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@. u = grid.x + 2 * grid.y + grid.z^2</code></pre><p>Here, <code>grid.x</code>, <code>grid.y</code> and <code>grid.z</code> are a convenient way of extracting the three components of the grid. Alternatively, one can use the syntax <code>grid[1]</code>, <code>grid[2]</code>, etc..., which is in particularly useful when working in dimensions higher than 3.</p><p>Note that one could do the same as above using indexing instead of broadcasting:</p><pre><code class="language-julia hljs">for I ∈ eachindex(grid)
x, y, z = grid[I]
u[I] = x + 2y + z^2
end</code></pre><h2 id="Library"><a class="docs-heading-anchor" href="#Library">Library</a><a id="Library-1"></a><a class="docs-heading-anchor-permalink" href="#Library" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="PencilArrays.LocalGrids.AbstractLocalGrid" href="#PencilArrays.LocalGrids.AbstractLocalGrid"><code>PencilArrays.LocalGrids.AbstractLocalGrid</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">AbstractLocalGrid{N, Perm &lt;: AbstractPermutation}</code></pre><p>Abstract type specifying the local portion of an <code>N</code>-dimensional grid.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jipolanco/PencilArrays.jl/blob/4cc1ff5e8b8b22cbb825913a827777142dbbc4d3/src/LocalGrids/LocalGrids.jl#LL12-L16">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PencilArrays.LocalGrids.LocalRectilinearGrid" href="#PencilArrays.LocalGrids.LocalRectilinearGrid"><code>PencilArrays.LocalGrids.LocalRectilinearGrid</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">LocalRectilinearGrid{N, Perm} &lt;: AbstractLocalGrid{N, Perm}</code></pre><p>Defines the local portion of a rectilinear grid in <code>N</code> dimensions.</p><p>A rectilinear grid is represented by a set of orthogonal coordinates <code>(x, y, z, ...)</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jipolanco/PencilArrays.jl/blob/4cc1ff5e8b8b22cbb825913a827777142dbbc4d3/src/LocalGrids/rectilinear.jl#LL1-L7">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PencilArrays.LocalGrids.localgrid" href="#PencilArrays.LocalGrids.localgrid"><code>PencilArrays.LocalGrids.localgrid</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">localgrid(x::PencilArray, args...)</code></pre><p>Equivalent of <code>localgrid(pencil(x), args...)</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jipolanco/PencilArrays.jl/blob/4cc1ff5e8b8b22cbb825913a827777142dbbc4d3/src/arrays.jl#LL549-L553">source</a></section><section><div><pre><code class="nohighlight hljs">localgrid((xs, ys, ...), perm = NoPermutation()) -&gt; LocalRectilinearGrid</code></pre><p>Create a <a href="#PencilArrays.LocalGrids.LocalRectilinearGrid"><code>LocalRectilinearGrid</code></a> from a set of orthogonal coordinates <code>(xs, ys, ...)</code>, where each element is an <code>AbstractVector</code>.</p><p>Optionally, one can pass a static permutation (as in <code>Permutation(2, 1, 3)</code>) to change the order in which the coordinates are iterated.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jipolanco/PencilArrays.jl/blob/4cc1ff5e8b8b22cbb825913a827777142dbbc4d3/src/LocalGrids/rectilinear.jl#LL17-L25">source</a></section><section><div><pre><code class="nohighlight hljs">localgrid(p::Pencil, (x_global, y_global, ...)) -&gt; LocalRectilinearGrid
localgrid(u::PencilArray, (x_global, y_global, ...)) -&gt; LocalRectilinearGrid</code></pre><p>Create a <a href="#PencilArrays.LocalGrids.LocalRectilinearGrid"><code>LocalRectilinearGrid</code></a> from a decomposition configuration and from a set of orthogonal global coordinates <code>(x_global, y_global, ...)</code>.</p><p>In this case, each <code>*_global</code> is an <code>AbstractVector</code> describing the coordinates along one dimension of the global grid.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jipolanco/PencilArrays.jl/blob/4cc1ff5e8b8b22cbb825913a827777142dbbc4d3/src/Pencils/Pencils.jl#LL589-L599">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PencilArrays.LocalGrids.components" href="#PencilArrays.LocalGrids.components"><code>PencilArrays.LocalGrids.components</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">LocalGrids.components(g::LocalRectilinearGrid) -&gt; (xs, ys, zs, ...)</code></pre><p>Get coordinates associated to the current MPI process.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jipolanco/PencilArrays.jl/blob/4cc1ff5e8b8b22cbb825913a827777142dbbc4d3/src/LocalGrids/LocalGrids.jl#LL23-L27">source</a></section></article><h2 id="Index"><a class="docs-heading-anchor" href="#Index">Index</a><a id="Index-1"></a><a class="docs-heading-anchor-permalink" href="#Index" title="Permalink"></a></h2><ul><li><a href="#PencilArrays.LocalGrids.AbstractLocalGrid"><code>PencilArrays.LocalGrids.AbstractLocalGrid</code></a></li><li><a href="#PencilArrays.LocalGrids.LocalRectilinearGrid"><code>PencilArrays.LocalGrids.LocalRectilinearGrid</code></a></li><li><a href="#PencilArrays.LocalGrids.components"><code>PencilArrays.LocalGrids.components</code></a></li><li><a href="#PencilArrays.LocalGrids.localgrid"><code>PencilArrays.LocalGrids.localgrid</code></a></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../PencilArrays/">« Array wrappers</a><a class="docs-footer-nextpage" href="../Transpositions/">Global MPI operations »</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 0.27.24 on <span class="colophon-date" title="Tuesday 21 February 2023 08:44">Tuesday 21 February 2023</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
end</code></pre><h2 id="Library"><a class="docs-heading-anchor" href="#Library">Library</a><a id="Library-1"></a><a class="docs-heading-anchor-permalink" href="#Library" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="PencilArrays.LocalGrids.AbstractLocalGrid" href="#PencilArrays.LocalGrids.AbstractLocalGrid"><code>PencilArrays.LocalGrids.AbstractLocalGrid</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">AbstractLocalGrid{N, Perm &lt;: AbstractPermutation}</code></pre><p>Abstract type specifying the local portion of an <code>N</code>-dimensional grid.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jipolanco/PencilArrays.jl/blob/17af2d5f8ecb2b1459aa04691b200c0e521f7de3/src/LocalGrids/LocalGrids.jl#LL12-L16">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PencilArrays.LocalGrids.LocalRectilinearGrid" href="#PencilArrays.LocalGrids.LocalRectilinearGrid"><code>PencilArrays.LocalGrids.LocalRectilinearGrid</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">LocalRectilinearGrid{N, Perm} &lt;: AbstractLocalGrid{N, Perm}</code></pre><p>Defines the local portion of a rectilinear grid in <code>N</code> dimensions.</p><p>A rectilinear grid is represented by a set of orthogonal coordinates <code>(x, y, z, ...)</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jipolanco/PencilArrays.jl/blob/17af2d5f8ecb2b1459aa04691b200c0e521f7de3/src/LocalGrids/rectilinear.jl#LL1-L7">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PencilArrays.LocalGrids.localgrid" href="#PencilArrays.LocalGrids.localgrid"><code>PencilArrays.LocalGrids.localgrid</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">localgrid(x::PencilArray, args...)</code></pre><p>Equivalent of <code>localgrid(pencil(x), args...)</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jipolanco/PencilArrays.jl/blob/17af2d5f8ecb2b1459aa04691b200c0e521f7de3/src/arrays.jl#LL545-L549">source</a></section><section><div><pre><code class="nohighlight hljs">localgrid(p::Pencil, (x_global, y_global, ...)) -&gt; LocalRectilinearGrid
localgrid(u::PencilArray, (x_global, y_global, ...)) -&gt; LocalRectilinearGrid</code></pre><p>Create a <a href="#PencilArrays.LocalGrids.LocalRectilinearGrid"><code>LocalRectilinearGrid</code></a> from a decomposition configuration and from a set of orthogonal global coordinates <code>(x_global, y_global, ...)</code>.</p><p>In this case, each <code>*_global</code> is an <code>AbstractVector</code> describing the coordinates along one dimension of the global grid.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jipolanco/PencilArrays.jl/blob/17af2d5f8ecb2b1459aa04691b200c0e521f7de3/src/Pencils/Pencils.jl#LL589-L599">source</a></section><section><div><pre><code class="nohighlight hljs">localgrid((xs, ys, ...), perm = NoPermutation()) -&gt; LocalRectilinearGrid</code></pre><p>Create a <a href="#PencilArrays.LocalGrids.LocalRectilinearGrid"><code>LocalRectilinearGrid</code></a> from a set of orthogonal coordinates <code>(xs, ys, ...)</code>, where each element is an <code>AbstractVector</code>.</p><p>Optionally, one can pass a static permutation (as in <code>Permutation(2, 1, 3)</code>) to change the order in which the coordinates are iterated.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jipolanco/PencilArrays.jl/blob/17af2d5f8ecb2b1459aa04691b200c0e521f7de3/src/LocalGrids/rectilinear.jl#LL17-L25">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="PencilArrays.LocalGrids.components" href="#PencilArrays.LocalGrids.components"><code>PencilArrays.LocalGrids.components</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">LocalGrids.components(g::LocalRectilinearGrid) -&gt; (xs, ys, zs, ...)</code></pre><p>Get coordinates associated to the current MPI process.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jipolanco/PencilArrays.jl/blob/17af2d5f8ecb2b1459aa04691b200c0e521f7de3/src/LocalGrids/LocalGrids.jl#LL23-L27">source</a></section></article><h2 id="Index"><a class="docs-heading-anchor" href="#Index">Index</a><a id="Index-1"></a><a class="docs-heading-anchor-permalink" href="#Index" title="Permalink"></a></h2><ul><li><a href="#PencilArrays.LocalGrids.AbstractLocalGrid"><code>PencilArrays.LocalGrids.AbstractLocalGrid</code></a></li><li><a href="#PencilArrays.LocalGrids.LocalRectilinearGrid"><code>PencilArrays.LocalGrids.LocalRectilinearGrid</code></a></li><li><a href="#PencilArrays.LocalGrids.components"><code>PencilArrays.LocalGrids.components</code></a></li><li><a href="#PencilArrays.LocalGrids.localgrid"><code>PencilArrays.LocalGrids.localgrid</code></a></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../PencilArrays/">« Array wrappers</a><a class="docs-footer-nextpage" href="../Transpositions/">Global MPI operations »</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="Tuesday 19 September 2023 07:03">Tuesday 19 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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