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<title>sol_matrix_matrix</title><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
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<title>solutions</title><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
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<h1 id="Solution-to-Matrix-Multiplication-Exercises">Solution to Matrix Multiplication Exercises<a class="anchor-link" href="#Solution-to-Matrix-Multiplication-Exercises">¶</a></h1><h2 id="Implementation-of-Algorithm-3">Implementation of Algorithm 3<a class="anchor-link" href="#Implementation-of-Algorithm-3">¶</a></h2>
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<h1 id="Solutions-to-Notebook-Exercises">Solutions to Notebook Exercises<a class="anchor-link" href="#Solutions-to-Notebook-Exercises">¶</a></h1><h2 id="Matrix-Multiplication-:-Implementation-of-Algorithm-3">Matrix Multiplication : Implementation of Algorithm 3<a class="anchor-link" href="#Matrix-Multiplication-:-Implementation-of-Algorithm-3">¶</a></h2>
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<h2 id="Jacobi-Method-:-Exercise-1">Jacobi Method : Exercise 1<a class="anchor-link" href="#Jacobi-Method-:-Exercise-1">¶</a></h2>
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<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
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<div class="highlight hl-julia"><pre><span></span><span class="nd">@everywhere</span><span class="w"> </span><span class="n">workers</span><span class="p">()</span><span class="w"> </span><span class="k">begin</span>
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<span class="w"> </span><span class="k">using</span><span class="w"> </span><span class="n">MPI</span>
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<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Initialized</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Init</span><span class="p">()</span>
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<span class="w"> </span><span class="n">comm</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Comm_dup</span><span class="p">(</span><span class="n">MPI</span><span class="o">.</span><span class="n">COMM_WORLD</span><span class="p">)</span>
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<span class="w"> </span><span class="n">nw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Comm_size</span><span class="p">(</span><span class="n">comm</span><span class="p">)</span>
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<span class="w"> </span><span class="n">iw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Comm_rank</span><span class="p">(</span><span class="n">comm</span><span class="p">)</span><span class="o">+</span><span class="mi">1</span>
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<span class="w"> </span><span class="k">function</span><span class="w"> </span><span class="n">jacobi_mpi</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">niters</span><span class="p">)</span>
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<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">mod</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">nw</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span>
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<span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="s">"n must be a multiple of nw"</span><span class="p">)</span>
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<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Abort</span><span class="p">(</span><span class="n">comm</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
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<span class="w"> </span><span class="k">end</span>
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<span class="w"> </span><span class="n">n_own</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">div</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">nw</span><span class="p">)</span>
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<span class="w"> </span><span class="n">u</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">zeros</span><span class="p">(</span><span class="n">n_own</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span>
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<span class="w"> </span><span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
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<span class="w"> </span><span class="n">u</span><span class="p">[</span><span class="k">end</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
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<span class="w"> </span><span class="n">u_new</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">copy</span><span class="p">(</span><span class="n">u</span><span class="p">)</span>
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<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">:</span><span class="n">niters</span>
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<span class="w"> </span><span class="n">reqs_snd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Request</span><span class="p">[]</span>
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<span class="w"> </span><span class="n">reqs_rcv</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Request</span><span class="p">[]</span>
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<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">iw</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">1</span>
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<span class="w"> </span><span class="n">neig_rank</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">iw</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
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<span class="w"> </span><span class="n">req</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Isend</span><span class="p">(</span><span class="n">view</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="mi">2</span><span class="o">:</span><span class="mi">2</span><span class="p">),</span><span class="n">comm</span><span class="p">,</span><span class="n">dest</span><span class="o">=</span><span class="n">neig_rank</span><span class="p">,</span><span class="n">tag</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
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<span class="w"> </span><span class="n">push!</span><span class="p">(</span><span class="n">reqs_snd</span><span class="p">,</span><span class="n">req</span><span class="p">)</span>
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<span class="w"> </span><span class="n">req</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Irecv!</span><span class="p">(</span><span class="n">view</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="mi">1</span><span class="o">:</span><span class="mi">1</span><span class="p">),</span><span class="n">comm</span><span class="p">,</span><span class="n">source</span><span class="o">=</span><span class="n">neig_rank</span><span class="p">,</span><span class="n">tag</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
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<span class="w"> </span><span class="n">push!</span><span class="p">(</span><span class="n">reqs_rcv</span><span class="p">,</span><span class="n">req</span><span class="p">)</span>
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<span class="w"> </span><span class="k">end</span>
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<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">iw</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">nw</span>
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<span class="w"> </span><span class="n">neig_rank</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">iw</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
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<span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n_own</span><span class="o">-</span><span class="mi">1</span>
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<span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n_own</span>
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<span class="w"> </span><span class="n">req</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Isend</span><span class="p">(</span><span class="n">view</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="n">s</span><span class="o">:</span><span class="n">s</span><span class="p">),</span><span class="n">comm</span><span class="p">,</span><span class="n">dest</span><span class="o">=</span><span class="n">neig_rank</span><span class="p">,</span><span class="n">tag</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
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<span class="w"> </span><span class="n">push!</span><span class="p">(</span><span class="n">reqs_snd</span><span class="p">,</span><span class="n">req</span><span class="p">)</span>
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<span class="w"> </span><span class="n">req</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Irecv!</span><span class="p">(</span><span class="n">view</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="n">r</span><span class="o">:</span><span class="n">r</span><span class="p">),</span><span class="n">comm</span><span class="p">,</span><span class="n">source</span><span class="o">=</span><span class="n">neig_rank</span><span class="p">,</span><span class="n">tag</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
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<span class="w"> </span><span class="n">push!</span><span class="p">(</span><span class="n">reqs_rcv</span><span class="p">,</span><span class="n">req</span><span class="p">)</span>
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<span class="w"> </span><span class="k">end</span>
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<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">3</span><span class="o">:</span><span class="n">n_own</span>
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<span class="w"> </span><span class="n">u_new</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.5</span><span class="o">*</span><span class="p">(</span><span class="n">u</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="n">u</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">])</span>
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<span class="w"> </span><span class="k">end</span>
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<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Waitall</span><span class="p">(</span><span class="n">reqs_rcv</span><span class="p">)</span>
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<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="n">n_own</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
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<span class="w"> </span><span class="n">u_new</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.5</span><span class="o">*</span><span class="p">(</span><span class="n">u</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="n">u</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">])</span>
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<span class="w"> </span><span class="k">end</span>
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<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Waitall</span><span class="p">(</span><span class="n">reqs_snd</span><span class="p">)</span>
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<span class="w"> </span><span class="n">u</span><span class="p">,</span><span class="w"> </span><span class="n">u_new</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">u_new</span><span class="p">,</span><span class="w"> </span><span class="n">u</span>
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<span class="w"> </span><span class="k">end</span>
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<span class="w"> </span><span class="n">u</span>
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<span class="w"> </span><span class="k">end</span>
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<span class="w"> </span><span class="n">niters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100</span>
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<span class="w"> </span><span class="n">load</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span>
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<span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">load</span><span class="o">*</span><span class="n">nw</span>
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<span class="w"> </span><span class="n">jacobi_mpi</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">niters</span><span class="p">)</span>
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<span class="k">end</span>
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</pre></div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</main>
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</body>
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</html>
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<!DOCTYPE html>
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>- · XM_40017</title><script data-outdated-warner src="../../assets/warner.js"></script><link rel="canonical" href="https://fverdugo.github.io/XM_40017/notebooks/jacobi_2D/"/><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><link href="../../assets/favicon.ico" rel="icon" type="image/x-icon"/><script src="../../assets/iframeResizer.min.js"></script><link href="../../assets/custom.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="XM_40017 logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../">XM_40017</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_with_julia/">Getting started</a></li><li><span class="tocitem">Notebooks</span><ul><li><a class="tocitem" href="../julia_basics/">Julia Basics</a></li><li><a class="tocitem" href="../julia_async/">Tasks and channels</a></li><li><a class="tocitem" href="../julia_distributed/">Remote calls and remote channels</a></li><li><a class="tocitem" href="../matrix_matrix/">Matrix Multiplication</a></li><li><a class="tocitem" href="../jacobi_method/">Jacobi</a></li><li><a class="tocitem" href="../sol_matrix_matrix/">Solutions</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>-</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>-</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/fverdugo/XM_40017/blob/main/docs/src/notebooks/jacobi_2D.ipynb" 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"><div class="admonition is-success">
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>- · XM_40017</title><script data-outdated-warner src="../../assets/warner.js"></script><link rel="canonical" href="https://fverdugo.github.io/XM_40017/notebooks/notebook-hello/"/><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><link href="../../assets/favicon.ico" rel="icon" type="image/x-icon"/><script src="../../assets/iframeResizer.min.js"></script><link href="../../assets/custom.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="XM_40017 logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../">XM_40017</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_with_julia/">Getting started</a></li><li><span class="tocitem">Notebooks</span><ul><li><a class="tocitem" href="../julia_basics/">Julia Basics</a></li><li><a class="tocitem" href="../julia_async/">Tasks and channels</a></li><li><a class="tocitem" href="../julia_distributed/">Remote calls and remote channels</a></li><li><a class="tocitem" href="../matrix_matrix/">Matrix Multiplication</a></li><li><a class="tocitem" href="../jacobi_method/">Jacobi</a></li><li><a class="tocitem" href="../solutions/">Solutions</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>-</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>-</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/fverdugo/XM_40017/blob/main/docs/src/notebooks/notebook-hello.ipynb" 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"><div class="admonition is-success">
|
||||
<header class="admonition-header">Tip</header>
|
||||
<div class="admonition-body">
|
||||
<ul>
|
||||
@ -18,4 +18,4 @@
|
||||
var myIframe = document.getElementById("notebook");
|
||||
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></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 11 August 2023 13:46">Friday 11 August 2023</span>. Using Julia version 1.9.2.</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></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="Monday 14 August 2023 09:50">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||
|
||||
@ -1,60 +0,0 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "d6d12733",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Solution to Matrix Multiplication Exercises\n",
|
||||
"\n",
|
||||
"## Implementation of Algorithm 3"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "be73e87a",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"function matmul_dist_3!(C,A,B)\n",
|
||||
" m = size(C,1)\n",
|
||||
" n = size(C,2)\n",
|
||||
" l = size(A,2)\n",
|
||||
" @assert size(A,1) == m\n",
|
||||
" @assert size(B,2) == n\n",
|
||||
" @assert size(B,1) == l\n",
|
||||
" @assert mod(m,nworkers()) == 0\n",
|
||||
" # Implement here\n",
|
||||
" nrows_w = div(m,nworkers())\n",
|
||||
" @sync for (i,w) in enumerate(workers())\n",
|
||||
" rows_w = (1:nrows_w) .+ (i-1)*nrows_w\n",
|
||||
" Aw = A[rows_w,:]\n",
|
||||
" ftr = @spawnat w begin\n",
|
||||
" Cw = similar(Aw,nrows_w,n)\n",
|
||||
" matmul_seq!(Cw,Aw,B)\n",
|
||||
" Cw\n",
|
||||
" end\n",
|
||||
" @async C[rows_w,:] = fetch(ftr)\n",
|
||||
" end\n",
|
||||
" C\n",
|
||||
"end"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Julia 1.9.1",
|
||||
"language": "julia",
|
||||
"name": "julia-1.9"
|
||||
},
|
||||
"language_info": {
|
||||
"file_extension": ".jl",
|
||||
"mimetype": "application/julia",
|
||||
"name": "julia",
|
||||
"version": "1.9.1"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
@ -1,21 +0,0 @@
|
||||
<!DOCTYPE html>
|
||||
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Solutions · XM_40017</title><script data-outdated-warner src="../../assets/warner.js"></script><link rel="canonical" href="https://fverdugo.github.io/XM_40017/notebooks/sol_matrix_matrix/"/><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><link href="../../assets/favicon.ico" rel="icon" type="image/x-icon"/><script src="../../assets/iframeResizer.min.js"></script><link href="../../assets/custom.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="XM_40017 logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../">XM_40017</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_with_julia/">Getting started</a></li><li><span class="tocitem">Notebooks</span><ul><li><a class="tocitem" href="../julia_basics/">Julia Basics</a></li><li><a class="tocitem" href="../julia_async/">Tasks and channels</a></li><li><a class="tocitem" href="../julia_distributed/">Remote calls and remote channels</a></li><li><a class="tocitem" href="../matrix_matrix/">Matrix Multiplication</a></li><li><a class="tocitem" href="../jacobi_method/">Jacobi</a></li><li class="is-active"><a class="tocitem" href>Solutions</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><a class="is-disabled">Notebooks</a></li><li class="is-active"><a href>Solutions</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Solutions</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/fverdugo/XM_40017/blob/main/docs/src/notebooks/sol_matrix_matrix.ipynb" 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"><div class="admonition is-success">
|
||||
<header class="admonition-header">Tip</header>
|
||||
<div class="admonition-body">
|
||||
<ul>
|
||||
<li>
|
||||
Download this notebook and run it locally on your machine [recommended]. Click <a href="sol_matrix_matrix.ipynb" download>here</a>.
|
||||
</li>
|
||||
<li>
|
||||
You can also run this notebook in the cloud using Binder. Click <a href="https://mybinder.org/v2/gh/fverdugo/XM_40017/gh-pages?filepath=dev/notebooks/sol_matrix_matrix.ipynb">here</a>
|
||||
.
|
||||
</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div><iframe id="notebook" src="../notebook-html/sol_matrix_matrix.html" style="width:100%"></iframe>
|
||||
<script>
|
||||
document.addEventListener('DOMContentLoaded', function(){
|
||||
var myIframe = document.getElementById("notebook");
|
||||
iFrameResize({log:true}, myIframe);
|
||||
});
|
||||
</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../jacobi_method/">« Jacobi</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 11 August 2023 13:46">Friday 11 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||
129
dev/notebooks/solutions.ipynb
Normal file
129
dev/notebooks/solutions.ipynb
Normal file
@ -0,0 +1,129 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "d6d12733",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Solutions to Notebook Exercises\n",
|
||||
"\n",
|
||||
"## Matrix Multiplication : Implementation of Algorithm 3"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "be73e87a",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"function matmul_dist_3!(C,A,B)\n",
|
||||
" m = size(C,1)\n",
|
||||
" n = size(C,2)\n",
|
||||
" l = size(A,2)\n",
|
||||
" @assert size(A,1) == m\n",
|
||||
" @assert size(B,2) == n\n",
|
||||
" @assert size(B,1) == l\n",
|
||||
" @assert mod(m,nworkers()) == 0\n",
|
||||
" # Implement here\n",
|
||||
" nrows_w = div(m,nworkers())\n",
|
||||
" @sync for (i,w) in enumerate(workers())\n",
|
||||
" rows_w = (1:nrows_w) .+ (i-1)*nrows_w\n",
|
||||
" Aw = A[rows_w,:]\n",
|
||||
" ftr = @spawnat w begin\n",
|
||||
" Cw = similar(Aw,nrows_w,n)\n",
|
||||
" matmul_seq!(Cw,Aw,B)\n",
|
||||
" Cw\n",
|
||||
" end\n",
|
||||
" @async C[rows_w,:] = fetch(ftr)\n",
|
||||
" end\n",
|
||||
" C\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "2d9f4813",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Jacobi Method : Exercise 1"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "cf3b1e72",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"@everywhere workers() begin\n",
|
||||
" using MPI\n",
|
||||
" MPI.Initialized() || MPI.Init()\n",
|
||||
" comm = MPI.Comm_dup(MPI.COMM_WORLD)\n",
|
||||
" nw = MPI.Comm_size(comm)\n",
|
||||
" iw = MPI.Comm_rank(comm)+1\n",
|
||||
" function jacobi_mpi(n,niters)\n",
|
||||
" if mod(n,nw) != 0\n",
|
||||
" println(\"n must be a multiple of nw\")\n",
|
||||
" MPI.Abort(comm,1)\n",
|
||||
" end\n",
|
||||
" n_own = div(n,nw)\n",
|
||||
" u = zeros(n_own+2)\n",
|
||||
" u[1] = -1\n",
|
||||
" u[end] = 1\n",
|
||||
" u_new = copy(u)\n",
|
||||
" for t in 1:niters\n",
|
||||
" reqs_snd = MPI.Request[]\n",
|
||||
" reqs_rcv = MPI.Request[]\n",
|
||||
" if iw != 1\n",
|
||||
" neig_rank = (iw-1)-1\n",
|
||||
" req = MPI.Isend(view(u,2:2),comm,dest=neig_rank,tag=0)\n",
|
||||
" push!(reqs_snd,req)\n",
|
||||
" req = MPI.Irecv!(view(u,1:1),comm,source=neig_rank,tag=0)\n",
|
||||
" push!(reqs_rcv,req)\n",
|
||||
" end\n",
|
||||
" if iw != nw\n",
|
||||
" neig_rank = (iw+1)-1\n",
|
||||
" s = n_own-1\n",
|
||||
" r = n_own\n",
|
||||
" req = MPI.Isend(view(u,s:s),comm,dest=neig_rank,tag=0)\n",
|
||||
" push!(reqs_snd,req)\n",
|
||||
" req = MPI.Irecv!(view(u,r:r),comm,source=neig_rank,tag=0)\n",
|
||||
" push!(reqs_rcv,req)\n",
|
||||
" end\n",
|
||||
" for i in 3:n_own\n",
|
||||
" u_new[i] = 0.5*(u[i-1]+u[i+1])\n",
|
||||
" end\n",
|
||||
" MPI.Waitall(reqs_rcv)\n",
|
||||
" for i in (2,n_own+1)\n",
|
||||
" u_new[i] = 0.5*(u[i-1]+u[i+1])\n",
|
||||
" end\n",
|
||||
" MPI.Waitall(reqs_snd)\n",
|
||||
" u, u_new = u_new, u\n",
|
||||
" end\n",
|
||||
" u\n",
|
||||
" end\n",
|
||||
" niters = 100\n",
|
||||
" load = 4\n",
|
||||
" n = load*nw\n",
|
||||
" jacobi_mpi(n,niters)\n",
|
||||
"end"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Julia 1.9.1",
|
||||
"language": "julia",
|
||||
"name": "julia-1.9"
|
||||
},
|
||||
"language_info": {
|
||||
"file_extension": ".jl",
|
||||
"mimetype": "application/julia",
|
||||
"name": "julia",
|
||||
"version": "1.9.1"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
21
dev/notebooks/solutions/index.html
Normal file
21
dev/notebooks/solutions/index.html
Normal file
@ -0,0 +1,21 @@
|
||||
<!DOCTYPE html>
|
||||
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Solutions · XM_40017</title><script data-outdated-warner src="../../assets/warner.js"></script><link rel="canonical" href="https://fverdugo.github.io/XM_40017/notebooks/solutions/"/><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><link href="../../assets/favicon.ico" rel="icon" type="image/x-icon"/><script src="../../assets/iframeResizer.min.js"></script><link href="../../assets/custom.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="XM_40017 logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../">XM_40017</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_with_julia/">Getting started</a></li><li><span class="tocitem">Notebooks</span><ul><li><a class="tocitem" href="../julia_basics/">Julia Basics</a></li><li><a class="tocitem" href="../julia_async/">Tasks and channels</a></li><li><a class="tocitem" href="../julia_distributed/">Remote calls and remote channels</a></li><li><a class="tocitem" href="../matrix_matrix/">Matrix Multiplication</a></li><li><a class="tocitem" href="../jacobi_method/">Jacobi</a></li><li class="is-active"><a class="tocitem" href>Solutions</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><a class="is-disabled">Notebooks</a></li><li class="is-active"><a href>Solutions</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Solutions</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/fverdugo/XM_40017/blob/main/docs/src/notebooks/solutions.ipynb" 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"><div class="admonition is-success">
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Download this notebook and run it locally on your machine [recommended]. Click <a href="solutions.ipynb" download>here</a>.
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||||
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|
||||
You can also run this notebook in the cloud using Binder. Click <a href="https://mybinder.org/v2/gh/fverdugo/XM_40017/gh-pages?filepath=dev/notebooks/solutions.ipynb">here</a>
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.
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