build based on ebdeef8

dev/getting_started_with_julia/index.html

@@ -14,4 +14,4 @@ julia&gt; DataFrame(a=[1,2],b=[3,4])</code></pre><p>You should get an error or a
 BenchmarkTools = &quot;6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf&quot;
 DataFrames = &quot;a93c6f00-e57d-5684-b7b6-d8193f3e46c0&quot;
 MPI = &quot;da04e1cc-30fd-572f-bb4f-1f8673147195&quot;</code></pre><p>Copy the contents of previous code block into a file called  <code>Project.toml</code> and place it in an empty folder named <code>newproject</code>. It is important that the file is named <code>Project.toml</code>. You can create a new folder from the REPL with</p><pre><code class="language-julia hljs">julia&gt; mkdir(&quot;newproject&quot;)</code></pre><p>To install all the packages registered in this file you need to activate the folder containing your <code>Project.toml</code> file</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; activate newproject</code></pre><p>and then <em>instantiating</em> it</p><pre><code class="language-julia hljs">(newproject) pkg&gt; instantiate</code></pre><p>The instantiate command will download and install all listed packages and their dependencies in just one click.</p><h3 id="Getting-help-in-package-mode"><a class="docs-heading-anchor" href="#Getting-help-in-package-mode">Getting help in package mode</a><a id="Getting-help-in-package-mode-1"></a><a class="docs-heading-anchor-permalink" href="#Getting-help-in-package-mode" title="Permalink"></a></h3><p>You can get help about a particular package operator by writing <code>help</code> in front of it</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; help activate</code></pre><p>You can get an overview of all package commands by typing <code>help</code> alone</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; help</code></pre><h3 id="Package-operations-in-Julia-code"><a class="docs-heading-anchor" href="#Package-operations-in-Julia-code">Package operations in Julia code</a><a id="Package-operations-in-Julia-code-1"></a><a class="docs-heading-anchor-permalink" href="#Package-operations-in-Julia-code" title="Permalink"></a></h3><p>In some situations it is required to use package commands in Julia code, e.g., to automatize installation and deployment of Julia applications. This can be done using the <code>Pkg</code> package. For instance</p><pre><code class="language-julia hljs">julia&gt; using Pkg
-julia&gt; Pkg.status()</code></pre><p>is equivalent to call <code>status</code> in package mode.</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; status</code></pre><h2 id="Conclusion"><a class="docs-heading-anchor" href="#Conclusion">Conclusion</a><a id="Conclusion-1"></a><a class="docs-heading-anchor-permalink" href="#Conclusion" title="Permalink"></a></h2><p>We have learned the basics of how to work with Julia. If you want to further dig into the topics we have covered here, you can take a look and 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="../notebooks/julia_basics/">Julia Basics »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 09:50">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+julia&gt; Pkg.status()</code></pre><p>is equivalent to call <code>status</code> in package mode.</p><pre><code class="language-julia hljs">(@v1.8) pkg&gt; status</code></pre><h2 id="Conclusion"><a class="docs-heading-anchor" href="#Conclusion">Conclusion</a><a id="Conclusion-1"></a><a class="docs-heading-anchor-permalink" href="#Conclusion" title="Permalink"></a></h2><p>We have learned the basics of how to work with Julia. If you want to further dig into the topics we have covered here, you can take a look and 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="../notebooks/julia_basics/">Julia Basics »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 11:09">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/notebook-html/jacobi_method.html

@@ -7481,7 +7481,7 @@ a.anchor-link {
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 <div class="highlight hl-julia"><pre><span></span><span class="k">using</span><span class="w"> </span><span class="n">Printf</span>
@@ -7496,6 +7496,8 @@ a.anchor-link {
 <span class="n">gauss_seidel_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="s">"c"</span><span class="p">)</span>
 <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">jacobi_4_check</span><span class="p">(</span><span class="n">anwswer</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>
 </pre></div>
 </div>
 </div>
@@ -7506,9 +7508,9 @@ a.anchor-link {
 </div>
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-<pre>jacobi_2_check (generic function with 1 method)</pre>
+<pre>jacobi_4_check (generic function with 1 method)</pre>
 </div>
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@@ -7520,7 +7522,7 @@ a.anchor-link {
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-<h2 id="The-Jacobi-method-for-the-Laplace-equation">The Jacobi method for the Laplace equation<a class="anchor-link" href="#The-Jacobi-method-for-the-Laplace-equation">¶</a></h2><p>The <a href="https://en.wikipedia.org/wiki/Jacobi_method">Jacobi method</a> is a numerical tool to solve systems of linear algebraic equations. One of the main applications of the Jacobi method is to solve boundary value problems (BVPs). I.e., given the values at the boundary (of a grid), the Jacoby method will find the interior values that fulfill a certain equation.</p>
+<h2 id="The-Jacobi-method-for-the-Laplace-equation">The Jacobi method for the Laplace equation<a class="anchor-link" href="#The-Jacobi-method-for-the-Laplace-equation">¶</a></h2><p>The <a href="https://en.wikipedia.org/wiki/Jacobi_method">Jacobi method</a> is a numerical tool to solve systems of linear algebraic equations. One of the main applications of the method is to solve boundary value problems (BVPs). I.e., given the values at the boundary (of a grid), the Jacobi method will find the interior values that fulfill a certain equation.</p>
 </div>
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@@ -7651,7 +7653,7 @@ a.anchor-link {
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-<h3 id="Where-do-we-can-exploit-parallelism?">Where do we can exploit parallelism?<a class="anchor-link" href="#Where-do-we-can-exploit-parallelism?">¶</a></h3><p>Look at the two nested loops in the sequential implementation:</p>
+<h3 id="Where-can-we-exploit-parallelism?">Where can we exploit parallelism?<a class="anchor-link" href="#Where-can-we-exploit-parallelism?">¶</a></h3><p>Look at the two nested loops in the sequential implementation:</p>
 <div class="highlight"><pre><span></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">nsteps</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>
@@ -7661,7 +7663,7 @@ a.anchor-link {
 </pre></div>
 <ul>
 <li>The outer loop cannot be parallelized. The value of <code>u</code> at step <code>t+1</code> depends on the value at the previous step <code>t</code>.</li>
-<li>The inner loop can be parallelized</li>
+<li>The inner loop can be parallelized.</li>
 </ul>
 </div>
 </div>
@@ -7749,12 +7751,12 @@ d) The inner, but not the outer</code></pre>
 </div>
 </div>
 </div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=4edad93f">
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=4edad93f">
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 <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>
@@ -7764,19 +7766,6 @@ d) The inner, but not the outer</code></pre>
 </div>
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-<div class="jp-Cell-outputWrapper">
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-<pre>It's not correct. Keep trying! 💪
-</pre>
-</div>
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@@ -7868,12 +7857,12 @@ d) Communication: O(1), computation: O(N/P)</code></pre>
 </div>
 </div>
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-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell" id="cell-id=3a03fc4c">
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=3a03fc4c">
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-<div class="jp-InputPrompt jp-InputArea-prompt">In [4]:</div>
+<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>
@@ -7883,19 +7872,6 @@ d) Communication: O(1), computation: O(N/P)</code></pre>
 </div>
 </div>
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-<div class="jp-Cell-outputWrapper">
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-</div>
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-<div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
-<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain" tabindex="0">
-<pre>It's not correct. Keep trying! 💪
-</pre>
-</div>
-</div>
-</div>
-</div>
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@@ -7904,7 +7880,7 @@ d) Communication: O(1), computation: O(N/P)</code></pre>
 <div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
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 <h2 id="Implementation">Implementation<a class="anchor-link" href="#Implementation">¶</a></h2><p>We consider the implementation using MPI. The programming model of MPI is generally better suited for data-parallel algorithms like this one than the task-based model provided by Distributed.jl. In any case, one can also implement it using Distributed, but it requires some extra effort to setup remote channels right for the communication between neighbor processes.</p>
-<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>
+<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>
 </div>
 </div>
 </div>
@@ -7930,7 +7906,7 @@ d) Communication: O(1), computation: O(N/P)</code></pre>
 <div class="jp-InputPrompt jp-InputArea-prompt">In [ ]:</div>
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-<div class="highlight hl-julia"><pre><span></span><span class="k">using</span><span class="w"> </span><span class="n">MPIClusterManagers</span>
+<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>
 </pre></div>
 </div>
@@ -7955,6 +7931,22 @@ d) Communication: O(1), computation: O(N/P)</code></pre>
 </div>
 </div>
 </div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=a0923606">
+<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="c"># Test cell, remove me</span>
+<span class="n">u</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</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="w"> </span><span class="mi">6</span><span class="o">:</span><span class="mi">6</span><span class="p">)</span>
+</pre></div>
+</div>
+</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">
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@@ -7963,9 +7955,8 @@ d) Communication: O(1), computation: O(N/P)</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="nd">@mpi_do</span><span class="w"> </span><span class="n">manager</span><span class="w"> </span><span class="k">begin</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">MPI</span><span class="o">.</span><span class="n">Initialized</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Init</span><span class="p">()</span>
 <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">nw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Comm_size</span><span class="p">(</span><span class="n">comm</span><span class="p">)</span>
 <span class="w">    </span><span class="n">iw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Comm_rank</span><span class="p">(</span><span class="n">comm</span><span class="p">)</span><span class="o">+</span><span class="mi">1</span>
@@ -7981,6 +7972,7 @@ d) Communication: O(1), computation: O(N/P)</code></pre>
 <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"># Exchange cell values with neighbors</span>
 <span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">iw</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">1</span>
 <span class="w">                </span><span class="n">neig_rank</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">iw</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
 <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>
@@ -7990,8 +7982,8 @@ d) Communication: O(1), computation: O(N/P)</code></pre>
 <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">iw</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">nw</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="p">(</span><span class="n">iw</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
-<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">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="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>
@@ -8005,6 +7997,14 @@ d) Communication: O(1), computation: O(N/P)</code></pre>
 <span class="w">        </span><span class="k">end</span>
 <span class="w">        </span><span class="n">u</span>
 <span class="w">        </span><span class="nd">@show</span><span class="w"> </span><span class="n">u</span>
+<span class="w">        </span><span class="c"># Gather results in root process</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">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="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="n">root</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="w"> </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">iw</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</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="k">end</span><span class="w">            </span>
 <span class="w">    </span><span class="k">end</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">load</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span>
@@ -8043,7 +8043,70 @@ d) 4</code></pre>
 <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_2_check</span><span class="p">(</span><span class="n">answer</span><span class="p">)</span>
-<span class="c"># TODO: think of more questions</span>
+</pre></div>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div class="jp-Cell jp-MarkdownCell jp-Notebook-cell" id="cell-id=075dd6d8">
+<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">
+<div class="alert alert-block alert-success">
+<b>Question:</b>  After the end of the for-loop (line 43), ...
+</div>
+<pre><code>a) each worker holds the complete solution.
+b) the root process holds the solution. 
+c) the ghost cells contain redundant values. 
+d) all ghost cells contain the initial values -1 and 1. </code></pre>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=c3b58002">
+<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="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=4537661d">
+<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">
+<div class="alert alert-block alert-success">
+<b>Question:</b>  In line 35 of the code, we wait for all receive and send requests. Is it possible to instead wait for just the receive requests?
+</div>
+<pre><code>a) No, because the send buffer might be overwritten if we don't wait for send requests.
+b) No, because MPI does not allow an asynchronous send without a Wait().
+c) Yes, because each send has a matching receive, so all requests are done when the receive requests return.  
+d) Yes, because there are no writes to the send buffer in this iteration.</code></pre>
+</div>
+</div>
+</div>
+</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=e16ea5eb">
+<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="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_4_check</span><span class="p">(</span><span class="n">answer</span><span class="p">)</span>
 </pre></div>
 </div>
 </div>
@@ -8341,9 +8404,8 @@ d) 4</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="nd">@mpi_do</span><span class="w"> </span><span class="n">manager</span><span class="w"> </span><span class="k">begin</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">MPI</span><span class="o">.</span><span class="n">Initialized</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Init</span><span class="p">()</span>
 <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">nw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Comm_size</span><span class="p">(</span><span class="n">comm</span><span class="p">)</span>
 <span class="w">    </span><span class="n">iw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Comm_rank</span><span class="p">(</span><span class="n">comm</span><span class="p">)</span><span class="o">+</span><span class="mi">1</span>
@@ -8359,6 +8421,7 @@ d) 4</code></pre>
 <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"># Exchange cell values with neighbors</span>
 <span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">iw</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">1</span>
 <span class="w">                </span><span class="n">neig_rank</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">iw</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
 <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>
@@ -8368,8 +8431,8 @@ d) 4</code></pre>
 <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">iw</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">nw</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="p">(</span><span class="n">iw</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
-<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">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="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>
@@ -8383,85 +8446,14 @@ d) 4</code></pre>
 <span class="w">        </span><span class="k">end</span>
 <span class="w">        </span><span class="n">u</span>
 <span class="w">        </span><span class="nd">@show</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="c"># Gather results in root process</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">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">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">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">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">load</span><span class="o">*</span><span class="n">nw</span>
+<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">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">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="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="n">root</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">comm</span><span class="p">)</span>
-<span class="k">end</span>
+<span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">iw</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span>
-</pre></div>
+<span class="w">            </span><span class="nd">@show</span><span class="w"> </span><span class="n">results</span>
-</div>
+<span class="w">        </span><span class="k">end</span><span class="w">            </span>
-</div>
-</div>
-</div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=f302cce2">
-<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="c">## TODO move the following solution to its appropiate place:</span>
-</pre></div>
-</div>
-</div>
-</div>
-</div>
-</div><div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs" id="cell-id=4fa7fad3">
-<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="k">using</span><span class="w"> </span><span class="n">MPI</span>
-<span class="w">    </span><span class="n">MPI</span><span class="o">.</span><span class="n">Initialized</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Init</span><span class="p">()</span>
-<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">nw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Comm_size</span><span class="p">(</span><span class="n">comm</span><span class="p">)</span>
-<span class="w">    </span><span class="n">iw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Comm_rank</span><span class="p">(</span><span class="n">comm</span><span class="p">)</span><span class="o">+</span><span class="mi">1</span>
-<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="k">if</span><span class="w"> </span><span class="n">mod</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">nw</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">0</span>
-<span class="w">            </span><span class="n">println</span><span class="p">(</span><span class="s">"n must be a multiple of nw"</span><span class="p">)</span>
-<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">nw</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">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_snd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Request</span><span class="p">[]</span>
-<span class="w">            </span><span class="n">reqs_rcv</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Request</span><span class="p">[]</span>
-<span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="n">iw</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">1</span>
-<span class="w">                </span><span class="n">neig_rank</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">iw</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
-<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_snd</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_rcv</span><span class="p">,</span><span class="n">req</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">iw</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">nw</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="p">(</span><span class="n">iw</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
-<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="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_snd</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_rcv</span><span class="p">,</span><span class="n">req</span><span class="p">)</span>
-<span class="w">            </span><span class="k">end</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">3</span><span class="o">:</span><span class="n">n_own</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">MPI</span><span class="o">.</span><span class="n">Waitall</span><span class="p">(</span><span class="n">reqs_rcv</span><span class="p">)</span>
-<span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="n">n_own</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span>
-<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">MPI</span><span class="o">.</span><span class="n">Waitall</span><span class="p">(</span><span class="n">reqs_snd</span><span class="p">)</span>
-<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">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">load</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span>

dev/notebook-html/solutions.html

@@ -7502,9 +7502,8 @@ a.anchor-link {
 <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="nd">@mpi_do</span><span class="w"> </span><span class="n">manager</span><span class="w"> </span><span class="k">begin</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">MPI</span><span class="o">.</span><span class="n">Initialized</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Init</span><span class="p">()</span>
 <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">nw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Comm_size</span><span class="p">(</span><span class="n">comm</span><span class="p">)</span>
 <span class="w">    </span><span class="n">iw</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Comm_rank</span><span class="p">(</span><span class="n">comm</span><span class="p">)</span><span class="o">+</span><span class="mi">1</span>
@@ -7530,8 +7529,8 @@ a.anchor-link {
 <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">iw</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">nw</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="p">(</span><span class="n">iw</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span>
-<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">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="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_snd</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>
@@ -7548,6 +7547,7 @@ a.anchor-link {
 <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="nd">@show</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">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">load</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span>

dev/notebooks/jacobi_2D.ipynb

@@ -2110,7 +2110,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Julia 1.9.0",
+   "display_name": "Julia 1.9.1",
    "language": "julia",
    "name": "julia-1.9"
   },
@@ -2118,7 +2118,7 @@
    "file_extension": ".jl",
    "mimetype": "application/julia",
    "name": "julia",
-   "version": "1.9.0"
+   "version": "1.9.1"
   }
  },
  "nbformat": 4,

dev/notebooks/jacobi_2D/index.html

@@ -18,4 +18,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 09:50">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 11:09">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/notebooks/jacobi_method.ipynb

@@ -35,17 +35,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 2,
    "id": "1dc78750",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "jacobi_2_check (generic function with 1 method)"
+       "jacobi_4_check (generic function with 1 method)"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 2,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -62,7 +62,9 @@
     "end\n",
     "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\")"
+    "jacobi_2_check(answer) = answer_checker(answer, \"b\")\n",
+    "jacobi_3_check(answer) = answer_checker(answer, \"c\")\n",
+    "jacobi_4_check(anwswer) = answer_checker(answer, \"d\")"
    ]
   },
   {
@@ -73,7 +75,7 @@
     "## The Jacobi method for the Laplace equation\n",
     "\n",
     "\n",
-    "The [Jacobi method](https://en.wikipedia.org/wiki/Jacobi_method) is a numerical tool to solve systems of linear algebraic equations. One of the main applications of the Jacobi method is to solve boundary value problems (BVPs). I.e., given the values at the boundary (of a grid), the Jacoby method will find the interior values that fulfill a certain equation.\n",
+    "The [Jacobi method](https://en.wikipedia.org/wiki/Jacobi_method) is a numerical tool to solve systems of linear algebraic equations. One of the main applications of the method is to solve boundary value problems (BVPs). I.e., given the values at the boundary (of a grid), the Jacobi method will find the interior values that fulfill a certain equation.\n",
     "\n"
    ]
   },
@@ -184,7 +186,7 @@
    "metadata": {},
    "source": [
     "\n",
-    "### Where do we can exploit parallelism?\n",
+    "### Where can we exploit parallelism?\n",
     "\n",
     "Look at the two nested loops in the sequential implementation:\n",
     "\n",
@@ -198,7 +200,7 @@
     "```\n",
     "\n",
     "- The outer loop cannot be parallelized. The value of `u` at step `t+1` depends on the value at the previous step `t`.\n",
-    "- The inner loop can be parallelized\n",
+    "- The inner loop can be parallelized.\n",
     "\n"
    ]
   },
@@ -276,20 +278,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "id": "4edad93f",
    "metadata": {
     "scrolled": true
    },
-   "outputs": [
+   "outputs": [],
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "It's not correct. Keep trying! 💪\n"
-     ]
-    }
-   ],
    "source": [
     "answer = \"x\" # replace x with a, b, c or d\n",
     "gauss_seidel_1_check(answer)"
@@ -377,18 +371,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "id": "3a03fc4c",
    "metadata": {},
-   "outputs": [
+   "outputs": [],
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "It's not correct. Keep trying! 💪\n"
-     ]
-    }
-   ],
    "source": [
     "answer = \"x\" # replace x with a, b, c or d\n",
     "jacobi_1_check(answer)"
@@ -403,7 +389,7 @@
     "\n",
     "We consider the implementation using MPI. The programming model of MPI is generally better suited for data-parallel algorithms like this one than the task-based model provided by Distributed.jl. In any case, one can also implement it using Distributed, but it requires some extra effort to setup remote channels right for the communication between neighbor processes.\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. 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"
    ]
   },
   {
@@ -423,7 +409,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "using MPIClusterManagers\n",
+    "using MPIClusterManagers \n",
     "using Distributed"
    ]
   },
@@ -444,13 +430,26 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "68851107",
+   "id": "a0923606",
    "metadata": {},
    "outputs": [],
    "source": [
-    "@everywhere workers() begin\n",
+    "# Test cell, remove me\n",
+    "u = [-1, 0, 0, 0, 0, 1]\n",
+    "view(u, 6:6)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "68851107",
+   "metadata": {
+    "code_folding": []
+   },
+   "outputs": [],
+   "source": [
+    "@mpi_do manager begin\n",
     "    using MPI\n",
-    "    MPI.Initialized() || MPI.Init()\n",
     "    comm = MPI.Comm_dup(MPI.COMM_WORLD)\n",
     "    nw = MPI.Comm_size(comm)\n",
     "    iw = MPI.Comm_rank(comm)+1\n",
@@ -466,6 +465,7 @@
     "        u_new = copy(u)\n",
     "        for t in 1:niters\n",
     "            reqs = MPI.Request[]\n",
+    "            # Exchange cell values with neighbors\n",
     "            if iw != 1\n",
     "                neig_rank = (iw-1)-1\n",
     "                req = MPI.Isend(view(u,2:2),comm,dest=neig_rank,tag=0)\n",
@@ -475,8 +475,8 @@
     "            end\n",
     "            if iw != nw\n",
     "                neig_rank = (iw+1)-1\n",
-    "                s = n_own-1\n",
+    "                s = n_own+1\n",
-    "                r = n_own\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",
@@ -490,6 +490,14 @@
     "        end\n",
     "        u\n",
     "        @show u\n",
+    "        # Gather results in root process\n",
+    "        results = zeros(n+2)\n",
+    "        results[1] = -1\n",
+    "        results[n+2] = 1\n",
+    "        MPI.Gather!(view(u,2:n_own+1), view(results, 2:n+1), root=0, comm)\n",
+    "        if iw == 1\n",
+    "            @show results\n",
+    "        end            \n",
     "    end\n",
     "    niters = 100\n",
     "    load = 4\n",
@@ -522,8 +530,60 @@
    "outputs": [],
    "source": [
     "answer = \"x\" # replace x with a, b, c or d\n",
-    "jacobi_2_check(answer)\n",
+    "jacobi_2_check(answer)"
-    "# TODO: think of more questions"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "075dd6d8",
+   "metadata": {},
+   "source": [
+    "<div class=\"alert alert-block alert-success\">\n",
+    "<b>Question:</b>  After the end of the for-loop (line 43), ...\n",
+    "</div>\n",
+    "\n",
+    "    a) each worker holds the complete solution.\n",
+    "    b) the root process holds the solution. \n",
+    "    c) the ghost cells contain redundant values. \n",
+    "    d) all ghost cells contain the initial values -1 and 1. "
+   ]
+  },
+  {
+   "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": "4537661d",
+   "metadata": {},
+   "source": [
+    "<div class=\"alert alert-block alert-success\">\n",
+    "<b>Question:</b>  In line 35 of the code, we wait for all receive and send requests. Is it possible to instead wait for just the receive requests?\n",
+    "</div>\n",
+    "\n",
+    "  \n",
+    "    a) No, because the send buffer might be overwritten if we don't wait for send requests.\n",
+    "    b) No, because MPI does not allow an asynchronous send without a Wait().\n",
+    "    c) Yes, because each send has a matching receive, so all requests are done when the receive requests return.  \n",
+    "    d) Yes, because there are no writes to the send buffer in this iteration."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e16ea5eb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "answer = \"x\" # replace x with a, b, c or d.\n",
+    "jacobi_4_check(answer)"
    ]
   },
   {
@@ -801,9 +861,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "@everywhere workers() begin\n",
+    "@mpi_do manager begin\n",
     "    using MPI\n",
-    "    MPI.Initialized() || MPI.Init()\n",
     "    comm = MPI.Comm_dup(MPI.COMM_WORLD)\n",
     "    nw = MPI.Comm_size(comm)\n",
     "    iw = MPI.Comm_rank(comm)+1\n",
@@ -819,6 +878,7 @@
     "        u_new = copy(u)\n",
     "        for t in 1:niters\n",
     "            reqs = MPI.Request[]\n",
+    "            # Exchange cell values with neighbors\n",
     "            if iw != 1\n",
     "                neig_rank = (iw-1)-1\n",
     "                req = MPI.Isend(view(u,2:2),comm,dest=neig_rank,tag=0)\n",
@@ -828,8 +888,8 @@
     "            end\n",
     "            if iw != nw\n",
     "                neig_rank = (iw+1)-1\n",
-    "                s = n_own-1\n",
+    "                s = n_own+1\n",
-    "                r = n_own\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",
@@ -843,77 +903,14 @@
     "        end\n",
     "        u\n",
     "        @show u\n",
-    "    end\n",
+    "        # Gather results in root process\n",
-    "    niters = 100\n",
+    "        results = zeros(n+2)\n",
-    "    load = 4\n",
+    "        results[1] = -1\n",
-    "    n = load*nw\n",
+    "        results[n+2] = 1\n",
-    "    jacobi_mpi(n,niters)\n",
+    "        MPI.Gather!(view(u,2:n_own+1), view(results, 2:n+1), root=0, comm)\n",
-    "end"
+    "        if iw == 1\n",
-   ]
+    "            @show results\n",
-  },
+    "        end            \n",
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "f302cce2",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "## TODO move the following solution to its appropiate place:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "4fa7fad3",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "@everywhere workers() begin\n",
-    "    using MPI\n",
-    "    MPI.Initialized() || MPI.Init()\n",
-    "    comm = MPI.Comm_dup(MPI.COMM_WORLD)\n",
-    "    nw = MPI.Comm_size(comm)\n",
-    "    iw = MPI.Comm_rank(comm)+1\n",
-    "    function jacobi_mpi(n,niters)\n",
-    "        if mod(n,nw) != 0\n",
-    "            println(\"n must be a multiple of nw\")\n",
-    "            MPI.Abort(comm,1)\n",
-    "        end\n",
-    "        n_own = div(n,nw)\n",
-    "        u = zeros(n_own+2)\n",
-    "        u[1] = -1\n",
-    "        u[end] = 1\n",
-    "        u_new = copy(u)\n",
-    "        for t in 1:niters\n",
-    "            reqs_snd = MPI.Request[]\n",
-    "            reqs_rcv = MPI.Request[]\n",
-    "            if iw != 1\n",
-    "                neig_rank = (iw-1)-1\n",
-    "                req = MPI.Isend(view(u,2:2),comm,dest=neig_rank,tag=0)\n",
-    "                push!(reqs_snd,req)\n",
-    "                req = MPI.Irecv!(view(u,1:1),comm,source=neig_rank,tag=0)\n",
-    "                push!(reqs_rcv,req)\n",
-    "            end\n",
-    "            if iw != nw\n",
-    "                neig_rank = (iw+1)-1\n",
-    "                s = n_own-1\n",
-    "                r = n_own\n",
-    "                req = MPI.Isend(view(u,s:s),comm,dest=neig_rank,tag=0)\n",
-    "                push!(reqs_snd,req)\n",
-    "                req = MPI.Irecv!(view(u,r:r),comm,source=neig_rank,tag=0)\n",
-    "                push!(reqs_rcv,req)\n",
-    "            end\n",
-    "            for i in 3:n_own\n",
-    "                u_new[i] = 0.5*(u[i-1]+u[i+1])\n",
-    "            end\n",
-    "            MPI.Waitall(reqs_rcv)\n",
-    "            for i in (2,n_own+1)\n",
-    "                u_new[i] = 0.5*(u[i-1]+u[i+1])\n",
-    "            end\n",
-    "            MPI.Waitall(reqs_snd)\n",
-    "            u, u_new = u_new, u\n",
-    "        end\n",
-    "        u\n",
     "    end\n",
     "    niters = 100\n",
     "    load = 4\n",

dev/notebooks/jacobi_method/index.html

@@ -18,4 +18,4 @@
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dev/notebooks/julia_async/index.html

@@ -18,4 +18,4 @@
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     iFrameResize({log:true}, myIframe);	
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dev/notebooks/julia_basics/index.html

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dev/notebooks/julia_distributed/index.html

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dev/notebooks/julia_intro/index.html

@@ -18,4 +18,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 09:50">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 11:09">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/notebooks/julia_jacobi/index.html

@@ -18,4 +18,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 09:50">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 11:09">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/notebooks/julia_tutorial/index.html

@@ -18,4 +18,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 09:50">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 11:09">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/notebooks/matrix_matrix/index.html

@@ -18,4 +18,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../julia_distributed/">« Remote calls and remote channels</a><a class="docs-footer-nextpage" href="../jacobi_method/">Jacobi »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 09:50">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../julia_distributed/">« Remote calls and remote channels</a><a class="docs-footer-nextpage" href="../jacobi_method/">Jacobi »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 11:09">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/notebooks/mpi_tutorial/index.html

@@ -18,4 +18,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 09:50">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 11:09">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/notebooks/notebook-hello/index.html

@@ -18,4 +18,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 09:50">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 11:09">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/notebooks/solutions.ipynb

@@ -56,9 +56,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "@everywhere workers() begin\n",
+    "@mpi_do manager begin\n",
     "    using MPI\n",
-    "    MPI.Initialized() || MPI.Init()\n",
     "    comm = MPI.Comm_dup(MPI.COMM_WORLD)\n",
     "    nw = MPI.Comm_size(comm)\n",
     "    iw = MPI.Comm_rank(comm)+1\n",
@@ -84,8 +83,8 @@
     "            end\n",
     "            if iw != nw\n",
     "                neig_rank = (iw+1)-1\n",
-    "                s = n_own-1\n",
+    "                s = n_own+1\n",
-    "                r = n_own\n",
+    "                r = n_own+2\n",
     "                req = MPI.Isend(view(u,s:s),comm,dest=neig_rank,tag=0)\n",
     "                push!(reqs_snd,req)\n",
     "                req = MPI.Irecv!(view(u,r:r),comm,source=neig_rank,tag=0)\n",
@@ -102,6 +101,7 @@
     "            u, u_new = u_new, u\n",
     "        end\n",
     "        u\n",
+    "        @show u\n",
     "    end\n",
     "    niters = 100\n",
     "    load = 4\n",

dev/notebooks/solutions/index.html

@@ -18,4 +18,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../jacobi_method/">« Jacobi</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 09:50">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../jacobi_method/">« Jacobi</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 11:09">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/notebooks/tsp/index.html

@@ -18,4 +18,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 09:50">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 14 August 2023 11:09">Monday 14 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/search/index.html

@@ -1,2 +1,2 @@
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