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Documenter.jl
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{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-30T15:25:09","documenter_version":"1.7.0"}}
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{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-10-01T05:36:31","documenter_version":"1.7.0"}}
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@ -103,7 +103,7 @@
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"### Problem statement\n",
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"### Problem statement\n",
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"\n",
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"\n",
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"Let us consider a system of linear equations written in matrix form $Ax=b$, where $A$ is a nonsingular square matrix, and $x$ and $b$ are vectors. $A$ and $b$ are given, and $x$ is unknown. The goal of Gaussian elimination is to transform the system $Ax=b$, into a new system $Ux=c$ such that\n",
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"Let us consider a system of linear equations written in matrix form $Ax=b$, where $A$ is a nonsingular square matrix, and $x$ and $b$ are vectors. $A$ and $b$ are given, and $x$ is unknown. The goal of Gaussian elimination is to transform the system $Ax=b$, into a new system $Ux=c$ such that\n",
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"- both system have the same solution vector $x$,\n",
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"- both systems have the same solution vector $x$,\n",
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"- the matrix $U$ of the new system is *upper triangular* with unit diagonal, namely $U_{ii} = 1$ and $U_{ij} = 0$ for $i>j$.\n",
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"- the matrix $U$ of the new system is *upper triangular* with unit diagonal, namely $U_{ii} = 1$ and $U_{ij} = 0$ for $i>j$.\n",
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"\n",
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"\n",
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"\n",
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"\n",
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@ -398,7 +398,7 @@
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"source": [
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"source": [
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"### Data partition\n",
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"### Data partition\n",
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"\n",
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"\n",
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"Let start considering a row-wise block partition, as we did in previous algorithms.\n",
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"Let's start considering a row-wise block partition, as we did in previous algorithms.\n",
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"\n",
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"\n",
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"In the figure below, we use different colors to illustrate which entries are assigned to a CPU. All entries with the same color are assigned to the same CPU."
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"In the figure below, we use different colors to illustrate which entries are assigned to a CPU. All entries with the same color are assigned to the same CPU."
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]
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]
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@ -454,7 +454,7 @@
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"<b>Definition:</b> *Load imbalance*: is the problem when work is not equally distributed over all processes and consequently some processes do more work than others.\n",
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"<b>Definition:</b> *Load imbalance*: is the problem when work is not equally distributed over all processes and consequently some processes do more work than others.\n",
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"</div>\n",
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"</div>\n",
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"\n",
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"\n",
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"Having processors waiting for others is a waist of computational resources and affects negatively parallel speedups. The optimal speedup (speedup equal to the number of processors) assumes that the work is perfectly parallel and that it is evenly distributed. If there is load imbalance, the last assumption is not true anymore and the speedup will be suboptimal.\n"
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"Having processors waiting for others is a waste of computational resources and affects negatively parallel speedups. The optimal speedup (speedup equal to the number of processors) assumes that the work is perfectly parallel and that it is evenly distributed. If there is load imbalance, the last assumption is not true anymore and the speedup will be suboptimal.\n"
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]
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]
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},
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},
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{
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{
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@ -14,4 +14,4 @@
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var myIframe = document.getElementById("notebook");
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var myIframe = document.getElementById("notebook");
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iFrameResize({log:true}, myIframe);
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iFrameResize({log:true}, myIframe);
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});
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});
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</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../asp/">« All pairs of shortest paths</a><a class="docs-footer-nextpage" href="../tsp/">Traveling salesperson problem »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="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 30 September 2024 15:25">Monday 30 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="Tuesday 1 October 2024 05:36">Tuesday 1 October 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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@ -7618,7 +7618,7 @@ $$</p>
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<p>This is just a small example with three unknowns, but practical applications need to solve linear equations with large number of unknowns. Parallel processing is needed in these cases.</p>
|
<p>This is just a small example with three unknowns, but practical applications need to solve linear equations with large number of unknowns. Parallel processing is needed in these cases.</p>
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<h3 id="Problem-statement">Problem statement<a class="anchor-link" href="#Problem-statement">¶</a></h3><p>Let us consider a system of linear equations written in matrix form $Ax=b$, where $A$ is a nonsingular square matrix, and $x$ and $b$ are vectors. $A$ and $b$ are given, and $x$ is unknown. The goal of Gaussian elimination is to transform the system $Ax=b$, into a new system $Ux=c$ such that</p>
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<h3 id="Problem-statement">Problem statement<a class="anchor-link" href="#Problem-statement">¶</a></h3><p>Let us consider a system of linear equations written in matrix form $Ax=b$, where $A$ is a nonsingular square matrix, and $x$ and $b$ are vectors. $A$ and $b$ are given, and $x$ is unknown. The goal of Gaussian elimination is to transform the system $Ax=b$, into a new system $Ux=c$ such that</p>
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<ul>
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<ul>
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<li>both system have the same solution vector $x$,</li>
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<li>both systems have the same solution vector $x$,</li>
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<li>the matrix $U$ of the new system is <em>upper triangular</em> with unit diagonal, namely $U_{ii} = 1$ and $U_{ij} = 0$ for $i>j$.</li>
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<li>the matrix $U$ of the new system is <em>upper triangular</em> with unit diagonal, namely $U_{ii} = 1$ and $U_{ij} = 0$ for $i>j$.</li>
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</ul>
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</ul>
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<p>For the particular system shown above, the transformed one is the following:</p>
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<p>For the particular system shown above, the transformed one is the following:</p>
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@ -7933,7 +7933,7 @@ d) only the first inner loop</code></pre>
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</div>
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</div>
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<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
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<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
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</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
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</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
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<h3 id="Data-partition">Data partition<a class="anchor-link" href="#Data-partition">¶</a></h3><p>Let start considering a row-wise block partition, as we did in previous algorithms.</p>
|
<h3 id="Data-partition">Data partition<a class="anchor-link" href="#Data-partition">¶</a></h3><p>Let's start considering a row-wise block partition, as we did in previous algorithms.</p>
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<p>In the figure below, we use different colors to illustrate which entries are assigned to a CPU. All entries with the same color are assigned to the same CPU.</p>
|
<p>In the figure below, we use different colors to illustrate which entries are assigned to a CPU. All entries with the same color are assigned to the same CPU.</p>
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</div>
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</div>
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</div>
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</div>
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@ -7986,7 +7986,7 @@ d) only the first inner loop</code></pre>
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<div class="alert alert-block alert-info">
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<div class="alert alert-block alert-info">
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<b>Definition:</b> *Load imbalance*: is the problem when work is not equally distributed over all processes and consequently some processes do more work than others.
|
<b>Definition:</b> *Load imbalance*: is the problem when work is not equally distributed over all processes and consequently some processes do more work than others.
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</div>
|
</div>
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<p>Having processors waiting for others is a waist of computational resources and affects negatively parallel speedups. The optimal speedup (speedup equal to the number of processors) assumes that the work is perfectly parallel and that it is evenly distributed. If there is load imbalance, the last assumption is not true anymore and the speedup will be suboptimal.</p>
|
<p>Having processors waiting for others is a waste of computational resources and affects negatively parallel speedups. The optimal speedup (speedup equal to the number of processors) assumes that the work is perfectly parallel and that it is evenly distributed. If there is load imbalance, the last assumption is not true anymore and the speedup will be suboptimal.</p>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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@ -57,7 +57,7 @@
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"function q1_answer(bool)\n",
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"function q1_answer(bool)\n",
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" bool || return\n",
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" bool || return\n",
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" msg = \"\"\"\n",
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" msg = \"\"\"\n",
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" The we can change the loop order over i and j without changing the result. Rememeber:\n",
|
" Then we can change the loop order over i and j without changing the result. Remember:\n",
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" \n",
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" \n",
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" C[i,j] = min(C[i,j],C[i,k]+C[k,j])\n",
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" C[i,j] = min(C[i,j],C[i,k]+C[k,j])\n",
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" \n",
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" \n",
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@ -788,7 +788,7 @@
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" if rank == 0\n",
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" if rank == 0\n",
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" N = size(C,1)\n",
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" N = size(C,1)\n",
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" if mod(N,P) !=0\n",
|
" if mod(N,P) !=0\n",
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" println(\"N not multplie of P\")\n",
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" println(\"N not multiple of P\")\n",
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" MPI.Abort(comm,-1)\n",
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" MPI.Abort(comm,-1)\n",
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" end\n",
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" end\n",
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" Nref = Ref(N)\n",
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" Nref = Ref(N)\n",
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@ -14,4 +14,4 @@
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var myIframe = document.getElementById("notebook");
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var myIframe = document.getElementById("notebook");
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iFrameResize({log:true}, myIframe);
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iFrameResize({log:true}, myIframe);
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});
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});
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</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../jacobi_method/">« Jacobi method</a><a class="docs-footer-nextpage" href="../LEQ/">Gaussian elimination »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="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 30 September 2024 15:25">Monday 30 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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</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="Tuesday 1 October 2024 05:36">Tuesday 1 October 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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@ -7573,7 +7573,7 @@ a.anchor-link {
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<span class="k">function</span><span class="w"> </span><span class="n">q1_answer</span><span class="p">(</span><span class="n">bool</span><span class="p">)</span>
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<span class="k">function</span><span class="w"> </span><span class="n">q1_answer</span><span class="p">(</span><span class="n">bool</span><span class="p">)</span>
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<span class="w"> </span><span class="n">bool</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="k">return</span>
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<span class="w"> </span><span class="n">bool</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="k">return</span>
|
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<span class="w"> </span><span class="n">msg</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">"""</span>
|
<span class="w"> </span><span class="n">msg</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">"""</span>
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<span class="s"> The we can change the loop order over i and j without changing the result. Rememeber:</span>
|
<span class="s"> Then we can change the loop order over i and j without changing the result. Remember:</span>
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<span class="s"> </span>
|
<span class="s"> </span>
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<span class="s"> C[i,j] = min(C[i,j],C[i,k]+C[k,j])</span>
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<span class="s"> C[i,j] = min(C[i,j],C[i,k]+C[k,j])</span>
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<span class="s"> </span>
|
<span class="s"> </span>
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@ -8351,7 +8351,7 @@ send the pieces to all other ranks. This is done in the function below. We start
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<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">rank</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">rank</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
|
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<span class="w"> </span><span class="n">N</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">C</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
|
<span class="w"> </span><span class="n">N</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">C</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
|
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<span class="w"> </span><span class="k">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">P</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="mi">0</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">P</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="mi">0</span>
|
||||||
<span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="s">"N not multplie of P"</span><span class="p">)</span>
|
<span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="s">"N not multiple of P"</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="o">-</span><span class="mi">1</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="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="k">end</span>
|
||||||
<span class="w"> </span><span class="n">Nref</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kt">Ref</span><span class="p">(</span><span class="n">N</span><span class="p">)</span>
|
<span class="w"> </span><span class="n">Nref</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kt">Ref</span><span class="p">(</span><span class="n">N</span><span class="p">)</span>
|
||||||
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|||||||
@ -15,4 +15,4 @@ DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
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MPI = "da04e1cc-30fd-572f-bb4f-1f8673147195"</code></pre><p>Copy the contents of previous code block into a file called <code>Project.toml</code> and place it in an empty folder named <code>newproject</code>. It is important that the file is named <code>Project.toml</code>. You can create a new folder from the REPL with</p><pre><code class="language-julia hljs">julia> mkdir("newproject")</code></pre><p>To install all the packages registered in this file you need to activate the folder containing your <code>Project.toml</code> file</p><pre><code class="language-julia hljs">(@v1.10) pkg> activate newproject</code></pre><p>and then <em>instantiating</em> it</p><pre><code class="language-julia hljs">(newproject) pkg> instantiate</code></pre><p>The instantiate command will download and install all listed packages and their dependencies in just one click.</p><h3 id="Getting-help-in-package-mode"><a class="docs-heading-anchor" href="#Getting-help-in-package-mode">Getting help in package mode</a><a id="Getting-help-in-package-mode-1"></a><a class="docs-heading-anchor-permalink" href="#Getting-help-in-package-mode" title="Permalink"></a></h3><p>You can get help about a particular package operator by writing <code>help</code> in front of it</p><pre><code class="language-julia hljs">(@v1.10) pkg> help activate</code></pre><p>You can get an overview of all package commands by typing <code>help</code> alone</p><pre><code class="language-julia hljs">(@v1.10) pkg> help</code></pre><h3 id="Package-operations-in-Julia-code"><a class="docs-heading-anchor" href="#Package-operations-in-Julia-code">Package operations in Julia code</a><a id="Package-operations-in-Julia-code-1"></a><a class="docs-heading-anchor-permalink" href="#Package-operations-in-Julia-code" title="Permalink"></a></h3><p>In some situations it is required to use package commands in Julia code, e.g., to automatize installation and deployment of Julia applications. This can be done using the <code>Pkg</code> package. For instance</p><pre><code class="language-julia hljs">julia> using Pkg
|
MPI = "da04e1cc-30fd-572f-bb4f-1f8673147195"</code></pre><p>Copy the contents of previous code block into a file called <code>Project.toml</code> and place it in an empty folder named <code>newproject</code>. It is important that the file is named <code>Project.toml</code>. You can create a new folder from the REPL with</p><pre><code class="language-julia hljs">julia> mkdir("newproject")</code></pre><p>To install all the packages registered in this file you need to activate the folder containing your <code>Project.toml</code> file</p><pre><code class="language-julia hljs">(@v1.10) pkg> activate newproject</code></pre><p>and then <em>instantiating</em> it</p><pre><code class="language-julia hljs">(newproject) pkg> instantiate</code></pre><p>The instantiate command will download and install all listed packages and their dependencies in just one click.</p><h3 id="Getting-help-in-package-mode"><a class="docs-heading-anchor" href="#Getting-help-in-package-mode">Getting help in package mode</a><a id="Getting-help-in-package-mode-1"></a><a class="docs-heading-anchor-permalink" href="#Getting-help-in-package-mode" title="Permalink"></a></h3><p>You can get help about a particular package operator by writing <code>help</code> in front of it</p><pre><code class="language-julia hljs">(@v1.10) pkg> help activate</code></pre><p>You can get an overview of all package commands by typing <code>help</code> alone</p><pre><code class="language-julia hljs">(@v1.10) pkg> help</code></pre><h3 id="Package-operations-in-Julia-code"><a class="docs-heading-anchor" href="#Package-operations-in-Julia-code">Package operations in Julia code</a><a id="Package-operations-in-Julia-code-1"></a><a class="docs-heading-anchor-permalink" href="#Package-operations-in-Julia-code" title="Permalink"></a></h3><p>In some situations it is required to use package commands in Julia code, e.g., to automatize installation and deployment of Julia applications. This can be done using the <code>Pkg</code> package. For instance</p><pre><code class="language-julia hljs">julia> using Pkg
|
||||||
julia> Pkg.status()</code></pre><p>is equivalent to calling <code>status</code> in package mode.</p><pre><code class="language-julia hljs">(@v1.10) pkg> status</code></pre><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> 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> activate MyPackage
|
julia> Pkg.status()</code></pre><p>is equivalent to calling <code>status</code> in package mode.</p><pre><code class="language-julia hljs">(@v1.10) pkg> status</code></pre><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> 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> activate MyPackage
|
||||||
(MyPackage) pkg> 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> 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 "develop" 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) pkg> 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> 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 "develop" 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 30 September 2024 15:25">Monday 30 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="Tuesday 1 October 2024 05:36">Tuesday 1 October 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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</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 30 September 2024 15:25">Monday 30 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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</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="Tuesday 1 October 2024 05:36">Tuesday 1 October 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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"\n",
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"\n",
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"In this notebook, we will learn\n",
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"In this notebook, we will learn\n",
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"\n",
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"\n",
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"- How to paralleize the Jacobi method\n",
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"- How to parallelize the Jacobi method\n",
|
||||||
"- How the data partition can impact the performance of a distributed algorithm\n",
|
"- How the data partition can impact the performance of a distributed algorithm\n",
|
||||||
"- How to use latency hiding to improve parallel performance\n",
|
"- How to use latency hiding to improve parallel performance\n",
|
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"\n"
|
"\n"
|
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@ -452,7 +452,7 @@
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"- We need to get remote entries from 2 neighbors (2 messages per iteration)\n",
|
"- We need to get remote entries from 2 neighbors (2 messages per iteration)\n",
|
||||||
"- We need to communicate 1 entry per message\n",
|
"- We need to communicate 1 entry per message\n",
|
||||||
"- Thus, communication complexity is $O(1)$\n",
|
"- Thus, communication complexity is $O(1)$\n",
|
||||||
"- Communication/computation ration is $O(P/N)$, making the algorithm potentially scalable if $P<<N$.\n"
|
"- Communication/computation ratio is $O(P/N)$, making the algorithm potentially scalable if $P<<N$.\n"
|
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]
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]
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},
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},
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{
|
{
|
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"end\n",
|
"end\n",
|
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"```\n",
|
"```\n",
|
||||||
"\n",
|
"\n",
|
||||||
"- The outer loop cannot be parallelized (like in the 1d case). \n",
|
"- The outer loop cannot be parallelized (like in the 1D case). \n",
|
||||||
"- The two inner loops are trivially parallel\n"
|
"- The two inner loops are trivially parallel\n"
|
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]
|
]
|
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},
|
},
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@ -666,7 +666,7 @@
|
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"source": [
|
"source": [
|
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"### Parallelization strategies\n",
|
"### Parallelization strategies\n",
|
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"\n",
|
"\n",
|
||||||
"In 2d one has more flexibility in order to distribute the data over the processes. We consider these three alternatives:\n",
|
"In 2D, one has more flexibility in order to distribute the data over the processes. We consider these three alternatives:\n",
|
||||||
"\n",
|
"\n",
|
||||||
"- 1D block row partition (each worker handles a subset of consecutive rows and all columns)\n",
|
"- 1D block row partition (each worker handles a subset of consecutive rows and all columns)\n",
|
||||||
"- 2D block partition (each worker handles a subset of consecutive rows and columns)\n",
|
"- 2D block partition (each worker handles a subset of consecutive rows and columns)\n",
|
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"\n",
|
"\n",
|
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"|Partition | Messages <br> per iteration | Communication <br>per worker | Computation <br>per worker | Ratio communication/<br>computation |\n",
|
"|Partition | Messages <br> per iteration | Communication <br>per worker | Computation <br>per worker | Ratio communication/<br>computation |\n",
|
||||||
"|---|---|---|---|---|\n",
|
"|---|---|---|---|---|\n",
|
||||||
"| 1d block | 2 | O(N) | N²/P | O(P/N) |\n",
|
"| 1D block | 2 | O(N) | N²/P | O(P/N) |\n",
|
||||||
"| 2d block | 4 | O(N/√P) | N²/P | O(√P/N) |\n",
|
"| 2D block | 4 | O(N/√P) | N²/P | O(√P/N) |\n",
|
||||||
"| 2d cyclic | 4 |O(N²/P) | N²/P | O(1) |"
|
"| 2D cyclic | 4 |O(N²/P) | N²/P | O(1) |"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
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@ -862,9 +862,9 @@
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"\n",
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"\n",
|
||||||
"\n",
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
"- Both 1d and 2d block partitions are potentially scalable if $P<<N$\n",
|
"- Both 1D and 2D block partitions are potentially scalable if $P<<N$\n",
|
||||||
"- The 2d block partition has the lowest communication complexity\n",
|
"- The 2D block partition has the lowest communication complexity\n",
|
||||||
"- The 1d block partition requires to send less messages (It can be useful if the fixed cost of sending a message is high)\n",
|
"- The 1D block partition requires to send less messages (It can be useful if the fixed cost of sending a message is high)\n",
|
||||||
"- The best strategy for a given problem size will thus depend on the machine.\n",
|
"- The best strategy for a given problem size will thus depend on the machine.\n",
|
||||||
"- Cyclic partitions are impractical for this application (but they are useful in others) \n",
|
"- Cyclic partitions are impractical for this application (but they are useful in others) \n",
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</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 30 September 2024 15:25">Monday 30 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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</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="Tuesday 1 October 2024 05:36">Tuesday 1 October 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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||||||
<h2 id="Contents">Contents<a class="anchor-link" href="#Contents">¶</a></h2><p>In this notebook, we will learn</p>
|
<h2 id="Contents">Contents<a class="anchor-link" href="#Contents">¶</a></h2><p>In this notebook, we will learn</p>
|
||||||
<ul>
|
<ul>
|
||||||
<li>How to paralleize the Jacobi method</li>
|
<li>How to parallelize the Jacobi method</li>
|
||||||
<li>How the data partition can impact the performance of a distributed algorithm</li>
|
<li>How the data partition can impact the performance of a distributed algorithm</li>
|
||||||
<li>How to use latency hiding to improve parallel performance</li>
|
<li>How to use latency hiding to improve parallel performance</li>
|
||||||
</ul>
|
</ul>
|
||||||
@ -8009,7 +8009,7 @@ a.anchor-link {
|
|||||||
<li>We need to get remote entries from 2 neighbors (2 messages per iteration)</li>
|
<li>We need to get remote entries from 2 neighbors (2 messages per iteration)</li>
|
||||||
<li>We need to communicate 1 entry per message</li>
|
<li>We need to communicate 1 entry per message</li>
|
||||||
<li>Thus, communication complexity is $O(1)$</li>
|
<li>Thus, communication complexity is $O(1)$</li>
|
||||||
<li>Communication/computation ration is $O(P/N)$, making the algorithm potentially scalable if $P<<N$.</li>
|
<li>Communication/computation ratio is $O(P/N)$, making the algorithm potentially scalable if $P<<N$.</li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -8232,7 +8232,7 @@ a.anchor-link {
|
|||||||
<span class="k">end</span>
|
<span class="k">end</span>
|
||||||
</pre></div>
|
</pre></div>
|
||||||
<ul>
|
<ul>
|
||||||
<li>The outer loop cannot be parallelized (like in the 1d case).</li>
|
<li>The outer loop cannot be parallelized (like in the 1D case).</li>
|
||||||
<li>The two inner loops are trivially parallel</li>
|
<li>The two inner loops are trivially parallel</li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
@ -8245,7 +8245,7 @@ a.anchor-link {
|
|||||||
</div>
|
</div>
|
||||||
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
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<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
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||||||
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
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||||||
<h3 id="Parallelization-strategies">Parallelization strategies<a class="anchor-link" href="#Parallelization-strategies">¶</a></h3><p>In 2d one has more flexibility in order to distribute the data over the processes. We consider these three alternatives:</p>
|
<h3 id="Parallelization-strategies">Parallelization strategies<a class="anchor-link" href="#Parallelization-strategies">¶</a></h3><p>In 2D, one has more flexibility in order to distribute the data over the processes. We consider these three alternatives:</p>
|
||||||
<ul>
|
<ul>
|
||||||
<li>1D block row partition (each worker handles a subset of consecutive rows and all columns)</li>
|
<li>1D block row partition (each worker handles a subset of consecutive rows and all columns)</li>
|
||||||
<li>2D block partition (each worker handles a subset of consecutive rows and columns)</li>
|
<li>2D block partition (each worker handles a subset of consecutive rows and columns)</li>
|
||||||
@ -8457,21 +8457,21 @@ a.anchor-link {
|
|||||||
</thead>
|
</thead>
|
||||||
<tbody>
|
<tbody>
|
||||||
<tr>
|
<tr>
|
||||||
<td>1d block</td>
|
<td>1D block</td>
|
||||||
<td>2</td>
|
<td>2</td>
|
||||||
<td>O(N)</td>
|
<td>O(N)</td>
|
||||||
<td>N²/P</td>
|
<td>N²/P</td>
|
||||||
<td>O(P/N)</td>
|
<td>O(P/N)</td>
|
||||||
</tr>
|
</tr>
|
||||||
<tr>
|
<tr>
|
||||||
<td>2d block</td>
|
<td>2D block</td>
|
||||||
<td>4</td>
|
<td>4</td>
|
||||||
<td>O(N/√P)</td>
|
<td>O(N/√P)</td>
|
||||||
<td>N²/P</td>
|
<td>N²/P</td>
|
||||||
<td>O(√P/N)</td>
|
<td>O(√P/N)</td>
|
||||||
</tr>
|
</tr>
|
||||||
<tr>
|
<tr>
|
||||||
<td>2d cyclic</td>
|
<td>2D cyclic</td>
|
||||||
<td>4</td>
|
<td>4</td>
|
||||||
<td>O(N²/P)</td>
|
<td>O(N²/P)</td>
|
||||||
<td>N²/P</td>
|
<td>N²/P</td>
|
||||||
@ -8490,9 +8490,9 @@ a.anchor-link {
|
|||||||
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
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<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
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||||||
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
||||||
<h3 id="Which-partition-is-the-best-one?">Which partition is the best one?<a class="anchor-link" href="#Which-partition-is-the-best-one?">¶</a></h3><ul>
|
<h3 id="Which-partition-is-the-best-one?">Which partition is the best one?<a class="anchor-link" href="#Which-partition-is-the-best-one?">¶</a></h3><ul>
|
||||||
<li>Both 1d and 2d block partitions are potentially scalable if $P<<N$</li>
|
<li>Both 1D and 2D block partitions are potentially scalable if $P<<N$</li>
|
||||||
<li>The 2d block partition has the lowest communication complexity</li>
|
<li>The 2D block partition has the lowest communication complexity</li>
|
||||||
<li>The 1d block partition requires to send less messages (It can be useful if the fixed cost of sending a message is high)</li>
|
<li>The 1D block partition requires to send less messages (It can be useful if the fixed cost of sending a message is high)</li>
|
||||||
<li>The best strategy for a given problem size will thus depend on the machine.</li>
|
<li>The best strategy for a given problem size will thus depend on the machine.</li>
|
||||||
<li>Cyclic partitions are impractical for this application (but they are useful in others)</li>
|
<li>Cyclic partitions are impractical for this application (but they are useful in others)</li>
|
||||||
</ul>
|
</ul>
|
||||||
|
|||||||
@ -87,7 +87,7 @@
|
|||||||
"\n",
|
"\n",
|
||||||
"### Creating a task\n",
|
"### Creating a task\n",
|
||||||
"\n",
|
"\n",
|
||||||
"Technically, a task in Julia is a *symmetric* [*co-routine*](https://en.wikipedia.org/wiki/Coroutine). More informally, a task is a piece of computational work that can be started (scheduled) at some point in the future, and that can be interrupted and resumed. To create a task, we first need to create a function that represents the work to be done in the task. In next cell, we generate a task that generates and sums two matrices."
|
"Technically, a task in Julia is a *symmetric* [*co-routine*](https://en.wikipedia.org/wiki/Coroutine). More informally, a task is a piece of computational work that can be started (scheduled) at some point in the future, and that can be interrupted and resumed. To create a task, we first need to create a function that represents the work to be done in the task. In the next cell, we generate a task that generates and sums two matrices."
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
@ -322,7 +322,7 @@
|
|||||||
"source": [
|
"source": [
|
||||||
"### `yield`\n",
|
"### `yield`\n",
|
||||||
"\n",
|
"\n",
|
||||||
"If tasks do not run in parallel, what is the purpose of tasks? Tasks are handy since they can be interrupted and to switch control to other tasks. This is achieved via function `yield`. When we call yield, we provide the opportunity to switch to another task. The function below is a variation of function `compute_π` in which we yield every 1000 iterations. At the call to yield we allow other tasks to take over. Without this call to yield, once we start function `compute_π` we cannot start any other tasks until this function finishes."
|
"If tasks do not run in parallel, what is the purpose of tasks? Tasks are handy since they can be interrupted and to switch control to other tasks. This is achieved via function `yield`. When we call `yield`, we provide the opportunity to switch to another task. The function below is a variation of function `compute_π` in which we `yield` every 1000 iterations. At the call to `yield` we allow other tasks to take over. Without this call to `yield`, once we start function `compute_π` we cannot start any other tasks until this function finishes."
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
@ -349,7 +349,7 @@
|
|||||||
"id": "69fd4131",
|
"id": "69fd4131",
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"source": [
|
"source": [
|
||||||
"You can check this behavior experimentally with the two following cells. The next one creates and schedules a task that computes pi with the function `compute_π_yield`. Note that you can run the 2nd cell bellow while this task is running since we call to yield often inside `compute_π_yield`."
|
"You can check this behavior experimentally with the two following cells. The next one creates and schedules a task that computes pi with the function `compute_π_yield`. Note that you can run the 2nd cell bellow while this task is running since we call to `yield` often inside `compute_π_yield`."
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
@ -381,7 +381,7 @@
|
|||||||
"source": [
|
"source": [
|
||||||
"### Example: Implementing function sleep\n",
|
"### Example: Implementing function sleep\n",
|
||||||
"\n",
|
"\n",
|
||||||
"Using yield, we can implement our own version of the sleep function as follows:"
|
"Using `yield`, we can implement our own version of the sleep function as follows:"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
|
|||||||
@ -14,4 +14,4 @@
|
|||||||
var myIframe = document.getElementById("notebook");
|
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|
||||||
iFrameResize({log:true}, myIframe);
|
iFrameResize({log:true}, myIframe);
|
||||||
});
|
});
|
||||||
</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../julia_basics/">« Julia Basics</a><a class="docs-footer-nextpage" href="../julia_distributed/">Distributed computing in Julia »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="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 30 September 2024 15:25">Monday 30 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="../julia_basics/">« Julia Basics</a><a class="docs-footer-nextpage" href="../julia_distributed/">Distributed computing in Julia »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="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="Tuesday 1 October 2024 05:36">Tuesday 1 October 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||||
|
|||||||
@ -7603,7 +7603,7 @@ a.anchor-link {
|
|||||||
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|
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|
||||||
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|
||||||
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||||||
<h2 id="Tasks">Tasks<a class="anchor-link" href="#Tasks">¶</a></h2><h3 id="Creating--a-task">Creating a task<a class="anchor-link" href="#Creating--a-task">¶</a></h3><p>Technically, a task in Julia is a <em>symmetric</em> <a href="https://en.wikipedia.org/wiki/Coroutine"><em>co-routine</em></a>. More informally, a task is a piece of computational work that can be started (scheduled) at some point in the future, and that can be interrupted and resumed. To create a task, we first need to create a function that represents the work to be done in the task. In next cell, we generate a task that generates and sums two matrices.</p>
|
<h2 id="Tasks">Tasks<a class="anchor-link" href="#Tasks">¶</a></h2><h3 id="Creating--a-task">Creating a task<a class="anchor-link" href="#Creating--a-task">¶</a></h3><p>Technically, a task in Julia is a <em>symmetric</em> <a href="https://en.wikipedia.org/wiki/Coroutine"><em>co-routine</em></a>. More informally, a task is a piece of computational work that can be started (scheduled) at some point in the future, and that can be interrupted and resumed. To create a task, we first need to create a function that represents the work to be done in the task. In the next cell, we generate a task that generates and sums two matrices.</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -7910,7 +7910,7 @@ a.anchor-link {
|
|||||||
</div>
|
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|
||||||
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|
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|
||||||
<h3 id="yield"><code>yield</code><a class="anchor-link" href="#yield">¶</a></h3><p>If tasks do not run in parallel, what is the purpose of tasks? Tasks are handy since they can be interrupted and to switch control to other tasks. This is achieved via function <code>yield</code>. When we call yield, we provide the opportunity to switch to another task. The function below is a variation of function <code>compute_π</code> in which we yield every 1000 iterations. At the call to yield we allow other tasks to take over. Without this call to yield, once we start function <code>compute_π</code> we cannot start any other tasks until this function finishes.</p>
|
<h3 id="yield"><code>yield</code><a class="anchor-link" href="#yield">¶</a></h3><p>If tasks do not run in parallel, what is the purpose of tasks? Tasks are handy since they can be interrupted and to switch control to other tasks. This is achieved via function <code>yield</code>. When we call <code>yield</code>, we provide the opportunity to switch to another task. The function below is a variation of function <code>compute_π</code> in which we <code>yield</code> every 1000 iterations. At the call to <code>yield</code> we allow other tasks to take over. Without this call to <code>yield</code>, once we start function <code>compute_π</code> we cannot start any other tasks until this function finishes.</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -7944,7 +7944,7 @@ a.anchor-link {
|
|||||||
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|
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|
||||||
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|
||||||
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|
||||||
<p>You can check this behavior experimentally with the two following cells. The next one creates and schedules a task that computes pi with the function <code>compute_π_yield</code>. Note that you can run the 2nd cell bellow while this task is running since we call to yield often inside <code>compute_π_yield</code>.</p>
|
<p>You can check this behavior experimentally with the two following cells. The next one creates and schedules a task that computes pi with the function <code>compute_π_yield</code>. Note that you can run the 2nd cell bellow while this task is running since we call to <code>yield</code> often inside <code>compute_π_yield</code>.</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -7985,7 +7985,7 @@ a.anchor-link {
|
|||||||
</div>
|
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|
||||||
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
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|
||||||
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|
||||||
<h3 id="Example:-Implementing-function-sleep">Example: Implementing function sleep<a class="anchor-link" href="#Example:-Implementing-function-sleep">¶</a></h3><p>Using yield, we can implement our own version of the sleep function as follows:</p>
|
<h3 id="Example:-Implementing-function-sleep">Example: Implementing function sleep<a class="anchor-link" href="#Example:-Implementing-function-sleep">¶</a></h3><p>Using <code>yield</code>, we can implement our own version of the sleep function as follows:</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|||||||
@ -37,7 +37,7 @@
|
|||||||
"source": [
|
"source": [
|
||||||
"## Using Jupyter notebooks in Julia\n",
|
"## Using Jupyter notebooks in Julia\n",
|
||||||
"\n",
|
"\n",
|
||||||
"We are going to use Jupyter notebooks in this and other lectures. You provably have worked with notebooks (in Python). If not, here are the basic concepts you need to know to follow the lessons.\n",
|
"We are going to use Jupyter notebooks in this and other lectures. You probably have worked with notebooks (in Python). If not, here are the basic concepts you need to know to follow the lessons.\n",
|
||||||
"\n",
|
"\n",
|
||||||
"<div class=\"alert alert-block alert-info\">\n",
|
"<div class=\"alert alert-block alert-info\">\n",
|
||||||
"<b>Tip:</b> Did you know that Jupyter stands for Julia, Python and R?\n",
|
"<b>Tip:</b> Did you know that Jupyter stands for Julia, Python and R?\n",
|
||||||
|
|||||||
@ -14,4 +14,4 @@
|
|||||||
var myIframe = document.getElementById("notebook");
|
var myIframe = document.getElementById("notebook");
|
||||||
iFrameResize({log:true}, myIframe);
|
iFrameResize({log:true}, myIframe);
|
||||||
});
|
});
|
||||||
</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../getting_started_with_julia/">« Getting started</a><a class="docs-footer-nextpage" href="../julia_async/">Asynchronous programming in Julia »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="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 30 September 2024 15:25">Monday 30 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="../getting_started_with_julia/">« Getting started</a><a class="docs-footer-nextpage" href="../julia_async/">Asynchronous programming in Julia »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="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="Tuesday 1 October 2024 05:36">Tuesday 1 October 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||||
|
|||||||
@ -7547,7 +7547,7 @@ a.anchor-link {
|
|||||||
</div>
|
</div>
|
||||||
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
||||||
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
||||||
<h2 id="Using-Jupyter-notebooks-in-Julia">Using Jupyter notebooks in Julia<a class="anchor-link" href="#Using-Jupyter-notebooks-in-Julia">¶</a></h2><p>We are going to use Jupyter notebooks in this and other lectures. You provably have worked with notebooks (in Python). If not, here are the basic concepts you need to know to follow the lessons.</p>
|
<h2 id="Using-Jupyter-notebooks-in-Julia">Using Jupyter notebooks in Julia<a class="anchor-link" href="#Using-Jupyter-notebooks-in-Julia">¶</a></h2><p>We are going to use Jupyter notebooks in this and other lectures. You probably have worked with notebooks (in Python). If not, here are the basic concepts you need to know to follow the lessons.</p>
|
||||||
<div class="alert alert-block alert-info">
|
<div class="alert alert-block alert-info">
|
||||||
<b>Tip:</b> Did you know that Jupyter stands for Julia, Python and R?
|
<b>Tip:</b> Did you know that Jupyter stands for Julia, Python and R?
|
||||||
</div>
|
</div>
|
||||||
|
|||||||
@ -137,7 +137,7 @@
|
|||||||
"\n",
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
"<div class=\"alert alert-block alert-info\">\n",
|
"<div class=\"alert alert-block alert-info\">\n",
|
||||||
"<b>Tip:</b> We can also start new processes when launching Julia from the command line by suing the `-p` command-line argument. E.g., `$ julia -p 3 ` would launch Julia with 3 extra processes.\n",
|
"<b>Tip:</b> We can also start new processes when launching Julia from the command line by using the `-p` command-line argument. E.g., `$ julia -p 3 ` would launch Julia with 3 extra processes.\n",
|
||||||
"</div>\n"
|
"</div>\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
@ -251,7 +251,7 @@
|
|||||||
"source": [
|
"source": [
|
||||||
"### Creating workers in other machines\n",
|
"### Creating workers in other machines\n",
|
||||||
"\n",
|
"\n",
|
||||||
"For large parallel computations, one typically needs to use different computers in parallel. Function `addprocs` also provides a low-level method to start workers in other machines. Next code example would create 3 workers in `server1` and 4 new workers in server `server2` (see figure below). Under the hood, Julia connects via ssh to the other machines and starts the new processes there. In order this to work, the local computer and the remote servers need to be properly configured (see the Julia manual for details). \n",
|
"For large parallel computations, one typically needs to use different computers in parallel. Function `addprocs` also provides a low-level method to start workers in other machines. Next code example would create 3 workers in `server1` and 4 new workers in `server2` (see figure below). Under the hood, Julia connects via ssh to the other machines and starts the new processes there. In order this to work, the local computer and the remote servers need to be properly configured (see the Julia manual for details). \n",
|
||||||
"\n",
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
@ -514,7 +514,7 @@
|
|||||||
"id": "10899cd4",
|
"id": "10899cd4",
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"source": [
|
"source": [
|
||||||
"### Another usefull macro: `@fetchfrom`\n",
|
"### Another useful macro: `@fetchfrom`\n",
|
||||||
"\n",
|
"\n",
|
||||||
"Macro `@fetchfrom` is the blocking version of `@spawnat`. It blocks and returns the corresponding result instead of a `Future` object. "
|
"Macro `@fetchfrom` is the blocking version of `@spawnat`. It blocks and returns the corresponding result instead of a `Future` object. "
|
||||||
]
|
]
|
||||||
@ -552,7 +552,7 @@
|
|||||||
"source": [
|
"source": [
|
||||||
"### Explicit data movement in `remotecall` / `fetch`\n",
|
"### Explicit data movement in `remotecall` / `fetch`\n",
|
||||||
"\n",
|
"\n",
|
||||||
"When usig `remotecall` we send to the remote process a function and its arguments. In this example, we send function name `+` and matrices `a` and `b` to proc 4. When fetching the result we receive a copy of the matrix from proc 4."
|
"When using `remotecall` we send to the remote process a function and its arguments. In this example, we send function name `+` and matrices `a` and `b` to proc 4. When fetching the result we receive a copy of the matrix from proc 4."
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
|
|||||||
@ -14,4 +14,4 @@
|
|||||||
var myIframe = document.getElementById("notebook");
|
var myIframe = document.getElementById("notebook");
|
||||||
iFrameResize({log:true}, myIframe);
|
iFrameResize({log:true}, myIframe);
|
||||||
});
|
});
|
||||||
</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../julia_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 30 September 2024 15:25">Monday 30 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="../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="Tuesday 1 October 2024 05:36">Tuesday 1 October 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||||
|
|||||||
@ -7671,7 +7671,7 @@ a.anchor-link {
|
|||||||
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
||||||
<p>Last cell created 3 new Julia processes. By default, they run locally in the same computer as the current Julia session, using multiple cores if possible. However, it is also possible to start the new processes in other machines as long as they are interconnected (more details on this later).</p>
|
<p>Last cell created 3 new Julia processes. By default, they run locally in the same computer as the current Julia session, using multiple cores if possible. However, it is also possible to start the new processes in other machines as long as they are interconnected (more details on this later).</p>
|
||||||
<div class="alert alert-block alert-info">
|
<div class="alert alert-block alert-info">
|
||||||
<b>Tip:</b> We can also start new processes when launching Julia from the command line by suing the `-p` command-line argument. E.g., `$ julia -p 3 ` would launch Julia with 3 extra processes.
|
<b>Tip:</b> We can also start new processes when launching Julia from the command line by using the `-p` command-line argument. E.g., `$ julia -p 3 ` would launch Julia with 3 extra processes.
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -7813,7 +7813,7 @@ a.anchor-link {
|
|||||||
</div>
|
</div>
|
||||||
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
||||||
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
||||||
<h3 id="Creating-workers-in-other-machines">Creating workers in other machines<a class="anchor-link" href="#Creating-workers-in-other-machines">¶</a></h3><p>For large parallel computations, one typically needs to use different computers in parallel. Function <code>addprocs</code> also provides a low-level method to start workers in other machines. Next code example would create 3 workers in <code>server1</code> and 4 new workers in server <code>server2</code> (see figure below). Under the hood, Julia connects via ssh to the other machines and starts the new processes there. In order this to work, the local computer and the remote servers need to be properly configured (see the Julia manual for details).</p>
|
<h3 id="Creating-workers-in-other-machines">Creating workers in other machines<a class="anchor-link" href="#Creating-workers-in-other-machines">¶</a></h3><p>For large parallel computations, one typically needs to use different computers in parallel. Function <code>addprocs</code> also provides a low-level method to start workers in other machines. Next code example would create 3 workers in <code>server1</code> and 4 new workers in <code>server2</code> (see figure below). Under the hood, Julia connects via ssh to the other machines and starts the new processes there. In order this to work, the local computer and the remote servers need to be properly configured (see the Julia manual for details).</p>
|
||||||
<div class="highlight"><pre><span></span><span class="k">using</span><span class="w"> </span><span class="n">Distributed</span>
|
<div class="highlight"><pre><span></span><span class="k">using</span><span class="w"> </span><span class="n">Distributed</span>
|
||||||
<span class="n">machines</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[(</span><span class="s">"user@server1"</span><span class="p">,</span><span class="mi">3</span><span class="p">),(</span><span class="s">"user@server2"</span><span class="p">,</span><span class="mi">4</span><span class="p">)]</span>
|
<span class="n">machines</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[(</span><span class="s">"user@server1"</span><span class="p">,</span><span class="mi">3</span><span class="p">),(</span><span class="s">"user@server2"</span><span class="p">,</span><span class="mi">4</span><span class="p">)]</span>
|
||||||
<span class="n">addprocs</span><span class="p">(</span><span class="n">machines</span><span class="p">)</span>
|
<span class="n">addprocs</span><span class="p">(</span><span class="n">machines</span><span class="p">)</span>
|
||||||
@ -8133,7 +8133,7 @@ a.anchor-link {
|
|||||||
</div>
|
</div>
|
||||||
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
||||||
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
||||||
<h3 id="Another-usefull-macro:-@fetchfrom">Another usefull macro: <code>@fetchfrom</code><a class="anchor-link" href="#Another-usefull-macro:-@fetchfrom">¶</a></h3><p>Macro <code>@fetchfrom</code> is the blocking version of <code>@spawnat</code>. It blocks and returns the corresponding result instead of a <code>Future</code> object.</p>
|
<h3 id="Another-useful-macro:-@fetchfrom">Another useful macro: <code>@fetchfrom</code><a class="anchor-link" href="#Another-useful-macro:-@fetchfrom">¶</a></h3><p>Macro <code>@fetchfrom</code> is the blocking version of <code>@spawnat</code>. It blocks and returns the corresponding result instead of a <code>Future</code> object.</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -8173,7 +8173,7 @@ bottlenecks. Being aware of the data we are moving when using functions such as
|
|||||||
</div>
|
</div>
|
||||||
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
||||||
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
||||||
<h3 id="Explicit-data-movement-in-remotecall-/-fetch">Explicit data movement in <code>remotecall</code> / <code>fetch</code><a class="anchor-link" href="#Explicit-data-movement-in-remotecall-/-fetch">¶</a></h3><p>When usig <code>remotecall</code> we send to the remote process a function and its arguments. In this example, we send function name <code>+</code> and matrices <code>a</code> and <code>b</code> to proc 4. When fetching the result we receive a copy of the matrix from proc 4.</p>
|
<h3 id="Explicit-data-movement-in-remotecall-/-fetch">Explicit data movement in <code>remotecall</code> / <code>fetch</code><a class="anchor-link" href="#Explicit-data-movement-in-remotecall-/-fetch">¶</a></h3><p>When using <code>remotecall</code> we send to the remote process a function and its arguments. In this example, we send function name <code>+</code> and matrices <code>a</code> and <code>b</code> to proc 4. When fetching the result we receive a copy of the matrix from proc 4.</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|||||||
@ -14,4 +14,4 @@
|
|||||||
var myIframe = document.getElementById("notebook");
|
var myIframe = document.getElementById("notebook");
|
||||||
iFrameResize({log:true}, myIframe);
|
iFrameResize({log:true}, myIframe);
|
||||||
});
|
});
|
||||||
</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="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 30 September 2024 15:25">Monday 30 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="Tuesday 1 October 2024 05:36">Tuesday 1 October 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||||
|
|||||||
@ -14,4 +14,4 @@
|
|||||||
var myIframe = document.getElementById("notebook");
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|
||||||
iFrameResize({log:true}, myIframe);
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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 30 September 2024 15:25">Monday 30 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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</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="Tuesday 1 October 2024 05:36">Tuesday 1 October 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||||
|
|||||||
@ -167,7 +167,7 @@
|
|||||||
"```julia\n",
|
"```julia\n",
|
||||||
"using MPI\n",
|
"using MPI\n",
|
||||||
"MPI.Init()\n",
|
"MPI.Init()\n",
|
||||||
"# Your MPI programm here\n",
|
"# Your MPI program here\n",
|
||||||
"MPI.Finalize() # Optional\n",
|
"MPI.Finalize() # Optional\n",
|
||||||
"```\n",
|
"```\n",
|
||||||
"\n",
|
"\n",
|
||||||
@ -176,7 +176,7 @@
|
|||||||
"```julia\n",
|
"```julia\n",
|
||||||
"using MPI\n",
|
"using MPI\n",
|
||||||
"MPI.Init(finalize_atexit=false)\n",
|
"MPI.Init(finalize_atexit=false)\n",
|
||||||
"# Your MPI programm here\n",
|
"# Your MPI program here\n",
|
||||||
"MPI.Finalize() # Mandatory\n",
|
"MPI.Finalize() # Mandatory\n",
|
||||||
"```\n",
|
"```\n",
|
||||||
"\n",
|
"\n",
|
||||||
@ -186,7 +186,7 @@
|
|||||||
"#include <mpi.h>\n",
|
"#include <mpi.h>\n",
|
||||||
"int main(int argc, char** argv) {\n",
|
"int main(int argc, char** argv) {\n",
|
||||||
" MPI_Init(NULL, NULL);\n",
|
" MPI_Init(NULL, NULL);\n",
|
||||||
" /* Your MPI Programm here */\n",
|
" /* Your MPI Program here */\n",
|
||||||
" MPI_Finalize();\n",
|
" MPI_Finalize();\n",
|
||||||
"}\n",
|
"}\n",
|
||||||
"```\n",
|
"```\n",
|
||||||
@ -612,7 +612,7 @@
|
|||||||
"id": "4b455f98",
|
"id": "4b455f98",
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"source": [
|
"source": [
|
||||||
"So, the full MPI program needs to be in the source file passed to Julia or the quote block. In practice, long MPI programms are written as Julia packages using several files, which are then loaded by each MPI process. For our simple example, we just need to include the definition of `foo` inside the quote block."
|
"So, the full MPI program needs to be in the source file passed to Julia or the quote block. In practice, long MPI programs are written as Julia packages using several files, which are then loaded by each MPI process. For our simple example, we just need to include the definition of `foo` inside the quote block."
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
@ -920,7 +920,7 @@
|
|||||||
" source = MPI.ANY_SOURCE\n",
|
" source = MPI.ANY_SOURCE\n",
|
||||||
" tag = MPI.ANY_TAG\n",
|
" tag = MPI.ANY_TAG\n",
|
||||||
" status = MPI.Probe(comm,MPI.Status; source, tag)\n",
|
" status = MPI.Probe(comm,MPI.Status; source, tag)\n",
|
||||||
" count = MPI.Get_count(status,Int) # Get incomming message length\n",
|
" count = MPI.Get_count(status,Int) # Get incoming message length\n",
|
||||||
" println(\"I am about to receive $count integers.\")\n",
|
" println(\"I am about to receive $count integers.\")\n",
|
||||||
" rcvbuf = zeros(Int,count) # Allocate \n",
|
" rcvbuf = zeros(Int,count) # Allocate \n",
|
||||||
" MPI.Recv!(rcvbuf, comm, MPI.Status; source, tag)\n",
|
" MPI.Recv!(rcvbuf, comm, MPI.Status; source, tag)\n",
|
||||||
@ -973,7 +973,7 @@
|
|||||||
" if rank == 3\n",
|
" if rank == 3\n",
|
||||||
" rcvbuf = zeros(Int,5)\n",
|
" rcvbuf = zeros(Int,5)\n",
|
||||||
" MPI.Recv!(rcvbuf, comm, MPI.Status; source=2, tag=0)\n",
|
" MPI.Recv!(rcvbuf, comm, MPI.Status; source=2, tag=0)\n",
|
||||||
" # recvbuf will have the incomming message fore sure. Recv! has returned.\n",
|
" # recvbuf will have the incoming message fore sure. Recv! has returned.\n",
|
||||||
" @show rcvbuf\n",
|
" @show rcvbuf\n",
|
||||||
" end\n",
|
" end\n",
|
||||||
"end\n",
|
"end\n",
|
||||||
|
|||||||
@ -14,4 +14,4 @@
|
|||||||
var myIframe = document.getElementById("notebook");
|
var myIframe = document.getElementById("notebook");
|
||||||
iFrameResize({log:true}, myIframe);
|
iFrameResize({log:true}, myIframe);
|
||||||
});
|
});
|
||||||
</script></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../matrix_matrix/">« Matrix-matrix multiplication</a><a class="docs-footer-nextpage" href="../mpi_collectives/">MPI (collectives) »</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 30 September 2024 15:25">Monday 30 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="../matrix_matrix/">« Matrix-matrix multiplication</a><a class="docs-footer-nextpage" href="../mpi_collectives/">MPI (collectives) »</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="Tuesday 1 October 2024 05:36">Tuesday 1 October 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||||
|
|||||||
@ -7692,20 +7692,20 @@ a.anchor-link {
|
|||||||
<p>In Julia (option 1, recommended):</p>
|
<p>In Julia (option 1, recommended):</p>
|
||||||
<div class="highlight"><pre><span></span><span class="k">using</span><span class="w"> </span><span class="n">MPI</span>
|
<div class="highlight"><pre><span></span><span class="k">using</span><span class="w"> </span><span class="n">MPI</span>
|
||||||
<span class="n">MPI</span><span class="o">.</span><span class="n">Init</span><span class="p">()</span>
|
<span class="n">MPI</span><span class="o">.</span><span class="n">Init</span><span class="p">()</span>
|
||||||
<span class="c"># Your MPI programm here</span>
|
<span class="c"># Your MPI program here</span>
|
||||||
<span class="n">MPI</span><span class="o">.</span><span class="n">Finalize</span><span class="p">()</span><span class="w"> </span><span class="c"># Optional</span>
|
<span class="n">MPI</span><span class="o">.</span><span class="n">Finalize</span><span class="p">()</span><span class="w"> </span><span class="c"># Optional</span>
|
||||||
</pre></div>
|
</pre></div>
|
||||||
<p>In Julia (option 2, advanced):</p>
|
<p>In Julia (option 2, advanced):</p>
|
||||||
<div class="highlight"><pre><span></span><span class="k">using</span><span class="w"> </span><span class="n">MPI</span>
|
<div class="highlight"><pre><span></span><span class="k">using</span><span class="w"> </span><span class="n">MPI</span>
|
||||||
<span class="n">MPI</span><span class="o">.</span><span class="n">Init</span><span class="p">(</span><span class="n">finalize_atexit</span><span class="o">=</span><span class="nb">false</span><span class="p">)</span>
|
<span class="n">MPI</span><span class="o">.</span><span class="n">Init</span><span class="p">(</span><span class="n">finalize_atexit</span><span class="o">=</span><span class="nb">false</span><span class="p">)</span>
|
||||||
<span class="c"># Your MPI programm here</span>
|
<span class="c"># Your MPI program here</span>
|
||||||
<span class="n">MPI</span><span class="o">.</span><span class="n">Finalize</span><span class="p">()</span><span class="w"> </span><span class="c"># Mandatory</span>
|
<span class="n">MPI</span><span class="o">.</span><span class="n">Finalize</span><span class="p">()</span><span class="w"> </span><span class="c"># Mandatory</span>
|
||||||
</pre></div>
|
</pre></div>
|
||||||
<p>In C:</p>
|
<p>In C:</p>
|
||||||
<div class="highlight"><pre><span></span><span class="cp">#include</span><span class="w"> </span><span class="cpf"><mpi.h></span>
|
<div class="highlight"><pre><span></span><span class="cp">#include</span><span class="w"> </span><span class="cpf"><mpi.h></span>
|
||||||
<span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">argc</span><span class="p">,</span><span class="w"> </span><span class="kt">char</span><span class="o">**</span><span class="w"> </span><span class="n">argv</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">argc</span><span class="p">,</span><span class="w"> </span><span class="kt">char</span><span class="o">**</span><span class="w"> </span><span class="n">argv</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<span class="w"> </span><span class="n">MPI_Init</span><span class="p">(</span><span class="nb">NULL</span><span class="p">,</span><span class="w"> </span><span class="nb">NULL</span><span class="p">);</span>
|
<span class="w"> </span><span class="n">MPI_Init</span><span class="p">(</span><span class="nb">NULL</span><span class="p">,</span><span class="w"> </span><span class="nb">NULL</span><span class="p">);</span>
|
||||||
<span class="w"> </span><span class="cm">/* Your MPI Programm here */</span>
|
<span class="w"> </span><span class="cm">/* Your MPI Program here */</span>
|
||||||
<span class="w"> </span><span class="n">MPI_Finalize</span><span class="p">();</span>
|
<span class="w"> </span><span class="n">MPI_Finalize</span><span class="p">();</span>
|
||||||
<span class="p">}</span>
|
<span class="p">}</span>
|
||||||
</pre></div>
|
</pre></div>
|
||||||
@ -8216,7 +8216,7 @@ a.anchor-link {
|
|||||||
</div>
|
</div>
|
||||||
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
||||||
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
||||||
<p>So, the full MPI program needs to be in the source file passed to Julia or the quote block. In practice, long MPI programms are written as Julia packages using several files, which are then loaded by each MPI process. For our simple example, we just need to include the definition of <code>foo</code> inside the quote block.</p>
|
<p>So, the full MPI program needs to be in the source file passed to Julia or the quote block. In practice, long MPI programs are written as Julia packages using several files, which are then loaded by each MPI process. For our simple example, we just need to include the definition of <code>foo</code> inside the quote block.</p>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
@ -8547,7 +8547,7 @@ a.anchor-link {
|
|||||||
<span class="w"> </span><span class="n">source</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">ANY_SOURCE</span>
|
<span class="w"> </span><span class="n">source</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">ANY_SOURCE</span>
|
||||||
<span class="w"> </span><span class="n">tag</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">ANY_TAG</span>
|
<span class="w"> </span><span class="n">tag</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">ANY_TAG</span>
|
||||||
<span class="w"> </span><span class="n">status</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">Probe</span><span class="p">(</span><span class="n">comm</span><span class="p">,</span><span class="n">MPI</span><span class="o">.</span><span class="n">Status</span><span class="p">;</span><span class="w"> </span><span class="n">source</span><span class="p">,</span><span class="w"> </span><span class="n">tag</span><span class="p">)</span>
|
<span class="w"> </span><span class="n">status</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">Probe</span><span class="p">(</span><span class="n">comm</span><span class="p">,</span><span class="n">MPI</span><span class="o">.</span><span class="n">Status</span><span class="p">;</span><span class="w"> </span><span class="n">source</span><span class="p">,</span><span class="w"> </span><span class="n">tag</span><span class="p">)</span>
|
||||||
<span class="w"> </span><span class="n">count</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">Get_count</span><span class="p">(</span><span class="n">status</span><span class="p">,</span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="c"># Get incomming message length</span>
|
<span class="w"> </span><span class="n">count</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">Get_count</span><span class="p">(</span><span class="n">status</span><span class="p">,</span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="c"># Get incoming message length</span>
|
||||||
<span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="s">"I am about to receive </span><span class="si">$count</span><span class="s"> integers."</span><span class="p">)</span>
|
<span class="w"> </span><span class="n">println</span><span class="p">(</span><span class="s">"I am about to receive </span><span class="si">$count</span><span class="s"> integers."</span><span class="p">)</span>
|
||||||
<span class="w"> </span><span class="n">rcvbuf</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">zeros</span><span class="p">(</span><span class="kt">Int</span><span class="p">,</span><span class="n">count</span><span class="p">)</span><span class="w"> </span><span class="c"># Allocate </span>
|
<span class="w"> </span><span class="n">rcvbuf</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">zeros</span><span class="p">(</span><span class="kt">Int</span><span class="p">,</span><span class="n">count</span><span class="p">)</span><span class="w"> </span><span class="c"># Allocate </span>
|
||||||
<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Recv!</span><span class="p">(</span><span class="n">rcvbuf</span><span class="p">,</span><span class="w"> </span><span class="n">comm</span><span class="p">,</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Status</span><span class="p">;</span><span class="w"> </span><span class="n">source</span><span class="p">,</span><span class="w"> </span><span class="n">tag</span><span class="p">)</span>
|
<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Recv!</span><span class="p">(</span><span class="n">rcvbuf</span><span class="p">,</span><span class="w"> </span><span class="n">comm</span><span class="p">,</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Status</span><span class="p">;</span><span class="w"> </span><span class="n">source</span><span class="p">,</span><span class="w"> </span><span class="n">tag</span><span class="p">)</span>
|
||||||
@ -8608,7 +8608,7 @@ a.anchor-link {
|
|||||||
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">rank</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span>
|
<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">rank</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span>
|
||||||
<span class="w"> </span><span class="n">rcvbuf</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">zeros</span><span class="p">(</span><span class="kt">Int</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span>
|
<span class="w"> </span><span class="n">rcvbuf</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">zeros</span><span class="p">(</span><span class="kt">Int</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span>
|
||||||
<span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Recv!</span><span class="p">(</span><span class="n">rcvbuf</span><span class="p">,</span><span class="w"> </span><span class="n">comm</span><span class="p">,</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Status</span><span class="p">;</span><span class="w"> </span><span class="n">source</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span><span class="w"> </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">MPI</span><span class="o">.</span><span class="n">Recv!</span><span class="p">(</span><span class="n">rcvbuf</span><span class="p">,</span><span class="w"> </span><span class="n">comm</span><span class="p">,</span><span class="w"> </span><span class="n">MPI</span><span class="o">.</span><span class="n">Status</span><span class="p">;</span><span class="w"> </span><span class="n">source</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span><span class="w"> </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="c"># recvbuf will have the incomming message fore sure. Recv! has returned.</span>
|
<span class="w"> </span><span class="c"># recvbuf will have the incoming message fore sure. Recv! has returned.</span>
|
||||||
<span class="w"> </span><span class="nd">@show</span><span class="w"> </span><span class="n">rcvbuf</span>
|
<span class="w"> </span><span class="nd">@show</span><span class="w"> </span><span class="n">rcvbuf</span>
|
||||||
<span class="w"> </span><span class="k">end</span>
|
<span class="w"> </span><span class="k">end</span>
|
||||||
<span class="k">end</span>
|
<span class="k">end</span>
|
||||||
|
|||||||
@ -14,4 +14,4 @@
|
|||||||
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|
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|
||||||
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|
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|
||||||
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|
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|
||||||
</script></article><nav class="docs-footer"><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 30 September 2024 15:25">Monday 30 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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</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="Tuesday 1 October 2024 05:36">Tuesday 1 October 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||||
|
|||||||
@ -293,7 +293,7 @@
|
|||||||
"## Where can we exploit parallelism?\n",
|
"## Where can we exploit parallelism?\n",
|
||||||
"\n",
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
"The matrix-matrix multiplication is an example of [embarrassingly parallel algorithm](https://en.wikipedia.org/wiki/Embarrassingly_parallel). An embarrassingly parallel (also known as trivially parallel) algorithm is an algorithm that can be split in parallel tasks with no (or very few) dependences between them. Such algorithms are typically easy to parallelize.\n",
|
"The matrix-matrix multiplication is an example of [embarrassingly parallel algorithm](https://en.wikipedia.org/wiki/Embarrassingly_parallel). An embarrassingly parallel (also known as trivially parallel) algorithm is an algorithm that can be split in parallel tasks with no (or very few) dependencies between them. Such algorithms are typically easy to parallelize.\n",
|
||||||
"\n",
|
"\n",
|
||||||
"Which parts of an algorithm are completely independent and thus trivially parallel? To answer this question, it is useful to inspect the for loops, which are potential sources of parallelism. If the iterations are independent of each other, then they are trivial to parallelize. An easy check to find out if the iterations are dependent or not is to change their order (for instance changing `for j in 1:n` by `for j in n:-1:1`, i.e. doing the loop in reverse). If the result changes, then the iterations are not independent.\n",
|
"Which parts of an algorithm are completely independent and thus trivially parallel? To answer this question, it is useful to inspect the for loops, which are potential sources of parallelism. If the iterations are independent of each other, then they are trivial to parallelize. An easy check to find out if the iterations are dependent or not is to change their order (for instance changing `for j in 1:n` by `for j in n:-1:1`, i.e. doing the loop in reverse). If the result changes, then the iterations are not independent.\n",
|
||||||
"\n",
|
"\n",
|
||||||
@ -314,7 +314,7 @@
|
|||||||
"Note that:\n",
|
"Note that:\n",
|
||||||
"\n",
|
"\n",
|
||||||
"- Loops over `i` and `j` are trivially parallel.\n",
|
"- Loops over `i` and `j` are trivially parallel.\n",
|
||||||
"- The loop over `k` is not trivially parallel. The accumulation into the reduction variable `Cij` introduces extra dependences. In addition, remember that the addition of floating point numbers is not strictly associative due to rounding errors. Thus, the result of this loop may change with the loop order when using floating point numbers. In any case, this loop can also be parallelized, but it requires a parallel *fold* or a parallel *reduction*.\n",
|
"- The loop over `k` is not trivially parallel. The accumulation into the reduction variable `Cij` introduces extra dependencies. In addition, remember that the addition of floating point numbers is not strictly associative due to rounding errors. Thus, the result of this loop may change with the loop order when using floating point numbers. In any case, this loop can also be parallelized, but it requires a parallel *fold* or a parallel *reduction*.\n",
|
||||||
"\n"
|
"\n"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
|
|||||||
@ -14,4 +14,4 @@
|
|||||||
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|
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|
||||||
iFrameResize({log:true}, myIframe);
|
iFrameResize({log:true}, myIframe);
|
||||||
});
|
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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 30 September 2024 15:25">Monday 30 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="../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="Tuesday 1 October 2024 05:36">Tuesday 1 October 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||||
|
|||||||
@ -7855,7 +7855,7 @@ d) O(N³)</code></pre>
|
|||||||
</div>
|
</div>
|
||||||
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
|
||||||
</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput" data-mime-type="text/markdown">
|
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|
||||||
<h2 id="Where-can-we-exploit-parallelism?">Where can we exploit parallelism?<a class="anchor-link" href="#Where-can-we-exploit-parallelism?">¶</a></h2><p>The matrix-matrix multiplication is an example of <a href="https://en.wikipedia.org/wiki/Embarrassingly_parallel">embarrassingly parallel algorithm</a>. An embarrassingly parallel (also known as trivially parallel) algorithm is an algorithm that can be split in parallel tasks with no (or very few) dependences between them. Such algorithms are typically easy to parallelize.</p>
|
<h2 id="Where-can-we-exploit-parallelism?">Where can we exploit parallelism?<a class="anchor-link" href="#Where-can-we-exploit-parallelism?">¶</a></h2><p>The matrix-matrix multiplication is an example of <a href="https://en.wikipedia.org/wiki/Embarrassingly_parallel">embarrassingly parallel algorithm</a>. An embarrassingly parallel (also known as trivially parallel) algorithm is an algorithm that can be split in parallel tasks with no (or very few) dependencies between them. Such algorithms are typically easy to parallelize.</p>
|
||||||
<p>Which parts of an algorithm are completely independent and thus trivially parallel? To answer this question, it is useful to inspect the for loops, which are potential sources of parallelism. If the iterations are independent of each other, then they are trivial to parallelize. An easy check to find out if the iterations are dependent or not is to change their order (for instance changing <code>for j in 1:n</code> by <code>for j in n:-1:1</code>, i.e. doing the loop in reverse). If the result changes, then the iterations are not independent.</p>
|
<p>Which parts of an algorithm are completely independent and thus trivially parallel? To answer this question, it is useful to inspect the for loops, which are potential sources of parallelism. If the iterations are independent of each other, then they are trivial to parallelize. An easy check to find out if the iterations are dependent or not is to change their order (for instance changing <code>for j in 1:n</code> by <code>for j in n:-1:1</code>, i.e. doing the loop in reverse). If the result changes, then the iterations are not independent.</p>
|
||||||
<p>Look at the three nested loops in the sequential implementation of the matrix-matrix product:</p>
|
<p>Look at the three nested loops in the sequential implementation of the matrix-matrix product:</p>
|
||||||
<div class="highlight"><pre><span></span><span class="k">for</span><span class="w"> </span><span class="n">j</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">n</span>
|
<div class="highlight"><pre><span></span><span class="k">for</span><span class="w"> </span><span class="n">j</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">n</span>
|
||||||
@ -7871,7 +7871,7 @@ d) O(N³)</code></pre>
|
|||||||
<p>Note that:</p>
|
<p>Note that:</p>
|
||||||
<ul>
|
<ul>
|
||||||
<li>Loops over <code>i</code> and <code>j</code> are trivially parallel.</li>
|
<li>Loops over <code>i</code> and <code>j</code> are trivially parallel.</li>
|
||||||
<li>The loop over <code>k</code> is not trivially parallel. The accumulation into the reduction variable <code>Cij</code> introduces extra dependences. In addition, remember that the addition of floating point numbers is not strictly associative due to rounding errors. Thus, the result of this loop may change with the loop order when using floating point numbers. In any case, this loop can also be parallelized, but it requires a parallel <em>fold</em> or a parallel <em>reduction</em>.</li>
|
<li>The loop over <code>k</code> is not trivially parallel. The accumulation into the reduction variable <code>Cij</code> introduces extra dependencies. In addition, remember that the addition of floating point numbers is not strictly associative due to rounding errors. Thus, the result of this loop may change with the loop order when using floating point numbers. In any case, this loop can also be parallelized, but it requires a parallel <em>fold</em> or a parallel <em>reduction</em>.</li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|||||||
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|
|||||||
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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 30 September 2024 15:25">Monday 30 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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</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="Tuesday 1 October 2024 05:36">Tuesday 1 October 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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</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="Tuesday 1 October 2024 05:36">Tuesday 1 October 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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</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 30 September 2024 15:25">Monday 30 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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</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="Tuesday 1 October 2024 05:36">Tuesday 1 October 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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@ -333,4 +333,4 @@ end</code></pre><h2 id="All-pairs-of-shortest-paths"><a class="docs-heading-anch
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end
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|
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end
|
end
|
||||||
myC
|
myC
|
||||||
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 30 September 2024 15:25">Monday 30 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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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="Tuesday 1 October 2024 05:36">Tuesday 1 October 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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</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 30 September 2024 15:25">Monday 30 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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</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="Tuesday 1 October 2024 05:36">Tuesday 1 October 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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