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{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-02T08:36:51","documenter_version":"1.1.0"}} {"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-10-02T09:01:47","documenter_version":"1.1.0"}}

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</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../asp/">« All pairs of shortest paths</a><a class="docs-footer-nextpage" href="../tsp/">Traveling salesperson problem »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Monday 2 October 2023 08:36">Monday 2 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> </script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../asp/">« All pairs of shortest paths</a><a class="docs-footer-nextpage" href="../tsp/">Traveling salesperson problem »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Monday 2 October 2023 09:01">Monday 2 October 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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var myIframe = document.getElementById("notebook"); var myIframe = document.getElementById("notebook");
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}); });
</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../jacobi_method/">« Jacobi method</a><a class="docs-footer-nextpage" href="../LEQ/">Gaussian elimination »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Monday 2 October 2023 08:36">Monday 2 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> </script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../jacobi_method/">« Jacobi method</a><a class="docs-footer-nextpage" href="../LEQ/">Gaussian elimination »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Monday 2 October 2023 09:01">Monday 2 October 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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@ -13,4 +13,4 @@ julia&gt; DataFrame(a=[1,2],b=[3,4])</code></pre><p>You should get an error or a
BenchmarkTools = &quot;6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf&quot; BenchmarkTools = &quot;6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf&quot;
DataFrames = &quot;a93c6f00-e57d-5684-b7b6-d8193f3e46c0&quot; DataFrames = &quot;a93c6f00-e57d-5684-b7b6-d8193f3e46c0&quot;
MPI = &quot;da04e1cc-30fd-572f-bb4f-1f8673147195&quot;</code></pre><p>Copy the contents of previous code block into a file called <code>Project.toml</code> and place it in an empty folder named <code>newproject</code>. It is important that the file is named <code>Project.toml</code>. You can create a new folder from the REPL with</p><pre><code class="language-julia hljs">julia&gt; mkdir(&quot;newproject&quot;)</code></pre><p>To install all the packages registered in this file you need to activate the folder containing your <code>Project.toml</code> file</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; activate newproject</code></pre><p>and then <em>instantiating</em> it</p><pre><code class="language-julia hljs">(newproject) pkg&gt; instantiate</code></pre><p>The instantiate command will download and install all listed packages and their dependencies in just one click.</p><h3 id="Getting-help-in-package-mode"><a class="docs-heading-anchor" href="#Getting-help-in-package-mode">Getting help in package mode</a><a id="Getting-help-in-package-mode-1"></a><a class="docs-heading-anchor-permalink" href="#Getting-help-in-package-mode" title="Permalink"></a></h3><p>You can get help about a particular package operator by writing <code>help</code> in front of it</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; help activate</code></pre><p>You can get an overview of all package commands by typing <code>help</code> alone</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; help</code></pre><h3 id="Package-operations-in-Julia-code"><a class="docs-heading-anchor" href="#Package-operations-in-Julia-code">Package operations in Julia code</a><a id="Package-operations-in-Julia-code-1"></a><a class="docs-heading-anchor-permalink" href="#Package-operations-in-Julia-code" title="Permalink"></a></h3><p>In some situations it is required to use package commands in Julia code, e.g., to automatize installation and deployment of Julia applications. This can be done using the <code>Pkg</code> package. For instance</p><pre><code class="language-julia hljs">julia&gt; using Pkg MPI = &quot;da04e1cc-30fd-572f-bb4f-1f8673147195&quot;</code></pre><p>Copy the contents of previous code block into a file called <code>Project.toml</code> and place it in an empty folder named <code>newproject</code>. It is important that the file is named <code>Project.toml</code>. You can create a new folder from the REPL with</p><pre><code class="language-julia hljs">julia&gt; mkdir(&quot;newproject&quot;)</code></pre><p>To install all the packages registered in this file you need to activate the folder containing your <code>Project.toml</code> file</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; activate newproject</code></pre><p>and then <em>instantiating</em> it</p><pre><code class="language-julia hljs">(newproject) pkg&gt; instantiate</code></pre><p>The instantiate command will download and install all listed packages and their dependencies in just one click.</p><h3 id="Getting-help-in-package-mode"><a class="docs-heading-anchor" href="#Getting-help-in-package-mode">Getting help in package mode</a><a id="Getting-help-in-package-mode-1"></a><a class="docs-heading-anchor-permalink" href="#Getting-help-in-package-mode" title="Permalink"></a></h3><p>You can get help about a particular package operator by writing <code>help</code> in front of it</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; help activate</code></pre><p>You can get an overview of all package commands by typing <code>help</code> alone</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; help</code></pre><h3 id="Package-operations-in-Julia-code"><a class="docs-heading-anchor" href="#Package-operations-in-Julia-code">Package operations in Julia code</a><a id="Package-operations-in-Julia-code-1"></a><a class="docs-heading-anchor-permalink" href="#Package-operations-in-Julia-code" title="Permalink"></a></h3><p>In some situations it is required to use package commands in Julia code, e.g., to automatize installation and deployment of Julia applications. This can be done using the <code>Pkg</code> package. For instance</p><pre><code class="language-julia hljs">julia&gt; using Pkg
julia&gt; Pkg.status()</code></pre><p>is equivalent to calling <code>status</code> in package mode.</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; status</code></pre><h2 id="Conclusion"><a class="docs-heading-anchor" href="#Conclusion">Conclusion</a><a id="Conclusion-1"></a><a class="docs-heading-anchor-permalink" href="#Conclusion" title="Permalink"></a></h2><p>We have learned the basics of how to work with Julia. If you want to further dig into the topics we have covered here, you can take a look at the following links:</p><ul><li><a href="https://docs.julialang.org/en/v1/manual/getting-started/">Julia Manual</a></li><li><a href="https://pkgdocs.julialang.org/v1/getting-started/">Package manager</a></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../julia_basics/">Julia Basics »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Monday 2 October 2023 08:36">Monday 2 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> julia&gt; Pkg.status()</code></pre><p>is equivalent to calling <code>status</code> in package mode.</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; status</code></pre><h2 id="Conclusion"><a class="docs-heading-anchor" href="#Conclusion">Conclusion</a><a id="Conclusion-1"></a><a class="docs-heading-anchor-permalink" href="#Conclusion" title="Permalink"></a></h2><p>We have learned the basics of how to work with Julia. If you want to further dig into the topics we have covered here, you can take a look at the following links:</p><ul><li><a href="https://docs.julialang.org/en/v1/manual/getting-started/">Julia Manual</a></li><li><a href="https://pkgdocs.julialang.org/v1/getting-started/">Package manager</a></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../julia_basics/">Julia Basics »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Monday 2 October 2023 09:01">Monday 2 October 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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var myIframe = document.getElementById("notebook"); var myIframe = document.getElementById("notebook");
iFrameResize({log:true}, myIframe); iFrameResize({log:true}, myIframe);
}); });
</script></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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Monday 2 October 2023 08:36">Monday 2 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> </script></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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Monday 2 October 2023 09:01">Monday 2 October 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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@ -638,7 +638,7 @@
"source": [ "source": [
"### Latency hiding\n", "### Latency hiding\n",
"\n", "\n",
"Can our implementation above be improved? Note that we only need communications to update the values at the boundary of the portion owned by each process. The other values (the one in green in the figure below) can be updated without communications. This provides the opportunity of overlapping the computation of the interior values (green cells in the figure) with the communication of the ghost values. This technique is called latency hiding, since we are hiding communication latency by overlapping it with communication that we need to do anyway.\n", "Can our implementation above be improved? Note that we only need communications to update the values at the boundary of the portion owned by each process. The other values (the one in green in the figure below) can be updated without communications. This provides the opportunity of overlapping the computation of the interior values (green cells in the figure) with the communication of the ghost values. This technique is called latency hiding, since we are hiding communication latency by overlapping it with computation that we need to do anyway.\n",
"\n", "\n",
"The modification of the implementation above to include latency hiding is leaved as an exercise (see below).\n" "The modification of the implementation above to include latency hiding is leaved as an exercise (see below).\n"
] ]

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var myIframe = document.getElementById("notebook"); var myIframe = document.getElementById("notebook");
iFrameResize({log:true}, myIframe); iFrameResize({log:true}, myIframe);
}); });
</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../matrix_matrix/">« Matrix-matrix multiplication</a><a class="docs-footer-nextpage" href="../asp/">All pairs of shortest paths »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Monday 2 October 2023 08:36">Monday 2 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> </script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../matrix_matrix/">« Matrix-matrix multiplication</a><a class="docs-footer-nextpage" href="../asp/">All pairs of shortest paths »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Monday 2 October 2023 09:01">Monday 2 October 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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@ -8198,7 +8198,7 @@ d) the ghost cells of u contain the initial values -1 and 1 in all ranks</code><
</div> </div>
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt"> <div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown"> </div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
<h3 id="Latency-hiding">Latency hiding<a class="anchor-link" href="#Latency-hiding"></a></h3><p>Can our implementation above be improved? Note that we only need communications to update the values at the boundary of the portion owned by each process. The other values (the one in green in the figure below) can be updated without communications. This provides the opportunity of overlapping the computation of the interior values (green cells in the figure) with the communication of the ghost values. This technique is called latency hiding, since we are hiding communication latency by overlapping it with communication that we need to do anyway.</p> <h3 id="Latency-hiding">Latency hiding<a class="anchor-link" href="#Latency-hiding"></a></h3><p>Can our implementation above be improved? Note that we only need communications to update the values at the boundary of the portion owned by each process. The other values (the one in green in the figure below) can be updated without communications. This provides the opportunity of overlapping the computation of the interior values (green cells in the figure) with the communication of the ghost values. This technique is called latency hiding, since we are hiding communication latency by overlapping it with computation that we need to do anyway.</p>
<p>The modification of the implementation above to include latency hiding is leaved as an exercise (see below).</p> <p>The modification of the implementation above to include latency hiding is leaved as an exercise (see below).</p>
</div> </div>
</div> </div>

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var myIframe = document.getElementById("notebook"); var myIframe = document.getElementById("notebook");
iFrameResize({log:true}, myIframe); iFrameResize({log:true}, myIframe);
}); });
</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../julia_basics/">« Julia Basics</a><a class="docs-footer-nextpage" href="../julia_distributed/">Distributed computing in Julia »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Monday 2 October 2023 08:36">Monday 2 October 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> </script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../julia_basics/">« Julia Basics</a><a class="docs-footer-nextpage" href="../julia_distributed/">Distributed computing in Julia »</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><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.1.0 on <span class="colophon-date" title="Monday 2 October 2023 09:01">Monday 2 October 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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@ -152,4 +152,4 @@ end</code></pre><h3 id="Exercise-2-3"><a class="docs-heading-anchor" href="#Exer
end end
return u return u
end end
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iFrameResize({log:true}, myIframe); iFrameResize({log:true}, myIframe);
}); });
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