><code class="language-sh hljs">julia --project=docs --color=yes docs/make.jl</code></pre><p>The resulting <code>.html</code> files can then be found in <code>docs/build/</code> and you can look at them by opening them in a browser. For pull requests from the main repository (i.e. not from a fork), the documentation is automatically built and can be previewed under <code>https://joshualampert.github.io/KernelInterpolation.jl/previews/PRXXX/</code> where <code>XXX</code> is the number of the pull request.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tutorial_noisy_data/">« Dealing with noisy data</a><a class="docs-footer-nextpage" href="../ref/">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 1.8.0 on <span class="colophon-date" title="Friday 27 December 2024 13:36">Friday 27 December 2024</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR109/index.html

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month={06},
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howpublished={\url{https://github.com/JoshuaLampert/KernelInterpolation.jl}},
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doi={10.5281/zenodo.12599880}
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}</code></pre><h2 id="Authors"><a class="docs-heading-anchor" href="#Authors">Authors</a><a id="Authors-1"></a><a class="docs-heading-anchor-permalink" href="#Authors" title="Permalink"></a></h2><p>The package is developed and maintained by Joshua Lampert (University of Hamburg).</p><h2 id="License-and-contributing"><a class="docs-heading-anchor" href="#License-and-contributing">License and contributing</a><a id="License-and-contributing-1"></a><a class="docs-heading-anchor-permalink" href="#License-and-contributing" title="Permalink"></a></h2><p>KernelInterpolation.jl is published under the MIT license (see <a href="https://github.com/JoshuaLampert/KernelInterpolation.jl/blob/main/LICENSE">License</a>). We are pleased to accept contributions from everyone, preferably in the form of a PR.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="nodesets/">Sets of nodes »</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="Friday 27 December 2024 13:32">Friday 27 December 2024</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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}</code></pre><h2 id="Authors"><a class="docs-heading-anchor" href="#Authors">Authors</a><a id="Authors-1"></a><a class="docs-heading-anchor-permalink" href="#Authors" title="Permalink"></a></h2><p>The package is developed and maintained by Joshua Lampert (University of Hamburg).</p><h2 id="License-and-contributing"><a class="docs-heading-anchor" href="#License-and-contributing">License and contributing</a><a id="License-and-contributing-1"></a><a class="docs-heading-anchor-permalink" href="#License-and-contributing" title="Permalink"></a></h2><p>KernelInterpolation.jl is published under the MIT license (see <a href="https://github.com/JoshuaLampert/KernelInterpolation.jl/blob/main/LICENSE">License</a>). We are pleased to accept contributions from everyone, preferably in the form of a PR.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="nodesets/">Sets of nodes »</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="Friday 27 December 2024 13:36">Friday 27 December 2024</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR109/interpolation/index.html

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p_kernel = plot(x, kernel; label = &quot;Custom kernel&quot;)
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plot!(p_kernel, x, GaussKernel{2}(); label = &quot;Gauss kernel&quot;, title = &quot;Basic function&quot;)
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p_nodes = plot(kernel; title = &quot;Bivariate custom kernel&quot;)
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plot(p_kernel, p_nodes, layout = (1, 2))</code></pre><p><img src="../kernel_custom.png" alt="Custom kernel"/></p><h2 id="Next-steps"><a class="docs-heading-anchor" href="#Next-steps">Next steps</a><a id="Next-steps-1"></a><a class="docs-heading-anchor-permalink" href="#Next-steps" title="Permalink"></a></h2><p>More examples regarding interpolation can be found in the <a href="https://github.com/JoshuaLampert/KernelInterpolation.jl/tree/main/examples/interpolation">examples</a> folder of the repository. Some easy possible tasks for further investigation are to try different kernels, more complicated sets of nodes, or different functions. When you try out to use more complex node sets, you might want to use the <code>merge</code> function to combine different <a href="../ref/#KernelInterpolation.NodeSet"><code>NodeSet</code></a>s. Note, however, that the interpolation problem might become ill-posed if the nodes are too close to each other. If there are at least twice the same nodes, the system matrix will become singular. In this case, you might want to filter out the duplicate nodes, e.g., by using <code>unique!</code>. For more information on kernel-based interpolation methods, we recommend the following references:</p><h2 id="References"><a class="docs-heading-anchor" href="#References">References</a><a id="References-1"></a><a class="docs-heading-anchor-permalink" href="#References" title="Permalink"></a></h2><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-Wendland2004"><a class="tag is-link" href="#citeref-Wendland2004">Wendland2004</a>Wendland (2004): Scattered Data Approximation, Cambridge University Press, <a href="https://doi.org/10.1017/CBO9780511617539">DOI: 10.1017/CBO9780511617539</a>.</li><li class="footnote" id="footnote-Fasshauer2007"><a class="tag is-link" href="#citeref-Fasshauer2007">Fasshauer2007</a>Fasshauer (2007): Meshfree Approximation Methods with Matlab, World Scientific, <a href="https://doi.org/10.1142/6437">DOI: 10.1142/6437</a>.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../nodesets/">« Sets of nodes</a><a class="docs-footer-nextpage" href="../pdes/">Solving PDEs by collocation »</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="Friday 27 December 2024 13:32">Friday 27 December 2024</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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plot(p_kernel, p_nodes, layout = (1, 2))</code></pre><p><img src="../kernel_custom.png" alt="Custom kernel"/></p><h2 id="Next-steps"><a class="docs-heading-anchor" href="#Next-steps">Next steps</a><a id="Next-steps-1"></a><a class="docs-heading-anchor-permalink" href="#Next-steps" title="Permalink"></a></h2><p>More examples regarding interpolation can be found in the <a href="https://github.com/JoshuaLampert/KernelInterpolation.jl/tree/main/examples/interpolation">examples</a> folder of the repository. Some easy possible tasks for further investigation are to try different kernels, more complicated sets of nodes, or different functions. When you try out to use more complex node sets, you might want to use the <code>merge</code> function to combine different <a href="../ref/#KernelInterpolation.NodeSet"><code>NodeSet</code></a>s. Note, however, that the interpolation problem might become ill-posed if the nodes are too close to each other. If there are at least twice the same nodes, the system matrix will become singular. In this case, you might want to filter out the duplicate nodes, e.g., by using <code>unique!</code>. For more information on kernel-based interpolation methods, we recommend the following references:</p><h2 id="References"><a class="docs-heading-anchor" href="#References">References</a><a id="References-1"></a><a class="docs-heading-anchor-permalink" href="#References" title="Permalink"></a></h2><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-Wendland2004"><a class="tag is-link" href="#citeref-Wendland2004">Wendland2004</a>Wendland (2004): Scattered Data Approximation, Cambridge University Press, <a href="https://doi.org/10.1017/CBO9780511617539">DOI: 10.1017/CBO9780511617539</a>.</li><li class="footnote" id="footnote-Fasshauer2007"><a class="tag is-link" href="#citeref-Fasshauer2007">Fasshauer2007</a>Fasshauer (2007): Meshfree Approximation Methods with Matlab, World Scientific, <a href="https://doi.org/10.1142/6437">DOI: 10.1142/6437</a>.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../nodesets/">« Sets of nodes</a><a class="docs-footer-nextpage" href="../pdes/">Solving PDEs by collocation »</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="Friday 27 December 2024 13:36">Friday 27 December 2024</span>. Using Julia version 1.10.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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