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 <!DOCTYPE html>
-<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Exporting data products · Gradus.jl Documentation</title><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img src="../assets/logo.png" alt="Gradus.jl Documentation logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">Gradus.jl Documentation</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../getting-started/">Getting started</a></li><li><a class="tocitem" href="../examples/">Examples</a></li><li><span class="tocitem">Reference &amp; walkthroughs</span><ul><li><a class="tocitem" href="../metrics/">Catalogue of metrics</a></li><li><a class="tocitem" href="../accretion-geometry/">Accretion geometry</a></li><li><a class="tocitem" href="../problems-and-solvers/">Problems and solvers</a></li><li><a class="tocitem" href="../point-functions/">Point functions</a></li><li><a class="tocitem" href="../emissivity/">Disc emissivity</a></li></ul></li><li><span class="tocitem">Geodesics and integration</span><ul><li><a class="tocitem" href="../custom-metrics/">Implementing new metrics</a></li><li><a class="tocitem" href="../geodesic-integration/">Geodesic integration</a></li><li><a class="tocitem" href="../parallelism/">Parallelism and ensembles</a></li><li><a class="tocitem" href="../special-radii/">Special radii</a></li></ul></li><li><span class="tocitem">API</span><ul><li><a class="tocitem" href="../api-documentation/Gradus/">Gradus</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Exporting data products</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Exporting data products</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/astro-group-bristol/Gradus.jl/blob/main/docs/src/exports.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Exporting-data-products"><a class="docs-heading-anchor" href="#Exporting-data-products">Exporting data products</a><a id="Exporting-data-products-1"></a><a class="docs-heading-anchor-permalink" href="#Exporting-data-products" title="Permalink"></a></h1></article><nav class="docs-footer"><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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Friday 4 August 2023 14:36">Friday 4 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Exporting data products · Gradus.jl Documentation</title><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img src="../assets/logo.png" alt="Gradus.jl Documentation logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">Gradus.jl Documentation</a></span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../getting-started/">Getting started</a></li><li><a class="tocitem" href="../examples/">Examples</a></li><li><span class="tocitem">Reference &amp; walkthroughs</span><ul><li><a class="tocitem" href="../metrics/">Catalogue of metrics</a></li><li><a class="tocitem" href="../accretion-geometry/">Accretion geometry</a></li><li><a class="tocitem" href="../problems-and-solvers/">Problems and solvers</a></li><li><a class="tocitem" href="../point-functions/">Point functions</a></li><li><a class="tocitem" href="../emissivity/">Disc emissivity</a></li></ul></li><li><span class="tocitem">Geodesics and integration</span><ul><li><a class="tocitem" href="../custom-metrics/">Implementing new metrics</a></li><li><a class="tocitem" href="../geodesic-integration/">Geodesic integration</a></li><li><a class="tocitem" href="../parallelism/">Parallelism and ensembles</a></li><li><a class="tocitem" href="../special-radii/">Special radii</a></li></ul></li><li><span class="tocitem">API</span><ul><li><a class="tocitem" href="../api-documentation/Gradus/">Gradus</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Exporting data products</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Exporting data products</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/astro-group-bristol/Gradus.jl/blob/main/docs/src/exports.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Exporting-data-products"><a class="docs-heading-anchor" href="#Exporting-data-products">Exporting data products</a><a id="Exporting-data-products-1"></a><a class="docs-heading-anchor-permalink" href="#Exporting-data-products" title="Permalink"></a></h1></article><nav class="docs-footer"><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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 9 September 2023 23:55">Saturday 9 September 2023</span>. 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diff --git a/dev/geodesic-integration/index.html b/dev/geodesic-integration/index.html
@@ -8,9 +8,9 @@
     \partial_{\nu}g_{\rho \sigma}
     + \partial_{\sigma}g_{\rho \nu}
     - \partial_{\rho}g_{\sigma \nu}
-\right).\]</p><p>Limitations:</p><ul><li>currenly pre-supposes static, axis-symmetric metric.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/astro-group-bristol/Gradus.jl/blob/38a1801a5fe3f14ff9ee00398d8a9e691dd1803a/src/tracing/method-implementations/auto-diff.jl#L79-L113">source</a></section></article><p>The above can be solved as a second-order ODE, subject to an initial position and initial velocity</p><p class="math-container">\[u^\mu = \left(t, r, \theta, \phi \right),
+\right).\]</p><p>Limitations:</p><ul><li>currenly pre-supposes static, axis-symmetric metric.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/astro-group-bristol/Gradus.jl/blob/b7a11de5556c35ff06118eeb6fe59fab67b5db45/src/tracing/method-implementations/auto-diff.jl#L79-L113">source</a></section></article><p>The above can be solved as a second-order ODE, subject to an initial position and initial velocity</p><p class="math-container">\[u^\mu = \left(t, r, \theta, \phi \right),
 \quad
 \text{and}
 \quad
 \dot{u}^\mu  
-    = \left( \dot{t}, \dot{r}, \dot{\theta}, \dot{\phi} \right),\]</p><p>where the dot refers to the derivative with respect to <span>$\lambda$</span>. In general, the spatial components of the initial velocity are known <em>a priori</em>, and the time-component is determined via the constraint:</p><article class="docstring"><header><a class="docstring-binding" id="Gradus.constrain_time" href="#Gradus.constrain_time"><code>Gradus.constrain_time</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">constrain_time(g_comp, v, μ = 0.0, positive::Bool = true)</code></pre><p>Constrains the time component of the four-velocity <code>v</code>, given metric components <code>g_comp</code> and effective mass <code>μ</code>.</p><p class="math-container">\[g_{\sigma\nu} \dot{u}^\sigma \dot{u}^\nu = -\mu^2,\]</p><p>for <span>$v^t$</span>. The argument <code>positive</code> allows the sign of <span>$\mu$</span> to be changed. <code>true</code> corresponds to time-like geodesics, <code>false</code> to space-like.</p><p>This function should rarely be directly called, and instead is invoked by <a href="../getting-started/#Gradus.constrain"><code>constrain</code></a>.</p><p>Limitations:</p><ul><li>currenly pre-supposes static, axis-symmetric metric.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/astro-group-bristol/Gradus.jl/blob/38a1801a5fe3f14ff9ee00398d8a9e691dd1803a/src/tracing/method-implementations/auto-diff.jl#L142-L159">source</a></section></article><h2 id="Using-callbacks"><a class="docs-heading-anchor" href="#Using-callbacks">Using callbacks</a><a id="Using-callbacks-1"></a><a class="docs-heading-anchor-permalink" href="#Using-callbacks" title="Permalink"></a></h2></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../custom-metrics/">« Implementing new metrics</a><a class="docs-footer-nextpage" href="../parallelism/">Parallelism and ensembles »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Friday 4 August 2023 14:36">Friday 4 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+    = \left( \dot{t}, \dot{r}, \dot{\theta}, \dot{\phi} \right),\]</p><p>where the dot refers to the derivative with respect to <span>$\lambda$</span>. In general, the spatial components of the initial velocity are known <em>a priori</em>, and the time-component is determined via the constraint:</p><article class="docstring"><header><a class="docstring-binding" id="Gradus.constrain_time" href="#Gradus.constrain_time"><code>Gradus.constrain_time</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">constrain_time(g_comp, v, μ = 0.0, positive::Bool = true)</code></pre><p>Constrains the time component of the four-velocity <code>v</code>, given metric components <code>g_comp</code> and effective mass <code>μ</code>.</p><p class="math-container">\[g_{\sigma\nu} \dot{u}^\sigma \dot{u}^\nu = -\mu^2,\]</p><p>for <span>$v^t$</span>. The argument <code>positive</code> allows the sign of <span>$\mu$</span> to be changed. <code>true</code> corresponds to time-like geodesics, <code>false</code> to space-like.</p><p>This function should rarely be directly called, and instead is invoked by <a href="@ref"><code>_constrain</code></a>.</p><p>Limitations:</p><ul><li>currenly pre-supposes static, axis-symmetric metric.</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/astro-group-bristol/Gradus.jl/blob/b7a11de5556c35ff06118eeb6fe59fab67b5db45/src/tracing/method-implementations/auto-diff.jl#L142-L159">source</a></section></article><h2 id="Using-callbacks"><a class="docs-heading-anchor" href="#Using-callbacks">Using callbacks</a><a id="Using-callbacks-1"></a><a class="docs-heading-anchor-permalink" href="#Using-callbacks" title="Permalink"></a></h2></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../custom-metrics/">« Implementing new metrics</a><a class="docs-footer-nextpage" href="../parallelism/">Parallelism and ensembles »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Saturday 9 September 2023 23:55">Saturday 9 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>