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Documenter.jl committed Nov 2, 2024
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{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-02T14:12:56","documenter_version":"1.7.0"}}
{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-02T14:27:28","documenter_version":"1.7.0"}}
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end

system = generate_gravitational(123, 1000)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Main.Gravitational{Float64}(Main.Body{Float64}[Main.Body{Float64}([0.9191811597933967, 0.42601923740838954, 0.7465863168484385], 0.0025604152001830723, 0.2538490889415096), Main.Body{Float64}([0.8192008435733007, 0.9541592624784624, 0.8458950823510601], 0.0006827573756872869, 0.03209667335274724), Main.Body{Float64}([0.586748700554989, 0.12181263792534469, 0.7894931647499924], 0.0007507747324898641, 0.8935369466209786), Main.Body{Float64}([0.6192588014774537, 0.47764531343080796, 0.8041934288169849], 0.0016891198058446176, 0.8236563299357046), Main.Body{Float64}([0.12353811904859124, 0.7400202596259494, 0.7057473220960516], 0.002309311138669132, 0.9340155879013086), Main.Body{Float64}([0.9919607797239652, 0.8036971367794874, 0.29827230692896456], 0.003091032513338926, 0.4842893268146866), Main.Body{Float64}([0.49265789199054244, 0.17985285886739166, 0.6397154045236242], 0.0018668795350337605, 0.6922349538863742), Main.Body{Float64}([0.22768758746068596, 0.26780944724527167, 0.8309795986773825], 0.003157596343481429, 0.6911617055492341), Main.Body{Float64}([0.621178864455285, 0.7425206336869923, 0.15487161620983314], 0.0004839315045437943, 0.09206661519876747), Main.Body{Float64}([0.5733898483119126, 0.5900840309886971, 0.7659266276192337], 0.0029381492555510935, 0.37737321139310276) … Main.Body{Float64}([0.2812234741618985, 0.27708389819825585, 0.4235731630417695], 0.0034210382558890573, 0.21244265959226383), Main.Body{Float64}([0.18233133223758657, 0.14916241688519882, 0.20618207218201223], 0.004302370469688393, 0.11811367096065306), Main.Body{Float64}([0.6538431813324862, 0.18465961144472087, 0.6987624957781595], 0.0032758534628382265, 0.1146339723247145), Main.Body{Float64}([0.502384784571667, 0.07721752813458782, 0.044128253140823026], 0.0012068237929352668, 0.8824300122645492), Main.Body{Float64}([0.10622545957526253, 0.23136923168145673, 0.07315362621407251], 0.004639824685179317, 0.5202481974492436), Main.Body{Float64}([0.2644435533586268, 0.3676770504551723, 0.9608299085823863], 0.0009116451209061823, 0.14299177749328063), Main.Body{Float64}([0.44451280995349074, 0.6545010003851659, 0.7398328188365615], 0.000762117045391454, 0.4548855071076938), Main.Body{Float64}([0.7393125867689954, 0.9345095474243973, 0.7672377064661036], 0.004141438543486005, 0.5686419495976187), Main.Body{Float64}([0.6678036693907312, 0.21007708769686184, 0.24471486161349698], 0.004755798682676574, 0.48026240320564606), Main.Body{Float64}([0.4422922153896224, 0.5903414423174669, 0.6120978024383686], 0.0005905059991398905, 0.649924587497539)], [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0])</code></pre><h2 id="Evaluate-The-Potential-at-Each-Body"><a class="docs-heading-anchor" href="#Evaluate-The-Potential-at-Each-Body">Evaluate The Potential at Each Body</a><a id="Evaluate-The-Potential-at-Each-Body-1"></a><a class="docs-heading-anchor-permalink" href="#Evaluate-The-Potential-at-Each-Body" title="Permalink"></a></h2><p>The <code>fmm!</code> function evaluates the gravitational potential induced by <code>system</code> in-place. We can control the tradeoff between performance and accuracy by tuning a handful of parameters for our particular system, but we&#39;ll stick with the defaults for this example:</p><pre><code class="language-julia hljs">fmm.fmm!(system)</code></pre><p>The resulting potential can then be accessed as a field of <code>system</code>.</p><pre><code class="language-julia hljs">@show system.potential[1,:]</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">1000-element Vector{Float64}:
74.34534899255411
63.16302812527192
77.69886677802258
87.80436433007651
76.87041445838584
65.8198268481202
87.03697204997485
78.8849052429896
78.82253402891475
88.2007352913844
74.34535006666736
63.16303142306167
77.69886045695277
87.80436385765044
76.87039459587758
65.8198175648441
87.03696306210689
78.8848821122295
78.82253221081596
88.20073499522836
71.43329657927653
83.25350073954752
65.1298298950103
62.18259687156562
72.94949145243523
71.43329666653969
83.2535031282214
65.12979096714376
62.18260070014051
72.94948420007046
86.42278009063244
68.06275993943673
84.0384452262423
68.06274582312719
84.03846816243086
93.17295917707808</code></pre><h2 id="Accuracy-of-FMM-Call"><a class="docs-heading-anchor" href="#Accuracy-of-FMM-Call">Accuracy of FMM Call</a><a id="Accuracy-of-FMM-Call-1"></a><a class="docs-heading-anchor-permalink" href="#Accuracy-of-FMM-Call" title="Permalink"></a></h2><p>By using the <code>direct!</code> function, we can check the accuracy of the <code>fmm!</code> call by evaluating the &#39;&#39;N&#39;&#39;-body problem naively, without fast multipole acceleration.</p><pre><code class="language-julia hljs">direct_system = deepcopy(system)
direct_system.potential .= 0

fmm.direct!(direct_system)

percent_error = abs.((system.potential[1,:] .- direct_system.potential[1,:]) ./ direct_system.potential[1,:])

@show maximum(percent_error)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">8.797758382673223e-7</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Introduction</a><a class="docs-footer-nextpage" href="../guided_examples/">Guided Examples »</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="Saturday 2 November 2024 14:12">Saturday 2 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
@show maximum(percent_error)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">4.748757699729193e-7</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Introduction</a><a class="docs-footer-nextpage" href="../guided_examples/">Guided Examples »</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="Saturday 2 November 2024 14:27">Saturday 2 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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