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{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-07-18T09:19:36","documenter_version":"1.5.0"}}
{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-07-18T09:28:36","documenter_version":"1.5.0"}}
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Atomic Models · BcdiCore.jl</title><meta name="title" content="Atomic Models · BcdiCore.jl"/><meta property="og:title" content="Atomic Models · BcdiCore.jl"/><meta property="twitter:title" content="Atomic Models · BcdiCore.jl"/><meta name="description" content="Documentation for BcdiCore.jl."/><meta property="og:description" content="Documentation for BcdiCore.jl."/><meta property="twitter:description" content="Documentation for BcdiCore.jl."/><script data-outdated-warner src="../../assets/warner.js"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/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" 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class="docs-menu"><li><a class="tocitem" href="../../">Main</a></li><li><span class="tocitem">Usage</span><ul><li><a class="tocitem" href="../overview/">Overview</a></li><li class="is-active"><a class="tocitem" href>Atomic Models</a><ul class="internal"><li><a class="tocitem" href="#Mathematical-Definitions"><span>Mathematical Definitions</span></a></li><li><a class="tocitem" href="#Usage"><span>Usage</span></a></li></ul></li><li><a class="tocitem" href="../meso/">Mesoscale Models</a></li><li><a class="tocitem" href="../trad/">Traditional Models</a></li><li><a class="tocitem" href="../multi/">Multiscale Modes</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"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Usage</a></li><li class="is-active"><a href>Atomic Models</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Atomic Models</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/byu-cig/BcdiCore.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/byu-cig/BcdiCore.jl/blob/main/docs/src/use/atomic.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h2 id="Mathematical-Definitions"><a class="docs-heading-anchor" href="#Mathematical-Definitions">Mathematical Definitions</a><a id="Mathematical-Definitions-1"></a><a class="docs-heading-anchor-permalink" href="#Mathematical-Definitions" title="Permalink"></a></h2><p>For the atomic model, <span>$G(u)$</span> is defined as</p><p class="math-container">\[G(h,k,l) = \sum_j e^{-i (x_j (h+G_h) + y_j (k+G_k) + z_j (l+G_l))} \\\]</p><p>where <span>$x_j, y_j, z_j$</span> are atom positions and <span>$h,k,l$</span> represent a distance away from some scattering vector <span>$G_h, G_k, G_l$</span> in reciprocal space. It is important that the <span>$h,k,l$</span> value are integers and that they range from <span>$-\frac{n}{2} \to \frac{n}{2}-1$</span>, so both real space and reciprocal space positions must be scaled. The <span>$x_j,y_j,z_j$</span> positions should be shifted to lie between <span>$0 \to 1$</span> and should be multiplied by <span>$2\pi$</span> to capture the missing <span>$2 \pi$</span> scaling in the Fourier transform exponent.</p><h2 id="Usage"><a class="docs-heading-anchor" href="#Usage">Usage</a><a id="Usage-1"></a><a class="docs-heading-anchor-permalink" href="#Usage" title="Permalink"></a></h2><p>Calculating the loss function and its derivative for the atomic model is done in three steps. First, the <code>BcdiCore.AtomicState</code> struct is created. Then, the atom positions are set by calling <code>BcdiCore.setpts!</code>. Finally, the loss function is calculated with <code>BcdiCore.loss</code>.</p><pre><code class="nohighlight hljs">state = AtomicState(lossType, scale, intens, G, h, k, l)
setpts!(state, x, y, z, getDeriv)
lossVal = loss(state, getDeriv, getLoss)</code></pre><p>If the derivative is requested with the <code>getDeriv</code> variable, the results are stored in <code>state.xDeriv</code>, <code>state.yDeriv</code>, and <code>state.zDeriv</code>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../overview/">« Overview</a><a class="docs-footer-nextpage" href="../meso/">Mesoscale Models »</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 1.5.0 on <span class="colophon-date" title="Thursday 18 July 2024 09:19">Thursday 18 July 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
lossVal = loss(state, getDeriv, getLoss)</code></pre><p>If the derivative is requested with the <code>getDeriv</code> variable, the results are stored in <code>state.xDeriv</code>, <code>state.yDeriv</code>, and <code>state.zDeriv</code>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../overview/">« Overview</a><a class="docs-footer-nextpage" href="../meso/">Mesoscale Models »</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 1.5.0 on <span class="colophon-date" title="Thursday 18 July 2024 09:28">Thursday 18 July 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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