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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><meta name="title" content="- · XM_40017"/><meta property="og:title" content="- · XM_40017"/><meta property="twitter:title" content="- · XM_40017"/><meta name="description" content="Documentation for XM_40017."/><meta property="og:description" content="Documentation for XM_40017."/><meta property="twitter:description" content="Documentation for XM_40017."/><meta property="og:url" content="https://fverdugo.github.io/XM_40017/LEQ/"/><meta property="twitter:url" content="https://fverdugo.github.io/XM_40017/LEQ/"/><link rel="canonical" href="https://fverdugo.github.io/XM_40017/LEQ/"/><script data-outdated-warner src="../assets/warner.js"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 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href="#The-Julia-REPL"><span>The Julia REPL</span></a></li><li><a class="tocitem" href="#Running-Julia-code"><span>Running Julia code</span></a></li><li><a class="tocitem" href="#Package-manager"><span>Package manager</span></a></li><li><a class="tocitem" href="#Conclusion"><span>Conclusion</span></a></li></ul></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/">Asynchronous programming in Julia</a></li><li><a class="tocitem" href="../julia_distributed/">Distributed computing in Julia</a></li><li><a class="tocitem" href="../matrix_matrix/">Matrix-matrix multiplication</a></li><li><a class="tocitem" href="../julia_mpi/">MPI (point-to-point)</a></li><li><a class="tocitem" href="../jacobi_method/">Jacobi method</a></li></ul></li><li><a class="tocitem" href="../solutions_for_all_notebooks/">Solutions</a></li></ul><div class="docs-version-selector field has-addons"><div 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julia> @everywhere println("Hello, world! I am proc $(myid()) from $(nprocs())")</code></pre><p>Here, we are using the <code>Distributed</code> package, which is part of the Julia standard library that provides distributed memory parallel support. The code prints the process id and the number of processes in the current Julia session.</p><p>You will probably only see output from 1 process. We need to add more processes to run the example in parallel. This is done with the <code>addprocs</code> function.</p><pre><code class="language-julia hljs">julia> addprocs(3)</code></pre><p>We have added 3 new processes. Plus the old one, we have 4 processes. Run the code again.</p><pre><code class="language-julia hljs">julia> @everywhere println("Hello, world! I am proc $(myid()) from $(nprocs())")</code></pre><p>Now, you should see output from 4 processes.</p><p>It is possible to specify the number of processes when starting Julia from the terminal with the <code>-p</code> argument (useful, e.g., when running in a cluster). If you launch Julia from the terminal as</p><pre><code class="nohighlight hljs">$ julia -p 3</code></pre><p>and then run</p><pre><code class="language-julia hljs">julia> @everywhere println("Hello, world! I am proc $(myid()) from $(nprocs())")</code></pre><p>You should get output from 4 processes as before.</p><h3 id="Installing-packages"><a class="docs-heading-anchor" href="#Installing-packages">Installing packages</a><a id="Installing-packages-1"></a><a class="docs-heading-anchor-permalink" href="#Installing-packages" title="Permalink"></a></h3><p>One of the most useful features of Julia is its package manager. It allows one to install Julia packages in a straightforward and platform independent way. To illustrate this, let us consider the following parallel "Hello world" example. This example uses the Message Passing Interface (MPI). We will learn more about MPI later in the course.</p><p>Copy the following block of code into a new file named <code>"hello_mpi.jl"</code></p><pre><code class="language-julia hljs"># file hello_mpi.jl
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using MPI
|
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MPI.Init()
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@@ -13,4 +13,4 @@ julia> DataFrame(a=[1,2],b=[3,4])</code></pre><p>You should get an error or a
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BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
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DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
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MPI = "da04e1cc-30fd-572f-bb4f-1f8673147195"</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> mkdir("newproject")</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">(@v1.10) pkg> activate newproject</code></pre><p>and then <em>instantiating</em> it</p><pre><code class="language-julia hljs">(newproject) pkg> 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">(@v1.10) pkg> 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">(@v1.10) pkg> 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> using Pkg
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julia> Pkg.status()</code></pre><p>is equivalent to calling <code>status</code> in package mode.</p><pre><code class="language-julia hljs">(@v1.10) pkg> 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="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="Tuesday 20 August 2024 12:05">Tuesday 20 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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julia> Pkg.status()</code></pre><p>is equivalent to calling <code>status</code> in package mode.</p><pre><code class="language-julia hljs">(@v1.10) pkg> 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="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="Tuesday 20 August 2024 13:32">Tuesday 20 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></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>Home · XM_40017</title><meta name="title" content="Home · XM_40017"/><meta property="og:title" content="Home · XM_40017"/><meta property="twitter:title" content="Home · XM_40017"/><meta name="description" content="Documentation for XM_40017."/><meta property="og:description" content="Documentation for XM_40017."/><meta property="twitter:description" content="Documentation for XM_40017."/><meta property="og:url" content="https://fverdugo.github.io/XM_40017/"/><meta property="twitter:url" content="https://fverdugo.github.io/XM_40017/"/><link rel="canonical" href="https://fverdugo.github.io/XM_40017/"/><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" 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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/">Asynchronous programming in Julia</a></li><li><a class="tocitem" href="julia_distributed/">Distributed computing in Julia</a></li><li><a class="tocitem" href="matrix_matrix/">Matrix-matrix multiplication</a></li><li><a class="tocitem" href="julia_mpi/">MPI (point-to-point)</a></li><li><a class="tocitem" href="jacobi_method/">Jacobi method</a></li></ul></li><li><a class="tocitem" href="solutions_for_all_notebooks/">Solutions</a></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-solLine truncated
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julia> Pkg.add("IJulia")
|
||||
julia> using IJulia
|
||||
julia> notebook()</code></pre><ul><li>These commands will open a jupyter in your web browser. Navigate in jupyter to the notebook file you have downloaded and open it.</li></ul><h2 id="Authors"><a class="docs-heading-anchor" href="#Authors">Authors</a><a id="Authors-1"></a><a class="docs-heading-anchor-permalink" href="#Authors" title="Permalink"></a></h2><p>This material is created by <a href="https://github.com/fverdugo/">Francesc Verdugo</a> with the help of <a href="https://www.linkedin.com/in/gelieza-k/">Gelieza Kötterheinrich</a>. Part of the notebooks are based on the course slides by <a href="https://www.vuhpdc.net/henri-bal/">Henri Bal</a>.</p><h2 id="License"><a class="docs-heading-anchor" href="#License">License</a><a id="License-1"></a><a class="docs-heading-anchor-permalink" href="#License" title="Permalink"></a></h2><p>All material on this page that is original to this course may be used under a <a href="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0</a> license.</p><h2 id="Acknowledgment"><a class="docs-heading-anchor" href="#Acknowledgment">Acknowledgment</a><a id="Acknowledgment-1"></a><a class="docs-heading-anchor-permalink" href="#Acknowledgment" title="Permalink"></a></h2><p>This page was created with the support of the Faculty of Science of <a href="https://vu.nl">Vrije Universiteit Amsterdam</a> in the framework of the project "Interactive lecture notes and exercises for the Programming Large-Scale Parallel Systems course" funded by the "Innovation budget BETA 2023 Studievoorschotmiddelen (SVM) towards Activated Blended Learning".</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="getting_started_with_julia/">Getting started »</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="Tuesday 20 August 2024 12:05">Tuesday 20 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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||||
julia> notebook()</code></pre><ul><li>These commands will open a jupyter in your web browser. Navigate in jupyter to the notebook file you have downloaded and open it.</li></ul><h2 id="Authors"><a class="docs-heading-anchor" href="#Authors">Authors</a><a id="Authors-1"></a><a class="docs-heading-anchor-permalink" href="#Authors" title="Permalink"></a></h2><p>This material is created by <a href="https://github.com/fverdugo/">Francesc Verdugo</a> with the help of <a href="https://www.linkedin.com/in/gelieza-k/">Gelieza Kötterheinrich</a>. Part of the notebooks are based on the course slides by <a href="https://www.vuhpdc.net/henri-bal/">Henri Bal</a>.</p><h2 id="License"><a class="docs-heading-anchor" href="#License">License</a><a id="License-1"></a><a class="docs-heading-anchor-permalink" href="#License" title="Permalink"></a></h2><p>All material on this page that is original to this course may be used under a <a href="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0</a> license.</p><h2 id="Acknowledgment"><a class="docs-heading-anchor" href="#Acknowledgment">Acknowledgment</a><a id="Acknowledgment-1"></a><a class="docs-heading-anchor-permalink" href="#Acknowledgment" title="Permalink"></a></h2><p>This page was created with the support of the Faculty of Science of <a href="https://vu.nl">Vrije Universiteit Amsterdam</a> in the framework of the project "Interactive lecture notes and exercises for the Programming Large-Scale Parallel Systems course" funded by the "Innovation budget BETA 2023 Studievoorschotmiddelen (SVM) towards Activated Blended Learning".</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="getting_started_with_julia/">Getting started »</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="Tuesday 20 August 2024 13:32">Tuesday 20 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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@@ -1,5 +1,5 @@
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<!DOCTYPE html>
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iFrameResize({log:true}, myIframe);
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</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="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="Tuesday 20 August 2024 12:05">Tuesday 20 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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|
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+140
-158
@@ -62,7 +62,8 @@
|
||||
"gauss_seidel_1_check(answer) = answer_checker(answer,\"c\")\n",
|
||||
"jacobi_1_check(answer) = answer_checker(answer, \"d\")\n",
|
||||
"jacobi_2_check(answer) = answer_checker(answer, \"b\")\n",
|
||||
"jacobi_3_check(answer) = answer_checker(answer, \"c\")"
|
||||
"jacobi_3_check(answer) = answer_checker(answer, \"c\")\n",
|
||||
"println(\"🥳 Well done! \")"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -145,7 +146,7 @@
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div class=\"alert alert-block alert-info\">\n",
|
||||
"<b>Note:</b> In our version of the jacobi method, we return after a given number of iterations. Other stopping criteria are possible. For instance, iterate until the difference between u and u_new is below a tolerance. \n",
|
||||
"<b>Note:</b> In our version of the jacobi method, we return after a given number of iterations. Other stopping criteria are possible. For instance, iterate until the difference between u and u_new is below a tolerance.\n",
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
@@ -178,7 +179,7 @@
|
||||
"id": "798968b1",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### The Gauss-Seidel method\n",
|
||||
"### The Gauss-Seidel method \n",
|
||||
"\n",
|
||||
"The usage of `u_new` seems a bit unnecessary at first sight, right?. If we remove it, we get another method called Gauss-Seidel.\n",
|
||||
"\n"
|
||||
@@ -275,7 +276,7 @@
|
||||
"source": [
|
||||
"### Parallelization strategy\n",
|
||||
"\n",
|
||||
"Remember that a sufficiently large grain size is needed to achieve performance in a distributed algorithm. For Jacobi, one could update each entry of vector `u_new` in a different worker, but this would not be efficient. Instead, we use a parallelization strategy with a larger grain size that is analogous to the algorithm 3 we studied for the matrix-matrix multiplication:\n",
|
||||
"Remember that a sufficiently large grain size is needed to achieve performance in a distributed algorithm. For Jacobi, one could update each entry of vector `u_new` in a different process, but this would not be efficient. Instead, we use a parallelization strategy with a larger grain size that is analogous to the algorithm 3 we studied for the matrix-matrix multiplication:\n",
|
||||
"\n",
|
||||
"- Each worker updates a consecutive section of the array `u_new` \n",
|
||||
"\n",
|
||||
@@ -299,16 +300,68 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "3f90d701",
|
||||
"id": "22dc6e54",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Data dependencies\n",
|
||||
"\n",
|
||||
"Recall the Jacobi update:\n",
|
||||
"\n",
|
||||
"`u_new[i] = 0.5*(u[i-1]+u[i+1])`\n",
|
||||
"\n",
|
||||
"Thus, in order to update the local entries in `u_new`, we also need remote entries of vector `u` located in neighboring processes. Figure below shows the entries of `u` needed to update the local entries of `u_new` in a particular process (CPU 2)."
|
||||
"`u_new[i] = 0.5*(u[i-1]+u[i+1])`"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "ba4113af",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Note that an entry in the interior of the locally stored vector can be updated using local data only. For this one, communication is not needed."
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
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"f1.png": {
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truncated
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"cell_type": "markdown",
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||||
"id": "97a5079d",
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||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA6gAAADyCAYAAABAvOgkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAewgAAHsIBbtB1PgAAABl0RVh0U29mdHdhcmUAd3d3Lmlua3NjYXBlLm9yZ5vuPBoAABgzSURBVHic7d19mF11YSfw750kBBIigWJiADUEBOXdRYvgCwtCX/VhH0TbLRVrdUlod/Gpq0+7a1uoL1316RarqzSpZXe77q61Pmu73bZYEFOtFUSs4BsCQhCEEEyUd4aQ3P3jnGHOTO6duTOZmfObyefzPPfJ79x7zr1fZm5O7pfzO+d2Nm7c2A0AAAC0bKjtAAAAAJAoqAAAABRi8bjln+50OlvaCAIAAMC+pdvtrk3y2ZHlMQW10+lsufjii2+b61AAAADsezZt2pRud/SySKb4AgAAUAQFFQAAgCIoqAAAABRBQQUAAKAICioAAABFUFABAAAogoIKAABAERRUAAAAiqCgAgAAUAQFFQAAgCIoqAAAABRBQQUAAKAICioAAABFUFABAAAowuK2AwAAPb05yZIkVyf5fstZAGBOKKgAUKY/SrIiyWsz/YK6JMmJSU5N8pIkB9f3/26SW/c2YGH+KMnLk/z3JB9p4fUXp/p9JcnjSYZbyAAw7ymoALAw/U6SdyVZ2uOxD89xlrlwdKoifu0cvd6aJOemKv6nJjklybL6sfVJNs1RDoAFRUEFgDK9LdUR0Fumuf2aVOW0m+T2JPcmOXtmopHkgizMog/QKgUVAMr0X/dy+08m+VSSryV5OMlLk3xlb0MV7Oenud2FqaZBfzrJV6e47ZYkN9W3byf5y2lmAKCmoAJAmdamutr+1lTnNE7VF2Y0zcL1r1IdDf1uplZQP5qx57oun8lQAPsqXzMDAGW6Jcn3YlruoN6c5P1JfnaOXm/3HL0OwD7FEVQAYCG4IMnP1eO/azMIANPnCCoAAABFUFABAAAogoIKAABAEZyDCgDzx7IkZ/R57LYk35/DLPPJLyZ5S5/HTqr/fEeSX+qzzvokd850KAD2pKACwPxxWJJr+jz29iRXzGGW+eTIJOdMss5x9a2XA2c2DgD9KKgAMH88nuTaPo85etrfZ5Lc0eextyd5WZKPJdncZ527ZyETAD0oqAAwf9yX5Ny2Q8xDt9a3Xt5Q//nVJH8xN3EA6MdFkgAAACiCggoAAEARTPEFgIVpbZINjeU1jfGGJK9pLH88/c/RBIA5o6ACwML03CS/2eexC8ctXxMFdaoOTvK9xnKnMb4iyfsby7+VZNNchAKY7xRUACjTFUmWZvrF8Z4kHxhwXVepnbpOqpLay7L6NmL/2Y8DsDAoqABQpsv2cvstqY7c7SvekqoU/niK2/3bVEeaH5zidj9OctSA626f4nMD7LMUVABgIdg6ze0emOZ2u5PcOc1tAejDVXwBAAAogoIKAABAERRUAAAAiqCgAgAAUAQFFQAAgCIoqAAAABRBQQUAAKAICioAAABFUFABAAAogoIKAABAERRUAAAAirC47QDQy5VXXnn40NDQG9rOMZGrrrrqVUk6SXLXXXfdsm3bth+1HGm8E5McUo/vSXJni1l6OSLJUfX40SQ3tZhlEFcmebLtEAzkDUkObzvEBJ6fZG09fijJ19uL0tOzkry4sfzFJLtbytLPKzP6P9m/kWRHi1km87Uk/9B2CAby/CTntx1iAp0kr2osfz3VPqQkJydZWY/vTrKlvSh7Wrt27fNXr169NklWrlz50Pnnn1/a/neM+++//yOXX375023nmGsKKkVatGjR0d1u9w/bzjGRG2+8Mbt3P/OZ7bw2sywQF7YdYBJ/FgV1vrg0ycvbDjEFF7UdYBKl799Kz/ehKKjzxYuSFP3ZY5zS3/vF2bJlS7Zs2ZIkWbduXVL4/nfNmjUbk+xzBdUUXwAAAIrgCCrzxS1tB+jhpJHB0qVLtw4PD29rM0wPx2X07/gTSW5vMUsva1NNJUySbqppeiXZP8kxbYdgrz1Q30pyVJLl1XBod7KssOn3wwclO5/duOObKW+K70mjw/13JIsLm+L7xGHJrmVtp2CvlfbZo5Pq9J0R9yX5YUtZ+jk+yaJ6/FiS77WYZQ9Lly5dNzw8fGCSdLvd3an2byVZluTotkO0TUFlvnjJ+vXrd7YdomloaKg7Mj799NM/unnz5ve2maeHB5McWo+/leSlLWbp5a+TvKYeP5nqvJWSvDjVuWPMb3+c5PK2Q4yzOcmZ1XD5E8nDhU1vP+P1yZff0bjj5UkebitNH93R4Wn/J9n8J+1F6WXVFcmDZ7Sdgr2yK+X9u7QsVekb8YEkH24pSz8/TnJQPf7nVOeLF+OEE0647qabbjorSXbu3PnY+vXri/odb9q06Yxut/ultnO0zRRfAAAAiqCgAgAAUAQFFQAAgCIoqAAAABRBQQUAAKAICioAAABFUFABAAAogoIKAABAERRUAAAAiqCgAgAAUAQFFQAAgCIoqAAAABRBQQUAAKAICioAAABFUFABAAAogoIKAABAERRUAAAAiqCgAgAAUAQFFQAAgCIoqAvHjUm+Wt+OG3CbzzS2+alZygUAADCQxW0HYMacmqRTj5cPuM0JSY6ux4fMeCIAAIApcAQVAACAIiioAAAAFEFBBQAAoAgKKgAAAEVQUAEAACiCggoAAEARFFQAAACKoKACAABQBAUVAACAIiio+7YlbQcAAAAYoaAuHMON8dIB1u8kOXSWsgAAAEyZgrpwPNwYP2eA9Y9PsnyWsgAAAEyZgrpw3N4Ynz7A+r86W0EAAACmQ0FdOG5ojC9M8qwJ1v3JJL8+u3EAAACmZnHbAZgxn0jy9nq8OsmfJ/nlJNsb63SS/OskH0t1gaThDHa+aus6nc5LN27cuKvtHE2XXHLJM+OtW7cekeS09tL01Pz7vTzl5Tu4MR5KefmOaTsAM+LwlPfeWjE63DWUvO349qL0sn38aSKnJnm8jSSD+eGzy/sZPnVg2wmYEaXtO8Z/Znt+ysu4qDE+MIXle+SRR57Z/3Y6nUUbN24sKl+32z2u7QwlUFAXjn9OVUp/oV7+mSR3Jdmc5P5UZeCMVB/WkuSyJG9McvScppymbrf7pbYzTOTWW29dn2R92zkm8KIk17cdYgJLU3Y+5q+31rdCPX5A8uGr2k4xievaDjCxb51X3WBGLUr5/y69PaMHJ0p0Sgr7Gd52223PjJcsWbIsheWjoqAuLBtS/d+0l9XLK5K8dtw63SQfTPKeVAUVAACgCArqwvLjJGcluTTVEYMXNB7bleTqJB9Kcm193z8l2VKPt85NRAAAgN4U1IXnyVRHSD+Y5Nmpzkd9PMm9SZ4at+6b5jba4O67774vrlu3ruhzeF73utcte/rppztJ8o1vfOPJO+64o6hzZFNNmx35O74ze/7+27Y4o+fT7Er13i3ZY20HYGDnZOx5UKVZkmS/elzie38oyQGN5RLf+8tSXVchqX5+pe1/m3a2HYCBXZPqvMmSNb8i8Ikku9sK0sf+Gd3/PpXC3v+nnHLKkiOPPHK/JFmxYsWuAw44oLT97xgXXXRRwef/z57Oxo0bu88sdDrHXnzxxbdNtAEAAADMhE2bNh3T7Xa/O7Lsa2YAAAAogoIKAABAERRUAAAAiqCgAgAAUAQFFQAAgCIoqAAAABRBQQUAAKAICioAAABFUFABAAAogoIKAABAERRUAAAAiqCgAgAAUAQFFQAAgCIoqAAAABRBQQUAAKAICioAAABFUFABAAAogoIKAABAERRUAAAAiqCgAgAAUAQFFQAAgCIoqAAAABRBQQUAAKAICioAAABFUFABAAAogoIKAABAERRUAAAAiqCgAgAAUAQFFQAAgCIoqAAAABRBQQUAAKAICioAAABFUFABAAAogoIKAABAERRUAAAAiqCgAgCz7VNJrktydttBACibggoAzLZXJDkryeq2gwBQNgUVAACAIixuOwAAsOCdkmRRkh+1HQSAsimoAMBs29Z2AADmBwUVAJhtb05yYJKrk9zechYACqagAgCz7X1J1iT5pSioAEzARZIAAAAogoIKAABAERRUAAAAiqCgAgAAUAQFFQAAgCIoqAAAABRBQQUAAKAICioAAABFUFABAAAogoIKAABAERRUAAAAiqCgAgAAUITFbQcAABa885IsTXJr20EAKJuCCgDMthvbDgDA/GCKLwAAAEVQUAEAACiCggoAAEARFFQAAACKoKACAABQBAUVAACAIiioAAAAFEFBBQAAoAiL2w4AvWzatOmUbrf7sbZzTOR973vf8bt37+4kyfbt27c88cQTj7adaZy1SQ6sxz9MsrW9KD0dmuQ59fjJJHe0mGUQP5Pk4bZDMJArk5zcdogJrKpvSfJ4kjtbzNLL8iRHNpa/laTbUpZ+jk/Sqcd3J3mkxSyT+WSSD7cdgoGcluSKtkNMoJPqvT/iriSPtZSlnyNT7UOS5MEkD7SYZQ8HHXTQqhUrVqxKkjVr1jz+1re+tbT97xjDw8NnXXrppcNt55hrCiqlOijJ6W2HmMi9996b3bt3jyye2GaWAazI2A+cpVmR5Nlth5jEkrYDMLATU/j+o2FFktVth5jEy9oOMIkT2g4wiRvaDsDADs782XckyUltB5jEiiTr2g7R9NBDD+Whhx5Kkuy3337F73+XLl26qO0MbTDFFwAAgCI4gsq80Ol0LtvdOFxZiPeMDFatWvW5bdu2bW4xSy//IcmyevyDJH/cYpZefjnJsfX46SS/12KWXtYk+bW2Q7DXPp/kurZDjPOWVFPwk2Q4yXvbi9LTaUleM7p4wlXJop2tpenp5vWNhetS/Z5L8sYkx7Qdgr2yO8llbYcYZ0mS320s/02S61vK0s+7kuxfj+9O8vEWs+xh9erVb37ggQfWJcmuXbue6na775lsm7nU6XSem+TitnO0TUFlXuh2u/9pw4YNRX1AGhoaeLine truncated
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "343e60c3",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"However, to update the entries on the boundary of the locally stored vector we need entries stored on other processors."
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"f2.png": {
|
||||
"image/png": 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truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "fce954fe",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div>\n",
|
||||
"<img src=\"data:image/png;base64,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 truncated
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "3f90d701",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Thus, in order to update the local entries in `u_new`, we also need some remote entries of vector `u` located in neighboring processes. Figure below shows the entries of `u` needed to update the local entries of `u_new` in a particular process (CPU 2)."
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -404,10 +457,9 @@
|
||||
"id": "8ed4129c",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Code\n",
|
||||
"### MPI Code\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"Take a look at the implementation below and try to understand it. Note that we have used MPIClustermanagers and Distributed just to run the MPI code on the notebook. When running it on a cluster, MPIClustermanagers and Distributed are not needed.\n"
|
||||
"Take a look at the implementation below and try to understand it.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -417,7 +469,7 @@
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"] add MPI MPIClusterManagers"
|
||||
"] add MPI"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -427,30 +479,7 @@
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"using MPIClusterManagers \n",
|
||||
"using Distributed"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "e0d63c6b",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"if procs() == workers()\n",
|
||||
" nw = 3\n",
|
||||
" manager = MPIWorkerManager(nw)\n",
|
||||
" addprocs(manager)\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "d7fb9177",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"First, we implement the function to be called on the MPI ranks."
|
||||
"using MPI"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -462,120 +491,99 @@
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"@everywhere workers() begin\n",
|
||||
"code = quote\n",
|
||||
" using MPI\n",
|
||||
" comm = MPI.Comm_dup(MPI.COMM_WORLD)\n",
|
||||
" MPI.Init()\n",
|
||||
" function jacobi_mpi(n,niters)\n",
|
||||
" comm = MPI.COMM_WORLD\n",
|
||||
" nranks = MPI.Comm_size(comm)\n",
|
||||
" rank = MPI.Comm_rank(comm)\n",
|
||||
" if mod(n,nranks) != 0\n",
|
||||
" println(\"n must be a multiple of nranks\")\n",
|
||||
" MPI.Abort(comm,1)\n",
|
||||
" end\n",
|
||||
" n_own = div(n,nranks)\n",
|
||||
" u = zeros(n_own+2)\n",
|
||||
" load = div(n,nranks)\n",
|
||||
" u = zeros(load+2)\n",
|
||||
" u[1] = -1\n",
|
||||
" u[end] = 1\n",
|
||||
" u_new = copy(u)\n",
|
||||
" for t in 1:niters\n",
|
||||
" reqs = MPI.Request[]\n",
|
||||
" # Communication\n",
|
||||
" if rank != 0\n",
|
||||
" neig_rank = rank-1\n",
|
||||
" req = MPI.Isend(view(u,2:2),comm,dest=neig_rank,tag=0)\n",
|
||||
" push!(reqs,req)\n",
|
||||
" req = MPI.Irecv!(view(u,1:1),comm,source=neig_rank,tag=0)\n",
|
||||
" push!(reqs,req)\n",
|
||||
" s = 2\n",
|
||||
" r = 1\n",
|
||||
" MPI.Sendrecv!(view(u,s:s),view(u,r:r),comm;dest=neig_rank,source=neig_rank)\n",
|
||||
" end\n",
|
||||
" if rank != (nranks-1)\n",
|
||||
" neig_rank = rank+1\n",
|
||||
" s = n_own+1\n",
|
||||
" r = n_own+2\n",
|
||||
" req = MPI.Isend(view(u,s:s),comm,dest=neig_rank,tag=0)\n",
|
||||
" push!(reqs,req)\n",
|
||||
" req = MPI.Irecv!(view(u,r:r),comm,source=neig_rank,tag=0)\n",
|
||||
" push!(reqs,req)\n",
|
||||
" s = load+1\n",
|
||||
" r = load+2\n",
|
||||
" MPI.Sendrecv!(view(u,s:s),view(u,r:r),comm;dest=neig_rank,source=neig_rank)\n",
|
||||
" end\n",
|
||||
" MPI.Waitall(reqs)\n",
|
||||
" for i in 2:(n_own+1)\n",
|
||||
" # Local computation\n",
|
||||
" for i in 2:(load+1)\n",
|
||||
" u_new[i] = 0.5*(u[i-1]+u[i+1])\n",
|
||||
" end\n",
|
||||
" u, u_new = u_new, u\n",
|
||||
" end\n",
|
||||
" return u\n",
|
||||
" end\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "6eab32d0",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"In order to check the result, we will compare it against the serial implementation. To this end, we need to define the serial implementation also in the workers."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "f1a8db8f",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"@everywhere workers() function jacobi(n,niters)\n",
|
||||
" u = zeros(n+2)\n",
|
||||
" u[1] = -1\n",
|
||||
" u[end] = 1\n",
|
||||
" u_new = copy(u)\n",
|
||||
" for t in 1:niters\n",
|
||||
" for i in 2:(n+1)\n",
|
||||
" u_new[i] = 0.5*(u[i-1]+u[i+1])\n",
|
||||
" # Gather the results\n",
|
||||
" if rank !=0\n",
|
||||
" lb = 2\n",
|
||||
" ub = load+1\n",
|
||||
" MPI.Send(view(u,lb:ub),comm,dest=0)\n",
|
||||
" u_all = zeros(0) # This will nevel be used\n",
|
||||
" else\n",
|
||||
" u_all = zeros(n+2)\n",
|
||||
" # Set boundary\n",
|
||||
" u_all[1] = -1\n",
|
||||
" u_all[end] = 1\n",
|
||||
" # Set data for rank 0\n",
|
||||
" lb = 2\n",
|
||||
" ub = load+1\n",
|
||||
" u_all[lb:ub] = view(u,lb:ub)\n",
|
||||
" # Set data for other ranks\n",
|
||||
" for other_rank in 1:(nranks-1)\n",
|
||||
" lb += load\n",
|
||||
" ub += load\n",
|
||||
" MPI.Recv!(view(u_all,lb:ub),comm;source=other_rank)\n",
|
||||
" end\n",
|
||||
" end\n",
|
||||
" u, u_new = u_new, u\n",
|
||||
" return u_all\n",
|
||||
" end\n",
|
||||
" u\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "d2b04c67",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Finally, we call the parallel function on the workers, gather the results on the root rank, and compare against the sequential solution."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "68851107",
|
||||
"metadata": {
|
||||
"code_folding": []
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"@everywhere workers() begin\n",
|
||||
" # Call jacobi in parallel\n",
|
||||
" niters = 10\n",
|
||||
" load = 4\n",
|
||||
" nranks = MPI.Comm_size(comm)\n",
|
||||
" n = load*nranks\n",
|
||||
" u = jacobi_mpi(n,niters)\n",
|
||||
" # Gather results in root process and check\n",
|
||||
" rank = MPI.Comm_rank(comm)\n",
|
||||
" n_own = div(n,nranks)\n",
|
||||
" if rank == 0\n",
|
||||
" results = zeros(n+2)\n",
|
||||
" results[1] = -1\n",
|
||||
" results[n+2] = 1\n",
|
||||
" rcv = view(results, 2:n+1)\n",
|
||||
" else\n",
|
||||
" rcv = nothing\n",
|
||||
" function jacobi(n,niters)\n",
|
||||
" u = zeros(n+2)\n",
|
||||
" u[1] = -1\n",
|
||||
" u[end] = 1\n",
|
||||
" u_new = copy(u)\n",
|
||||
" for t in 1:niters\n",
|
||||
" for i in 2:(n+1)\n",
|
||||
" u_new[i] = 0.5*(u[i-1]+u[i+1])\n",
|
||||
" end\n",
|
||||
" u, u_new = u_new, u\n",
|
||||
" end\n",
|
||||
" u\n",
|
||||
" end\n",
|
||||
" MPI.Gather!(view(u,2:n_own+1),rcv,comm;root=0)\n",
|
||||
" if rank == 0\n",
|
||||
" @show results ≈ jacobi(n,niters)\n",
|
||||
" end \n",
|
||||
"end"
|
||||
" function testit(load)\n",
|
||||
" comm = MPI.COMM_WORLD\n",
|
||||
" nranks = MPI.Comm_size(comm)\n",
|
||||
" rank = MPI.Comm_rank(comm)\n",
|
||||
" n = load*nranks\n",
|
||||
" niters = 100\n",
|
||||
" u_par = jacobi_mpi(n,niters)\n",
|
||||
" if rank == 0\n",
|
||||
" # Compare agains serial\n",
|
||||
" u_seq = jacobi(n,niters)\n",
|
||||
" if u_par ≈ u_seq\n",
|
||||
" println(\"Test passed 🥳\")\n",
|
||||
" else\n",
|
||||
" println(\"Test failed\")\n",
|
||||
" end\n",
|
||||
" end\n",
|
||||
" end\n",
|
||||
" testit(3)\n",
|
||||
"end\n",
|
||||
"run(`$(mpiexec()) -np 4 julia --project=. -e $code`);"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -584,7 +592,7 @@
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div class=\"alert alert-block alert-success\">\n",
|
||||
"<b>Question:</b> In function jacobi_mpi, how many messages per iteration are sent from a process away from the boundary?\n",
|
||||
"<b>Question:</b> In function jacobi_mpi, how many messages per iteration are sent from a process away from the boundary (excluding the messages to collect the data on rank 0)?\n",
|
||||
"</div>\n",
|
||||
"\n",
|
||||
" a) 1\n",
|
||||
@@ -605,32 +613,6 @@
|
||||
"jacobi_2_check(answer)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "075dd6d8",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<div class=\"alert alert-block alert-success\">\n",
|
||||
"<b>Question:</b> At the end of function jacobi_mpi ...\n",
|
||||
"</div>\n",
|
||||
"\n",
|
||||
" a) each process holds the complete solution.\n",
|
||||
" b) the complete solution is gathered in the root process. \n",
|
||||
" c) each process contains the solution for the local partition. \n",
|
||||
" d) the ghost cells of u contain the initial values -1 and 1 in all processes."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "c3b58002",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"answer = \"x\" # replace x with a, b, c or d\n",
|
||||
"jacobi_3_check(answer)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "c9aa2901",
|
||||
@@ -842,7 +824,7 @@
|
||||
"- We update $N^2/P$ items per iteration\n",
|
||||
"- We need data from 2 neighbors (2 messages per iteration)\n",
|
||||
"- We communicate $N$ items per message\n",
|
||||
"- Communication/computation ratio is $O(P/N)$"
|
||||
"- Communication/computation ratio is $2N/(N^2/P) = 2P/N =O(P/N)$"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -876,7 +858,7 @@
|
||||
"- We update $N^2/P$ items per iteration\n",
|
||||
"- We need data from 4 neighbors (4 messages per iteration)\n",
|
||||
"- We communicate $N/\\sqrt{P}$ items per message\n",
|
||||
"- Communication/computation ratio is $O(\\sqrt{P}/N)$"
|
||||
"- Communication/computation ratio is $ (4N/\\sqrt{P})/(N^2/P)= 4\\sqrt{P}/N =O(\\sqrt{P}/N)$"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -939,7 +921,7 @@
|
||||
"- Both 1d and 2d block partitions are potentially scalable if $P<<N$\n",
|
||||
"- The 2d block partition has the lowest communication complexity\n",
|
||||
"- The 1d block partition requires to send less messages (It can be useful if the fixed cost of sending a message is high)\n",
|
||||
"- The best strategy for a given problem size will thus depend on the machine, but the 2d block partition is the one used in practice since it has the lowest communication complexity.\n",
|
||||
"- The best strategy for a given problem size will thus depend on the machine.\n",
|
||||
"- Cyclic partitions are impractical for this application (but they are useful in others) \n",
|
||||
"\n"
|
||||
]
|
||||
@@ -977,15 +959,15 @@
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Julia 1.9.1",
|
||||
"display_name": "Julia 1.10.0",
|
||||
"language": "julia",
|
||||
"name": "julia-1.9"
|
||||
"name": "julia-1.10"
|
||||
},
|
||||
"language_info": {
|
||||
"file_extension": ".jl",
|
||||
"mimetype": "application/julia",
|
||||
"name": "julia",
|
||||
"version": "1.9.1"
|
||||
"version": "1.10.0"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
@@ -1,5 +1,5 @@
|
||||
<!DOCTYPE html>
|
||||
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>- · XM_40017</title><meta name="title" content="- · XM_40017"/><meta property="og:title" content="- · XM_40017"/><meta property="twitter:title" content="- · XM_40017"/><meta name="description" content="Documentation for XM_40017."/><meta property="og:description" content="Documentation for XM_40017."/><meta property="twitter:description" content="Documentation for XM_40017."/><meta property="og:url" content="https://fverdugo.github.io/XM_40017/jacobi_method/"/><meta property="twitter:url" content="https://fverdugo.github.io/XM_40017/jacobi_method/"/><link rel="canonical" href="https://fverdugo.github.io/XM_40017/jacobi_method/"/><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" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/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="../search_index.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/catppuccin-mocha.css" data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><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><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><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/">Asynchronous programming in Julia</a></li><li><a class="tocitem" href="../julia_distributed/">Distributed computing in Julia</a></li><li><a class="tocitem" href="../matrix_matrix/">Matrix-matrix multiplication</a></li><li><a class="tocitem" href="../julia_mpi/">MPI (point-to-point)</a></li></ul></li><li><a class="tocitem" href="../solutions_for_all_notebooks/">Solutions</a></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 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-navbar-link" href="https://github.com/fverdugo/XM_40017/blob/main/notebooks/jacobi_method.ipynb" title="View source on GitHub"><span 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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Jacobi method · XM_40017</title><meta name="title" content="Jacobi method · XM_40017"/><meta property="og:title" content="Jacobi method · XM_40017"/><meta property="twitter:title" content="Jacobi method · XM_40017"/><meta name="description" content="Documentation for XM_40017."/><meta property="og:description" content="Documentation for XM_40017."/><meta property="twitter:description" content="Documentation for XM_40017."/><meta property="og:url" content="https://fverdugo.github.io/XM_40017/jacobi_method/"/><meta property="twitter:url" content="https://fverdugo.github.io/XM_40017/jacobi_method/"/><link rel="canonical" href="https://fverdugo.github.io/XM_40017/jacobi_method/"/><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" 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href="../matrix_matrix/">Matrix-matrix multiplication</a></li><li><a class="tocitem" href="../julia_mpi/">MPI (point-to-point)</a></li><li class="is-active"><a class="tocitem" href>Jacobi method</a></li></ul></li><li><a class="tocitem" href="../solutions_for_all_notebooks/">Solutions</a></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">Notebooks</a></li><li class="is-active"><a href>Jacobi method</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Jacobi method</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-liLine truncated
|
||||
<header class="admonition-header">Tip</header>
|
||||
<div class="admonition-body">
|
||||
<ul>
|
||||
@@ -14,4 +14,4 @@
|
||||
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="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="Tuesday 20 August 2024 12:05">Tuesday 20 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../julia_mpi/">« MPI (point-to-point)</a><a class="docs-footer-nextpage" href="../solutions_for_all_notebooks/">Solutions »</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="Tuesday 20 August 2024 13:32">Tuesday 20 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||
+137
-173
@@ -7584,6 +7584,7 @@ a.anchor-link {
|
||||
<span class="n">jacobi_1_check</span><span class="p">(</span><span class="n">answer</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">answer_checker</span><span class="p">(</span><span class="n">answer</span><span class="p">,</span><span class="w"> </span><span class="s">"d"</span><span class="p">)</span>
|
||||
<span class="n">jacobi_2_check</span><span class="p">(</span><span class="n">answer</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">answer_checker</span><span class="p">(</span><span class="n">answer</span><span class="p">,</span><span class="w"> </span><span class="s">"b"</span><span class="p">)</span>
|
||||
<span class="n">jacobi_3_check</span><span class="p">(</span><span class="n">answer</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">answer_checker</span><span class="p">(</span><span class="n">answer</span><span class="p">,</span><span class="w"> </span><span class="s">"c"</span><span class="p">)</span>
|
||||
<span class="n">println</span><span class="p">(</span><span class="s">"🥳 Well done! "</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -7684,7 +7685,7 @@ a.anchor-link {
|
||||
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
||||
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|
||||
<div class="alert alert-block alert-info">
|
||||
<b>Note:</b> In our version of the jacobi method, we return after a given number of iterations. Other stopping criteria are possible. For instance, iterate until the difference between u and u_new is below a tolerance.
|
||||
<b>Note:</b> In our version of the jacobi method, we return after a given number of iterations. Other stopping criteria are possible. For instance, iterate until the difference between u and u_new is below a tolerance.
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -7827,7 +7828,7 @@ d) The inner, but not the outer</code></pre>
|
||||
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|
||||
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|
||||
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|
||||
<h3 id="Parallelization-strategy">Parallelization strategy<a class="anchor-link" href="#Parallelization-strategy">¶</a></h3><p>Remember that a sufficiently large grain size is needed to achieve performance in a distributed algorithm. For Jacobi, one could update each entry of vector <code>u_new</code> in a different worker, but this would not be efficient. Instead, we use a parallelization strategy with a larger grain size that is analogous to the algorithm 3 we studied for the matrix-matrix multiplication:</p>
|
||||
<h3 id="Parallelization-strategy">Parallelization strategy<a class="anchor-link" href="#Parallelization-strategy">¶</a></h3><p>Remember that a sufficiently large grain size is needed to achieve performance in a distributed algorithm. For Jacobi, one could update each entry of vector <code>u_new</code> in a different process, but this would not be efficient. Instead, we use a parallelization strategy with a larger grain size that is analogous to the algorithm 3 we studied for the matrix-matrix multiplication:</p>
|
||||
<ul>
|
||||
<li>Each worker updates a consecutive section of the array <code>u_new</code></li>
|
||||
</ul>
|
||||
@@ -7849,7 +7850,7 @@ d) The inner, but not the outer</code></pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
@@ -7857,7 +7858,65 @@ d) The inner, but not the outer</code></pre>
|
||||
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|
||||
<h3 id="Data-dependencies">Data dependencies<a class="anchor-link" href="#Data-dependencies">¶</a></h3><p>Recall the Jacobi update:</p>
|
||||
<p><code>u_new[i] = 0.5*(u[i-1]+u[i+1])</code></p>
|
||||
<p>Thus, in order to update the local entries in <code>u_new</code>, we also need remote entries of vector <code>u</code> located in neighboring processes. Figure below shows the entries of <code>u</code> needed to update the local entries of <code>u_new</code> in a particular process (CPU 2).</p>
|
||||
</div>
|
||||
</div>
|
||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
<p>Note that an entry in the interior of the locally stored vector can be updated using local data only. For this one, communication is not needed.</p>
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<p>However, to update the entries on the boundary of the locally stored vector we need entries stored on other processors.</p>
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<p>Thus, in order to update the local entries in <code>u_new</code>, we also need some remote entries of vector <code>u</code> located in neighboring processes. Figure below shows the entries of <code>u</code> needed to update the local entries of <code>u_new</code> in a particular process (CPU 2).</p>
|
||||
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|
||||
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|
||||
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|
||||
@@ -7960,7 +8019,7 @@ d) The inner, but not the outer</code></pre>
|
||||
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|
||||
<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">
|
||||
<h3 id="Code">Code<a class="anchor-link" href="#Code">¶</a></h3><p>Take a look at the implementation below and try to understand it. Note that we have used MPIClustermanagers and Distributed just to run the MPI code on the notebook. When running it on a cluster, MPIClustermanagers and Distributed are not needed.</p>
|
||||
<h3 id="MPI-Code">MPI Code<a class="anchor-link" href="#MPI-Code">¶</a></h3><p>Take a look at the implementation below and try to understand it.</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -7972,7 +8031,7 @@ d) The inner, but not the outer</code></pre>
|
||||
<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
|
||||
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
|
||||
<div class="cm-editor cm-s-jupyter">
|
||||
<div class="highlight hl-julia"><pre><span></span><span class="p">]</span><span class="w"> </span><span class="n">add</span><span class="w"> </span><span class="n">MPI</span><span class="w"> </span><span class="n">MPIClusterManagers</span>
|
||||
<div class="highlight hl-julia"><pre><span></span><span class="p">]</span><span class="w"> </span><span class="n">add</span><span class="w"> </span><span class="n">MPI</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -7986,42 +8045,12 @@ d) The inner, but not the outer</code></pre>
|
||||
<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
|
||||
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
|
||||
<div class="cm-editor cm-s-jupyter">
|
||||
<div class="highlight hl-julia"><pre><span></span><span class="k">using</span><span class="w"> </span><span class="n">MPIClusterManagers</span><span class="w"> </span>
|
||||
<span class="k">using</span><span class="w"> </span><span class="n">Distributed</span>
|
||||
<div class="highlight hl-julia"><pre><span></span><span class="k">using</span><span class="w"> </span><span class="n">MPI</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=e0d63c6b">
|
||||
<div class="jp-Cell-inputWrapper" tabindex="0">
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||||
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|
||||
</div>
|
||||
<div class="jp-InputArea jp-Cell-inputArea">
|
||||
<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
|
||||
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
|
||||
<div class="cm-editor cm-s-jupyter">
|
||||
<div class="highlight hl-julia"><pre><span></span><span class="k">if</span><span class="w"> </span><span class="n">procs</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">workers</span><span class="p">()</span>
|
||||
<span class="w"> </span><span class="n">nw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span>
|
||||
<span class="w"> </span><span class="n">manager</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPIWorkerManager</span><span class="p">(</span><span class="n">nw</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="n">addprocs</span><span class="p">(</span><span class="n">manager</span><span class="p">)</span>
|
||||
<span class="k">end</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=d7fb9177">
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||||
<div class="jp-Cell-inputWrapper" tabindex="0">
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<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
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||||
</div>
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||||
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
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</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
||||
<p>First, we implement the function to be called on the MPI ranks.</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=d39c7bb2">
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<div class="jp-Cell-inputWrapper" tabindex="0">
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@@ -8030,132 +8059,99 @@ d) The inner, but not the outer</code></pre>
|
||||
<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
|
||||
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
|
||||
<div class="cm-editor cm-s-jupyter">
|
||||
<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>
|
||||
<div class="highlight hl-julia"><pre><span></span><span class="n">code</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">quote</span>
|
||||
<span class="w"> </span><span class="k">using</span><span class="w"> </span><span class="n">MPI</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Init</span><span class="p">()</span>
|
||||
<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>
|
||||
<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_WORLD</span>
|
||||
<span class="w"> </span><span class="n">nranks</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>
|
||||
<span class="w"> </span><span class="n">rank</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="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">nranks</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span>
|
||||
<span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="s">"n must be a multiple of nranks"</span><span class="p">)</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<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">nranks</span><span class="p">)</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="n">load</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">nranks</span><span class="p">)</span>
|
||||
<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">load</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<span class="w"> </span><span class="n">reqs</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>
|
||||
<span class="w"> </span><span class="c"># Communication</span>
|
||||
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">rank</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span>
|
||||
<span class="w"> </span><span class="n">neig_rank</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rank</span><span class="o">-</span><span class="mi">1</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="n">push!</span><span class="p">(</span><span class="n">reqs</span><span class="p">,</span><span class="n">req</span><span class="p">)</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="n">push!</span><span class="p">(</span><span class="n">reqs</span><span class="p">,</span><span class="n">req</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span>
|
||||
<span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Sendrecv!</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">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">dest</span><span class="o">=</span><span class="n">neig_rank</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="w"> </span><span class="k">end</span>
|
||||
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">rank</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="p">(</span><span class="n">nranks</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="n">neig_rank</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rank</span><span class="o">+</span><span class="mi">1</span>
|
||||
<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>
|
||||
<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><span class="o">+</span><span class="mi">2</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="n">push!</span><span class="p">(</span><span class="n">reqs</span><span class="p">,</span><span class="n">req</span><span class="p">)</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="n">push!</span><span class="p">(</span><span class="n">reqs</span><span class="p">,</span><span class="n">req</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">load</span><span class="o">+</span><span class="mi">1</span>
|
||||
<span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">load</span><span class="o">+</span><span class="mi">2</span>
|
||||
<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Sendrecv!</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">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">dest</span><span class="o">=</span><span class="n">neig_rank</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="w"> </span><span class="k">end</span>
|
||||
<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</span><span class="p">)</span>
|
||||
<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">2</span><span class="o">:</span><span class="p">(</span><span class="n">n_own</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="c"># Local computation</span>
|
||||
<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">2</span><span class="o">:</span><span class="p">(</span><span class="n">load</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">u</span>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<span class="k">end</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=6eab32d0">
|
||||
<div class="jp-Cell-inputWrapper" tabindex="0">
|
||||
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
|
||||
</div>
|
||||
<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">
|
||||
<p>In order to check the result, we will compare it against the serial implementation. To this end, we need to define the serial implementation also in the workers.</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=f1a8db8f">
|
||||
<div class="jp-Cell-inputWrapper" tabindex="0">
|
||||
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
|
||||
</div>
|
||||
<div class="jp-InputArea jp-Cell-inputArea">
|
||||
<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
|
||||
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
|
||||
<div class="cm-editor cm-s-jupyter">
|
||||
<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">function</span><span class="w"> </span><span class="n">jacobi</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">niters</span><span class="p">)</span>
|
||||
<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</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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">2</span><span class="o">:</span><span class="p">(</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="c"># Gather the results</span>
|
||||
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">rank</span><span class="w"> </span><span class="o">!=</span><span class="mi">0</span>
|
||||
<span class="w"> </span><span class="n">lb</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span>
|
||||
<span class="w"> </span><span class="n">ub</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">load</span><span class="o">+</span><span class="mi">1</span>
|
||||
<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Send</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">lb</span><span class="o">:</span><span class="n">ub</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="mi">0</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="n">u_all</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">zeros</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c"># This will nevel be used</span>
|
||||
<span class="w"> </span><span class="k">else</span>
|
||||
<span class="w"> </span><span class="n">u_all</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</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="c"># Set boundary</span>
|
||||
<span class="w"> </span><span class="n">u_all</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>
|
||||
<span class="w"> </span><span class="n">u_all</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>
|
||||
<span class="w"> </span><span class="c"># Set data for rank 0</span>
|
||||
<span class="w"> </span><span class="n">lb</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span>
|
||||
<span class="w"> </span><span class="n">ub</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">load</span><span class="o">+</span><span class="mi">1</span>
|
||||
<span class="w"> </span><span class="n">u_all</span><span class="p">[</span><span class="n">lb</span><span class="o">:</span><span class="n">ub</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">view</span><span class="p">(</span><span class="n">u</span><span class="p">,</span><span class="n">lb</span><span class="o">:</span><span class="n">ub</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="c"># Set data for other ranks</span>
|
||||
<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">other_rank</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="p">(</span><span class="n">nranks</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="n">lb</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">load</span>
|
||||
<span class="w"> </span><span class="n">ub</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">load</span>
|
||||
<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Recv!</span><span class="p">(</span><span class="n">view</span><span class="p">(</span><span class="n">u_all</span><span class="p">,</span><span class="n">lb</span><span class="o">:</span><span class="n">ub</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">other_rank</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">u_all</span>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<span class="w"> </span><span class="n">u</span>
|
||||
<span class="k">end</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=d2b04c67">
|
||||
<div class="jp-Cell-inputWrapper" tabindex="0">
|
||||
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|
||||
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|
||||
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|
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</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
||||
<p>Finally, we call the parallel function on the workers, gather the results on the root rank, and compare against the sequential solution.</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=68851107">
|
||||
<div class="jp-Cell-inputWrapper" tabindex="0">
|
||||
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
|
||||
</div>
|
||||
<div class="jp-InputArea jp-Cell-inputArea">
|
||||
<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
|
||||
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
|
||||
<div class="cm-editor cm-s-jupyter">
|
||||
<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>
|
||||
<span class="w"> </span><span class="c"># Call jacobi in parallel</span>
|
||||
<span class="w"> </span><span class="n">niters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">10</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="n">nranks</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>
|
||||
<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">nranks</span>
|
||||
<span class="w"> </span><span class="n">u</span><span class="w"> </span><span class="o">=</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>
|
||||
<span class="w"> </span><span class="c"># Gather results in root process and check</span>
|
||||
<span class="w"> </span><span class="n">rank</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="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">nranks</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">rank</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||||
<span class="w"> </span><span class="n">results</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</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="n">results</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>
|
||||
<span class="w"> </span><span class="n">results</span><span class="p">[</span><span class="n">n</span><span class="o">+</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span>
|
||||
<span class="w"> </span><span class="n">rcv</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">view</span><span class="p">(</span><span class="n">results</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="o">:</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="k">else</span>
|
||||
<span class="w"> </span><span class="n">rcv</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">nothing</span>
|
||||
<span class="w"> </span><span class="k">function</span><span class="w"> </span><span class="n">jacobi</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">niters</span><span class="p">)</span>
|
||||
<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</span><span class="o">+</span><span class="mi">2</span><span class="p">)</span>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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">2</span><span class="o">:</span><span class="p">(</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<span class="w"> </span><span class="n">u</span>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Gather!</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="n">n_own</span><span class="o">+</span><span class="mi">1</span><span class="p">),</span><span class="n">rcv</span><span class="p">,</span><span class="n">comm</span><span class="p">;</span><span class="n">root</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">rank</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||||
<span class="w"> </span><span class="nd">@show</span><span class="w"> </span><span class="n">results</span><span class="w"> </span><span class="o">≈</span><span class="w"> </span><span class="n">jacobi</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">niters</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="k">end</span><span class="w"> </span>
|
||||
<span class="w"> </span><span class="k">function</span><span class="w"> </span><span class="n">testit</span><span class="p">(</span><span class="n">load</span><span class="p">)</span>
|
||||
<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_WORLD</span>
|
||||
<span class="w"> </span><span class="n">nranks</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>
|
||||
<span class="w"> </span><span class="n">rank</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="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">nranks</span>
|
||||
<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>
|
||||
<span class="w"> </span><span class="n">u_par</span><span class="w"> </span><span class="o">=</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>
|
||||
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">rank</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
||||
<span class="w"> </span><span class="c"># Compare agains serial</span>
|
||||
<span class="w"> </span><span class="n">u_seq</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">jacobi</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">niters</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">u_par</span><span class="w"> </span><span class="o">≈</span><span class="w"> </span><span class="n">u_seq</span>
|
||||
<span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="s">"Test passed 🥳"</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="k">else</span>
|
||||
<span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="s">"Test failed"</span><span class="p">)</span>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<span class="w"> </span><span class="k">end</span>
|
||||
<span class="w"> </span><span class="n">testit</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
|
||||
<span class="k">end</span>
|
||||
<span class="n">run</span><span class="p">(</span><span class="sb">`</span><span class="si">$</span><span class="p">(</span><span class="n">mpiexec</span><span class="p">())</span><span class="sb"> -np 4 julia --project=. -e </span><span class="si">$code</span><span class="sb">`</span><span class="p">);</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -8169,7 +8165,7 @@ d) The inner, but not the outer</code></pre>
|
||||
<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 class="alert alert-block alert-success">
|
||||
<b>Question:</b> In function jacobi_mpi, how many messages per iteration are sent from a process away from the boundary?
|
||||
<b>Question:</b> In function jacobi_mpi, how many messages per iteration are sent from a process away from the boundary (excluding the messages to collect the data on rank 0)?
|
||||
</div>
|
||||
<pre><code>a) 1
|
||||
b) 2
|
||||
@@ -8194,38 +8190,6 @@ d) 4</code></pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=075dd6d8">
|
||||
<div class="jp-Cell-inputWrapper" tabindex="0">
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||||
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|
||||
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|
||||
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|
||||
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|
||||
<div class="alert alert-block alert-success">
|
||||
<b>Question:</b> At the end of function jacobi_mpi ...
|
||||
</div>
|
||||
<pre><code>a) each process holds the complete solution.
|
||||
b) the complete solution is gathered in the root process.
|
||||
c) each process contains the solution for the local partition.
|
||||
d) the ghost cells of u contain the initial values -1 and 1 in all processes.</code></pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=c3b58002">
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||||
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|
||||
</div>
|
||||
<div class="jp-InputArea jp-Cell-inputArea">
|
||||
<div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
|
||||
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
|
||||
<div class="cm-editor cm-s-jupyter">
|
||||
<div class="highlight hl-julia"><pre><span></span><span class="n">answer</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">"x"</span><span class="w"> </span><span class="c"># replace x with a, b, c or d</span>
|
||||
<span class="n">jacobi_3_check</span><span class="p">(</span><span class="n">answer</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=c9aa2901">
|
||||
<div class="jp-Cell-inputWrapper" tabindex="0">
|
||||
<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
|
||||
@@ -8446,7 +8410,7 @@ d) the ghost cells of u contain the initial values -1 and 1 in all processes.</c
|
||||
<li>We update $N^2/P$ items per iteration</li>
|
||||
<li>We need data from 2 neighbors (2 messages per iteration)</li>
|
||||
<li>We communicate $N$ items per message</li>
|
||||
<li>Communication/computation ratio is $O(P/N)$</li>
|
||||
<li>Communication/computation ratio is $2N/(N^2/P) = 2P/N =O(P/N)$</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
@@ -8486,7 +8450,7 @@ d) the ghost cells of u contain the initial values -1 and 1 in all processes.</c
|
||||
<li>We update $N^2/P$ items per iteration</li>
|
||||
<li>We need data from 4 neighbors (4 messages per iteration)</li>
|
||||
<li>We communicate $N/\sqrt{P}$ items per message</li>
|
||||
<li>Communication/computation ratio is $O(\sqrt{P}/N)$</li>
|
||||
<li>Communication/computation ratio is $ (4N/\sqrt{P})/(N^2/P)= 4\sqrt{P}/N =O(\sqrt{P}/N)$</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
@@ -8586,7 +8550,7 @@ d) the ghost cells of u contain the initial values -1 and 1 in all processes.</c
|
||||
<li>Both 1d and 2d block partitions are potentially scalable if $P<<N$</li>
|
||||
<li>The 2d block partition has the lowest communication complexity</li>
|
||||
<li>The 1d block partition requires to send less messages (It can be useful if the fixed cost of sending a message is high)</li>
|
||||
<li>The best strategy for a given problem size will thus depend on the machine, but the 2d block partition is the one used in practice since it has the lowest communication complexity.</li>
|
||||
<li>The best strategy for a given problem size will thus depend on the machine.</li>
|
||||
<li>Cyclic partitions are impractical for this application (but they are useful in others)</li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
@@ -1,5 +1,5 @@
|
||||
<!DOCTYPE html>
|
||||
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@@ -14,4 +14,4 @@
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iFrameResize({log:true}, myIframe);
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Solutions · XM_40017</title><meta name="title" content="Solutions · XM_40017"/><meta property="og:title" content="Solutions · XM_40017"/><meta property="twitter:title" content="Solutions · XM_40017"/><meta name="description" content="Documentation for XM_40017."/><meta property="og:description" content="Documentation for XM_40017."/><meta property="twitter:description" content="Documentation for XM_40017."/><meta property="og:url" content="https://fverdugo.github.io/XM_40017/solutions_for_all_notebooks/"/><meta property="twitter:url" content="https://fverdugo.github.io/XM_40017/solutions_for_all_notebooks/"/><link rel="canonical" href="https://fverdugo.github.io/XM_40017/solutions_for_all_notebooks/"/><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" 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href="../matrix_matrix/">Matrix-matrix multiplication</a></li><li><a class="tocitem" href="../julia_mpi/">MPI (point-to-point)</a></li><li><a class="tocitem" href="../jacobi_method/">Jacobi method</a></li></ul></li><li class="is-active"><a class="tocitem" href>Solutions</a><ul class="internal"><li><a class="tocitem" href="#Julia-Basics"><span>Julia Basics</span></a></li><li><a class="tocitem" href="#Asynchronous-programming-in-Julia"><span>Asynchronous programming in Julia</span></a></li><li><a class="tocitem" href="#Distributed-computing-in-Julia"><span>Distributed computing in Julia</span></a></li><li><a class="tocitem" href="#Matrix-matrix-multiplication"><span>Matrix-matrix multiplication</span></a></li><li><a class="tocitem" href="#MPI-(Point-to-point)"><span>MPI (Point-to-point)</span></a></li><li><a class="tocitem" href="#Jacobi-method"><span>Jacobi method</span></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><diLine truncated
|
||||
j = 1
|
||||
m = a[j]
|
||||
for (i,ai) in enumerate(a)
|
||||
@@ -108,48 +108,68 @@ else
|
||||
buffer[] += 1
|
||||
println("msg = $(buffer[])")
|
||||
MPI.Send(buffer,comm;dest,tag=0)
|
||||
end</code></pre><h2 id="Jacobi-method"><a class="docs-heading-anchor" href="#Jacobi-method">Jacobi method</a><a id="Jacobi-method-1"></a><a class="docs-heading-anchor-permalink" href="#Jacobi-method" title="Permalink"></a></h2><h3 id="Exercise-1-4"><a class="docs-heading-anchor" href="#Exercise-1-4">Exercise 1</a><a class="docs-heading-anchor-permalink" href="#Exercise-1-4" title="Permalink"></a></h3><pre><code class="language-julia hljs">@everywhere workers() begin
|
||||
using MPI
|
||||
comm = MPI.Comm_dup(MPI.COMM_WORLD)
|
||||
function jacobi_mpi(n,niters)
|
||||
nranks = MPI.Comm_size(comm)
|
||||
rank = MPI.Comm_rank(comm)
|
||||
if mod(n,nranks) != 0
|
||||
println("n must be a multiple of nranks")
|
||||
MPI.Abort(comm,1)
|
||||
end
|
||||
n_own = div(n,nranks)
|
||||
u = zeros(n_own+2)
|
||||
u[1] = -1
|
||||
u[end] = 1
|
||||
u_new = copy(u)
|
||||
for t in 1:niters
|
||||
reqs = MPI.Request[]
|
||||
if rank != 0
|
||||
neig_rank = rank-1
|
||||
req = MPI.Isend(view(u,2:2),comm,dest=neig_rank,tag=0)
|
||||
push!(reqs,req)
|
||||
req = MPI.Irecv!(view(u,1:1),comm,source=neig_rank,tag=0)
|
||||
push!(reqs,req)
|
||||
end
|
||||
if rank != (nranks-1)
|
||||
neig_rank = rank+1
|
||||
s = n_own+1
|
||||
r = n_own+2
|
||||
req = MPI.Isend(view(u,s:s),comm,dest=neig_rank,tag=0)
|
||||
push!(reqs,req)
|
||||
req = MPI.Irecv!(view(u,r:r),comm,source=neig_rank,tag=0)
|
||||
push!(reqs,req)
|
||||
end
|
||||
for i in 3:n_own
|
||||
u_new[i] = 0.5*(u[i-1]+u[i+1])
|
||||
end
|
||||
MPI.Waitall(reqs)
|
||||
for i in (2,n_own+1)
|
||||
u_new[i] = 0.5*(u[i-1]+u[i+1])
|
||||
end
|
||||
u, u_new = u_new, u
|
||||
end
|
||||
return u
|
||||
end</code></pre><h2 id="Jacobi-method"><a class="docs-heading-anchor" href="#Jacobi-method">Jacobi method</a><a id="Jacobi-method-1"></a><a class="docs-heading-anchor-permalink" href="#Jacobi-method" title="Permalink"></a></h2><h3 id="Exercise-1-4"><a class="docs-heading-anchor" href="#Exercise-1-4">Exercise 1</a><a class="docs-heading-anchor-permalink" href="#Exercise-1-4" title="Permalink"></a></h3><pre><code class="language-julia hljs">function jacobi_mpi(n,niters)
|
||||
comm = MPI.COMM_WORLD
|
||||
nranks = MPI.Comm_size(comm)
|
||||
rank = MPI.Comm_rank(comm)
|
||||
if mod(n,nranks) != 0
|
||||
println("n must be a multiple of nranks")
|
||||
MPI.Abort(comm,1)
|
||||
end
|
||||
end</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../julia_mpi/">« MPI (point-to-point)</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="Tuesday 20 August 2024 12:05">Tuesday 20 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||
load = div(n,nranks)
|
||||
u = zeros(load+2)
|
||||
u[1] = -1
|
||||
u[end] = 1
|
||||
u_new = copy(u)
|
||||
for t in 1:niters
|
||||
reqs = MPI.Request[]
|
||||
if rank != 0
|
||||
neig_rank = rank-1
|
||||
req = MPI.Isend(view(u,2:2),comm,dest=neig_rank,tag=0)
|
||||
push!(reqs,req)
|
||||
req = MPI.Irecv!(view(u,1:1),comm,source=neig_rank,tag=0)
|
||||
push!(reqs,req)
|
||||
end
|
||||
if rank != (nranks-1)
|
||||
neig_rank = rank+1
|
||||
s = load+1
|
||||
r = load+2
|
||||
req = MPI.Isend(view(u,s:s),comm,dest=neig_rank,tag=0)
|
||||
push!(reqs,req)
|
||||
req = MPI.Irecv!(view(u,r:r),comm,source=neig_rank,tag=0)
|
||||
push!(reqs,req)
|
||||
end
|
||||
for i in 3:load
|
||||
u_new[i] = 0.5*(u[i-1]+u[i+1])
|
||||
end
|
||||
MPI.Waitall(reqs)
|
||||
for i in (2,load+1)
|
||||
u_new[i] = 0.5*(u[i-1]+u[i+1])
|
||||
end
|
||||
u, u_new = u_new, u
|
||||
|
||||
end
|
||||
# Gather the results
|
||||
if rank !=0
|
||||
lb = 2
|
||||
ub = load+1
|
||||
MPI.Send(view(u,lb:ub),comm,dest=0)
|
||||
u_all = zeros(0) # This will nevel be used
|
||||
else
|
||||
u_all = zeros(n+2)
|
||||
# Set boundary
|
||||
u_all[1] = -1
|
||||
u_all[end] = 1
|
||||
# Set data for rank 0
|
||||
lb = 2
|
||||
ub = load+1
|
||||
u_all[lb:ub] = view(u,lb:ub)
|
||||
# Set data for other ranks
|
||||
for other_rank in 1:(nranks-1)
|
||||
lb += load
|
||||
ub += load
|
||||
MPI.Recv!(view(u_all,lb:ub),comm;source=other_rank)
|
||||
end
|
||||
end
|
||||
return u_all
|
||||
end</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../jacobi_method/">« Jacobi method</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="Tuesday 20 August 2024 13:32">Tuesday 20 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||
+2
-2
@@ -1,5 +1,5 @@
|
||||
<!DOCTYPE html>
|
||||
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>- · XM_40017</title><meta name="title" content="- · XM_40017"/><meta property="og:title" content="- · XM_40017"/><meta property="twitter:title" content="- · XM_40017"/><meta name="description" content="Documentation for XM_40017."/><meta property="og:description" content="Documentation for XM_40017."/><meta property="twitter:description" content="Documentation for XM_40017."/><meta property="og:url" content="https://fverdugo.github.io/XM_40017/tsp/"/><meta property="twitter:url" content="https://fverdugo.github.io/XM_40017/tsp/"/><link rel="canonical" href="https://fverdugo.github.io/XM_40017/tsp/"/><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 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class="tocitem" href="../julia_mpi/">MPI (point-to-point)</a></li></ul></li><li><a class="tocitem" href="../solutions_for_all_notebooks/">Solutions</a></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 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-navbar-link" href="https://github.com/fverdugo/XM_40017/blob/main/notebooks/tsp.ipynb" title="View source on GitHub"><span 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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><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><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/">Asynchronous programming in Julia</a></li><li><a class="tocitem" href="../julia_distributed/">Distributed computing in Julia</a></li><li><a class="tocitem" href="../matrix_matrix/">Matrix-matrix multiplication</a></li><li><a class="tocitem" href="../julia_mpi/">MPI (point-to-point)</a></li><li><a class="tocitem" href="../jacobi_method/">Jacobi method</a></li></ul></li><li><a class="tocitem" href="../solutions_for_all_notebooks/">Solutions</a></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 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-navbar-link" href="https://github.com/fverdugo/XM_40017/blob/main/notebooks/tsp.ipynb" title="View source on GitHub"><span class="docs-icon fa-solid"><Line truncated
|
||||
<header class="admonition-header">Tip</header>
|
||||
<div class="admonition-body">
|
||||
<ul>
|
||||
@@ -14,4 +14,4 @@
|
||||
var myIframe = document.getElementById("notebook");
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iFrameResize({log:true}, myIframe);
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});
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</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="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="Tuesday 20 August 2024 12:05">Tuesday 20 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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</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="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="Tuesday 20 August 2024 13:32">Tuesday 20 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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||||
Reference in new issue
Block a user