build based on b5efc3d

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-23T12:01:16","documenter_version":"1.7.0"}}
+{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-23T14:37:03","documenter_version":"1.7.0"}}

dev/LEQ/index.html

@@ -14,4 +14,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../asp/">« All pairs of shortest paths</a><a class="docs-footer-nextpage" href="../tsp/">Traveling salesperson problem »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 12:01">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../asp/">« All pairs of shortest paths</a><a class="docs-footer-nextpage" href="../tsp/">Traveling salesperson problem »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/asp/index.html

@@ -14,4 +14,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../jacobi_method/">« Jacobi method</a><a class="docs-footer-nextpage" href="../LEQ/">Gaussian elimination »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 12:01">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../jacobi_method/">« Jacobi method</a><a class="docs-footer-nextpage" href="../LEQ/">Gaussian elimination »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/getting_started_with_julia/index.html

@@ -15,4 +15,4 @@ DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 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">(@v1.10) 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">(@v1.10) 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">(@v1.10) pkg&gt; help</code></pre><h3 id="Package-operations-in-Julia-code"><a class="docs-heading-anchor" href="#Package-operations-in-Julia-code">Package operations in Julia code</a><a id="Package-operations-in-Julia-code-1"></a><a class="docs-heading-anchor-permalink" href="#Package-operations-in-Julia-code" title="Permalink"></a></h3><p>In some situations it is required to use package commands in Julia code, e.g., to automatize installation and deployment of Julia applications. This can be done using the <code>Pkg</code> package. For instance</p><pre><code class="language-julia hljs">julia&gt; using Pkg
 julia&gt; Pkg.status()</code></pre><p>is equivalent to calling <code>status</code> in package mode.</p><pre><code class="language-julia hljs">(@v1.10) pkg&gt; status</code></pre><h3 id="Creating-you-own-package"><a class="docs-heading-anchor" href="#Creating-you-own-package">Creating you own package</a><a id="Creating-you-own-package-1"></a><a class="docs-heading-anchor-permalink" href="#Creating-you-own-package" title="Permalink"></a></h3><p>In many situations, it is useful to create your own package, for instance, when working with a large code base, when you want to reduce compilation latency using <a href="https://github.com/timholy/Revise.jl"><code>Revise.jl</code></a>, or if you want to eventually <a href="https://github.com/JuliaRegistries/Registrator.jl">register your package</a> and share it with others.</p><p>The simplest way of generating a package (called <code>MyPackage</code>) is as follows. Open Julia, go to package mode, and type</p><pre><code class="language-julia hljs">(@v1.10) pkg&gt; generate MyPackage</code></pre><p>This will crate a minimal package consisting of a new folder <code>MyPackage</code> with two files:</p><ul><li><code>MyPackage/Project.toml</code>: Project file defining the direct dependencies of your package.</li><li><code>MyPackage/src/MyPackage.jl</code>: Main source file of your package. You can split your code in several files if needed, and include them in the package main file using function <code>include</code>.</li></ul><div class="admonition is-success"><header class="admonition-header">Tip</header><div class="admonition-body"><p>This approach only generates a very minimal package. To create a more sophisticated package skeleton (including unit testing, code coverage, readme file, licence, etc.) use <a href="https://github.com/JuliaCI/PkgTemplates.jl"><code>PkgTemplates.jl</code></a> or <a href="https://github.com/abelsiqueira/BestieTemplate.jl"><code>BestieTemplate.jl</code></a>. The later one is developed in Amsterdam at the <a href="https://www.esciencecenter.nl/">Netherlands eScience Center</a>.</p></div></div><p>You can add dependencies to the package by activating the <code>MyPackage</code> folder in package mode and adding new dependencies as always:</p><pre><code class="language-julia hljs">(@v1.10) pkg&gt; activate MyPackage
 (MyPackage) pkg&gt; add MPI</code></pre><p>This will add MPI to your package dependencies.</p><h3 id="Using-your-own-package"><a class="docs-heading-anchor" href="#Using-your-own-package">Using your own package</a><a id="Using-your-own-package-1"></a><a class="docs-heading-anchor-permalink" href="#Using-your-own-package" title="Permalink"></a></h3><p>To use your package you first need to add it to a package environment of your choice. This is done by changing to package mode and typing <code>develop</code> followed by the path to the folder containing the package. For instance:</p><pre><code class="language-julia hljs">(@v1.10) pkg&gt; develop MyPackage</code></pre><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>You do not need to &quot;develop&quot; your package if you activated the package folder <code>MyPackage</code>.</p></div></div><p>Now, we can go back to standard Julia mode and use it as any other package:</p><pre><code class="language-julia hljs">using MyPackage
-MyPackage.greet()</code></pre><p>Here, we just called the example function defined in <code>MyPackage/src/MyPackage.jl</code>.</p><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, including how to run serial and parallel code, and how to manage, create, and use Julia packages. This knowledge will allow you to follow the course effectively! If you want to further dig into the topics we have covered here, you can take a look at the following links:</p><ul><li><a href="https://docs.julialang.org/en/v1/manual/getting-started/">Julia Manual</a></li><li><a href="https://pkgdocs.julialang.org/v1/getting-started/">Package manager</a></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../julia_basics/">Julia Basics »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 12:01">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+MyPackage.greet()</code></pre><p>Here, we just called the example function defined in <code>MyPackage/src/MyPackage.jl</code>.</p><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, including how to run serial and parallel code, and how to manage, create, and use Julia packages. This knowledge will allow you to follow the course effectively! If you want to further dig into the topics we have covered here, you can take a look at the following links:</p><ul><li><a href="https://docs.julialang.org/en/v1/manual/getting-started/">Julia Manual</a></li><li><a href="https://pkgdocs.julialang.org/v1/getting-started/">Package manager</a></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../julia_basics/">Julia Basics »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/jacobi_2D/index.html

@@ -14,4 +14,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 12:01">Monday 23 September 2024</span>. Using Julia version 1.10.5.</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/jacobi_method.ipynb

@@ -281,7 +281,7 @@
    "outputs": [],
    "source": [
     "n = 5\n",
-    "tol = 1e-9\n",
+    "tol = 1e-10\n",
     "jacobi_with_tol(n,tol)"
    ]
   },
@@ -1531,7 +1531,7 @@
     "    u = jacobi_mpi(n,niters,comm)\n",
     "    @show u\n",
     "end\n",
-    "run(`$(mpiexec()) -np 1 julia --project=. -e $code`);"
+    "run(`$(mpiexec()) -np 3 julia --project=. -e $code`);"
    ]
   },
   {
@@ -1914,7 +1914,7 @@
    "source": [
     "### Exercise 2\n",
     "\n",
-    "In the parallel implementation of the Jacobi method, we assumed that the method runs for a given number of iterations. In function, `jacobi_with_tol` at the beginning of the notebook shows how the Jacobi iterations can be stopped when the difference between iterations is small. Implement a parallel version of this function. Start with the in Exercise 1 and add the stopping criterion implemented in `jacobi_with_tol`. Use a text editor and the Julia REPL. Do not try to implement the code in a notebook."
+    "In the parallel implementation of the Jacobi method, we assumed that the method runs for a given number of iterations. In function, `jacobi_with_tol` at the beginning of the notebook shows how the Jacobi iterations can be stopped when the difference between iterations is small. Implement a parallel version of this function. Start with the code in Exercise 1 and add the stopping criterion implemented in `jacobi_with_tol`. Use a text editor and the Julia REPL. Do not try to implement the code in a notebook."
    ]
   },
   {

dev/jacobi_method/index.html

@@ -14,4 +14,4 @@
     var myIframe = document.getElementById("notebook");
     iFrameResize({log:true}, myIframe);	
 });
-</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../mpi_collectives/">« MPI (collectives)</a><a class="docs-footer-nextpage" href="../asp/">All pairs of shortest paths »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 12:01">Monday 23 September 2024</span>. Using Julia version 1.10.5.</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="../mpi_collectives/">« MPI (collectives)</a><a class="docs-footer-nextpage" href="../asp/">All pairs of shortest paths »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/jacobi_method_src/index.html

@@ -7832,7 +7832,7 @@ a.anchor-link {
 <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">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">5</span>
-<span class="n">tol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1e-9</span>
+<span class="n">tol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1e-10</span>
 <span class="n">jacobi_with_tol</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">tol</span><span class="p">)</span>
 </pre></div>
 </div>
@@ -9261,7 +9261,7 @@ d) This implementation does not work when distributing over just a single MPI ra
 <span class="w">    </span><span class="n">u</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">jacobi_mpi</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">niters</span><span class="p">,</span><span class="n">comm</span><span class="p">)</span>
 <span class="w">    </span><span class="nd">@show</span><span class="w"> </span><span class="n">u</span>
 <span class="k">end</span>
-<span class="n">run</span><span class="p">(</span><span class="sb">`</span><span class="si">$</span><span class="p">(</span><span class="n">mpiexec</span><span class="p">())</span><span class="sb"> -np 1 julia --project=. -e </span><span class="si">$code</span><span class="sb">`</span><span class="p">);</span>
+<span class="n">run</span><span class="p">(</span><span class="sb">`</span><span class="si">$</span><span class="p">(</span><span class="n">mpiexec</span><span class="p">())</span><span class="sb"> -np 3 julia --project=. -e </span><span class="si">$code</span><span class="sb">`</span><span class="p">);</span>
 </pre></div>
 </div>
 </div>
@@ -9681,7 +9681,7 @@ d) MPI_Sendrecv</code></pre>
 </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">
-<h3 id="Exercise-2">Exercise 2<a class="anchor-link" href="#Exercise-2">¶</a></h3><p>In the parallel implementation of the Jacobi method, we assumed that the method runs for a given number of iterations. In function, <code>jacobi_with_tol</code> at the beginning of the notebook shows how the Jacobi iterations can be stopped when the difference between iterations is small. Implement a parallel version of this function. Start with the in Exercise 1 and add the stopping criterion implemented in <code>jacobi_with_tol</code>. Use a text editor and the Julia REPL. Do not try to implement the code in a notebook.</p>
+<h3 id="Exercise-2">Exercise 2<a class="anchor-link" href="#Exercise-2">¶</a></h3><p>In the parallel implementation of the Jacobi method, we assumed that the method runs for a given number of iterations. In function, <code>jacobi_with_tol</code> at the beginning of the notebook shows how the Jacobi iterations can be stopped when the difference between iterations is small. Implement a parallel version of this function. Start with the code in Exercise 1 and add the stopping criterion implemented in <code>jacobi_with_tol</code>. Use a text editor and the Julia REPL. Do not try to implement the code in a notebook.</p>
 </div>
 </div>
 </div>

dev/julia_async/index.html

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dev/julia_basics/index.html

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dev/julia_distributed/index.html

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+</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../julia_async/">« Asynchronous programming in Julia</a><a class="docs-footer-nextpage" href="../matrix_matrix/">Matrix-matrix multiplication »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/julia_intro/index.html

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+</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/julia_jacobi/index.html

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dev/julia_mpi/index.html

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dev/julia_tutorial/index.html

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dev/matrix_matrix/index.html

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+</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../julia_distributed/">« Distributed computing in Julia</a><a class="docs-footer-nextpage" href="../julia_mpi/">MPI (point-to-point) »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/mpi_collectives/index.html

@@ -14,4 +14,4 @@
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+</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../julia_mpi/">« MPI (point-to-point)</a><a class="docs-footer-nextpage" href="../jacobi_method/">Jacobi method »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/mpi_tutorial/index.html

@@ -14,4 +14,4 @@
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     iFrameResize({log:true}, myIframe);	
 });
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+</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/notebook-hello/index.html

@@ -14,4 +14,4 @@
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+</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/pdes.ipynb

@@ -1534,7 +1534,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Julia 1.9.1",
+   "display_name": "Julia 1.9.0",
    "language": "julia",
    "name": "julia-1.9"
   },
@@ -1542,7 +1542,7 @@
    "file_extension": ".jl",
    "mimetype": "application/julia",
    "name": "julia",
-   "version": "1.9.1"
+   "version": "1.9.0"
   }
  },
  "nbformat": 4,

dev/pdes/index.html

@@ -14,4 +14,4 @@
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     iFrameResize({log:true}, myIframe);	
 });
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+</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/solutions/index.html

@@ -14,4 +14,4 @@
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+</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/solutions_for_all_notebooks/index.html

@@ -212,67 +212,98 @@ end</code></pre><p>This other solution uses a column partition instead of a row
     MPI.Gather!(myC,C,comm;root)
     C
 end</code></pre><h2 id="Jacobi-method"><a class="docs-heading-anchor" href="#Jacobi-method">Jacobi method</a><a id="Jacobi-method-1"></a><a class="docs-heading-anchor-permalink" href="#Jacobi-method" title="Permalink"></a></h2><h3 id="Exercise-1-6"><a class="docs-heading-anchor" href="#Exercise-1-6">Exercise 1</a><a class="docs-heading-anchor-permalink" href="#Exercise-1-6" title="Permalink"></a></h3><pre><code class="language-julia hljs">function jacobi_mpi(n,niters)
-    comm = MPI.COMM_WORLD
+    u, u_new = init(n,comm)
-    nranks = MPI.Comm_size(comm)
+    load = length(u)-2
     rank = MPI.Comm_rank(comm)
-    if mod(n,nranks) != 0
+    nranks = MPI.Comm_size(comm)
-        println(&quot;n must be a multiple of nranks&quot;)
+    nreqs = 2*((rank != 0) + (rank != (nranks-1)))
-        MPI.Abort(comm,1)
+    reqs = MPI.MultiRequest(nreqs)
-    end
-    load = div(n,nranks)
-    u = zeros(load+2)
-    u[1] = -1
-    u[end] = 1
-    u_new = copy(u)
     for t in 1:niters
-        reqs = MPI.Request[]
+        ireq = 0
         if rank != 0
             neig_rank = rank-1
-            req = MPI.Isend(view(u,2:2),comm,dest=neig_rank,tag=0)
+            u_snd = view(u,2:2)
-            push!(reqs,req)
+            u_rcv = view(u,1:1)
-            req = MPI.Irecv!(view(u,1:1),comm,source=neig_rank,tag=0)
+            dest = neig_rank
-            push!(reqs,req)
+            source = neig_rank
+            ireq += 1
+            MPI.Isend(u_snd,comm,reqs[ireq];dest)
+            ireq += 1
+            MPI.Irecv!(u_rcv,comm,reqs[ireq];source)
         end
         if rank != (nranks-1)
             neig_rank = rank+1
-            s = load+1
+            u_snd = view(u,(load+1):(load+1))
-            r = load+2
+            u_rcv = view(u,(load+2):(load+2))
-            req = MPI.Isend(view(u,s:s),comm,dest=neig_rank,tag=0)
+            dest = neig_rank
-            push!(reqs,req)
+            source = neig_rank
-            req = MPI.Irecv!(view(u,r:r),comm,source=neig_rank,tag=0)
+            ireq += 1
-            push!(reqs,req)
+            MPI.Isend(u_snd,comm,reqs[ireq];dest)
+            ireq += 1
+            MPI.Irecv!(u_rcv,comm,reqs[ireq];source)
         end
+        # Upload interior cells
         for i in 3:load
             u_new[i] = 0.5*(u[i-1]+u[i+1])
         end
+        # Wait for the communications to finish
         MPI.Waitall(reqs)
+        # Update boundaries
         for i in (2,load+1)
             u_new[i] = 0.5*(u[i-1]+u[i+1])
         end
         u, u_new = u_new, u
-
     end
-    # Gather the results
+    return u
+end</code></pre><h3 id="Exercise-2-3"><a class="docs-heading-anchor" href="#Exercise-2-3">Exercise 2</a><a class="docs-heading-anchor-permalink" href="#Exercise-2-3" title="Permalink"></a></h3><pre><code class="language-julia hljs">function jacobi_mpi(n,niters,tol,comm) # new tol arg
+    u, u_new = init(n,comm)
+    load = length(u)-2
+    rank = MPI.Comm_rank(comm)
+    nranks = MPI.Comm_size(comm)
+    nreqs = 2*((rank != 0) + (rank != (nranks-1)))
+    reqs = MPI.MultiRequest(nreqs)
+    for t in 1:niters
+        ireq = 0
         if rank != 0
-        lb = 2
+            neig_rank = rank-1
-        ub = load+1
+            u_snd = view(u,2:2)
-        MPI.Send(view(u,lb:ub),comm,dest=0)
+            u_rcv = view(u,1:1)
-        u_all = zeros(0) # This will nevel be used
+            dest = neig_rank
-    else
+            source = neig_rank
-        u_all = zeros(n+2)
+            ireq += 1
-        # Set boundary
+            MPI.Isend(u_snd,comm,reqs[ireq];dest)
-        u_all[1] = -1
+            ireq += 1
-        u_all[end] = 1
+            MPI.Irecv!(u_rcv,comm,reqs[ireq];source)
-        # Set data for rank 0
-        lb = 2
-        ub = load+1
-        u_all[lb:ub] = view(u,lb:ub)
-        # Set data for other ranks
-        for other_rank in 1:(nranks-1)
-            lb += load
-            ub += load
-            MPI.Recv!(view(u_all,lb:ub),comm;source=other_rank)
         end
+        if rank != (nranks-1)
+            neig_rank = rank+1
+            u_snd = view(u,(load+1):(load+1))
+            u_rcv = view(u,(load+2):(load+2))
+            dest = neig_rank
+            source = neig_rank
+            ireq += 1
+            MPI.Isend(u_snd,comm,reqs[ireq];dest)
+            ireq += 1
+            MPI.Irecv!(u_rcv,comm,reqs[ireq];source)
         end
-    return u_all
+        MPI.Waitall(reqs)
-end</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tsp/">« Traveling salesperson problem</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 12:01">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+        # Compute the max diff in the current
+        # rank while doing the local update
+        mydiff = 0.0
+        for i in 2:load+1
+            u_new[i] = 0.5*(u[i-1]+u[i+1])
+            diff_i = abs(u_new[i] - u[i])
+            mydiff = max(mydiff,diff_i)
+        end
+        # Now we need to find the global diff
+        diff_ref = Ref(mydiff)
+        MPI.Allreduce!(diff_ref,max,comm)
+        diff = diff_ref[]
+        # If global diff below tol, stop!
+        if diff &lt; tol
+            return u_new
+        end
+        u, u_new = u_new, u
+    end
+    return u
+end</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tsp/">« Traveling salesperson problem</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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@@ -14,4 +14,4 @@
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-</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../LEQ/">« Gaussian elimination</a><a class="docs-footer-nextpage" href="../solutions_for_all_notebooks/">Solutions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 12:01">Monday 23 September 2024</span>. Using Julia version 1.10.5.</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="../LEQ/">« Gaussian elimination</a><a class="docs-footer-nextpage" href="../solutions_for_all_notebooks/">Solutions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 23 September 2024 14:37">Monday 23 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>