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https://github.com/fverdugo/XM_40017.git
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633 lines
192 KiB
Plaintext
633 lines
192 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "46d0dd15",
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"metadata": {},
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"source": [
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"<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/3/39/VU_logo.png/800px-VU_logo.png?20161029201021\" width=\"350\">\n",
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"\n",
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"### Programming large-scale parallel systems\n",
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"\n",
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"# Gaussian elimination"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ff0fbd76",
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"metadata": {},
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"source": [
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"## Contents\n",
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"\n",
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"In this notebook, we will learn\n",
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"\n",
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"- How to parallelize Gaussian elimination\n",
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"- What is load imbalance, and how to fix it in this algorithm"
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]
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},
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{
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"cell_type": "markdown",
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"id": "480af594",
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"metadata": {},
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"source": [
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"<div class=\"alert alert-block alert-info\">\n",
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"<b>Note:</b> Do not forget to execute the cell below before starting this notebook! \n",
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"</div>"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "7e93809a",
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"metadata": {},
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"outputs": [],
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"source": [
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"using Printf\n",
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"function answer_checker(answer,solution)\n",
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" if answer == solution\n",
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" \"🥳 Well done!\"\n",
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" else\n",
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" \"It's not correct. Keep trying! 💪\"\n",
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" end |> println\n",
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"end\n",
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"function ge_par_why()\n",
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" msg = \"The outer loop of the algorithm is not parallelizable, since the iterations depend on the results of the previous iterations. However, we can extract parallelism from the inner loops.\"\n",
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" println(msg)\n",
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"end\n",
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"ge_par_check(answer) = answer_checker(answer, \"a\")\n",
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"ge_dep_check(answer) = answer_checker(answer, \"b\")\n",
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"function ge_lb_answer()\n",
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" msg = \"It is a form of static load balancing. We know in advance the load distribution and the partition strategy does not depend on the actual values of the input matrix\"\n",
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" println(msg)\n",
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"end\n",
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"println(\"🥳 Well done!\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8ad95aa5",
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"metadata": {},
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"source": [
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"## Gaussian elimination\n",
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"\n",
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"\n",
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"[Gaussian elimination](https://en.wikipedia.org/wiki/Gaussian_elimination) is a method to solve systems of linear equations, like this one:\n",
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"\n",
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"$$\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"1 & 3 & 1 \\\\\n",
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"1 & 2 & -1 \\\\\n",
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"3 & 11 & 5 \\\\\n",
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"\\end{matrix}\n",
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"\\right]\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"x \\\\\n",
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"y \\\\\n",
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"z \\\\\n",
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"\\end{matrix}\n",
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"\\right]\n",
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"=\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"9 \\\\\n",
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"1 \\\\\n",
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"35 \\\\\n",
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"\\end{matrix}\n",
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"\\right].\n",
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"$$\n",
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"\n",
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"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.\n",
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"\n",
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"### Problem statement\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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"- both system 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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"\n",
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"\n",
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"For the particular system shown above, the transformed one is the following:\n",
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"\n",
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"$$\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"1 & 3 & 1 \\\\\n",
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"1 & 2 & -1 \\\\\n",
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"3 & 11 & 5 \\\\\n",
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"\\end{matrix}\n",
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"\\right]\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"x \\\\\n",
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"y \\\\\n",
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"z \\\\\n",
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"\\end{matrix}\n",
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"\\right]\n",
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"=\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"9 \\\\\n",
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"1 \\\\\n",
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"35 \\\\\n",
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"\\end{matrix}\n",
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"\\right]\n",
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"\\longrightarrow\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"1 & 3 & 1 \\\\\n",
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"0 & 1 & 2 \\\\\n",
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"0 & 0 & 1 \\\\\n",
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"\\end{matrix}\n",
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"\\right]\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"x \\\\\n",
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"y \\\\\n",
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"z \\\\\n",
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"\\end{matrix}\n",
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"\\right]\n",
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"=\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"9 \\\\\n",
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"8 \\\\\n",
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"4 \\\\\n",
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"\\end{matrix}\n",
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"\\right]\n",
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"$$\n",
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"\n",
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"The most challenging part of solving a system of linear equations is to transform it to upper triangular form. Afterwards, the solution vector can be obtained easily with a backward substitution. For this reason, we will study here the triangulation step only."
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]
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},
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{
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"cell_type": "markdown",
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"id": "980cb36f",
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"metadata": {},
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"source": [
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"\n",
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"\n",
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"### Augmented system matrix\n",
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"\n",
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"In practice, vector $b$ is added as an additional column to A forming the so-called *augmented* matrix $A^* = [A b]$. The augmented matrix in the example above is\n",
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"\n",
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"$$\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"1 & 3 & 1 \\\\\n",
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"1 & 2 & -1 \\\\\n",
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"3 & 11 & 5 \\\\\n",
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"\\end{matrix}\n",
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"\\right]\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"x \\\\\n",
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"y \\\\\n",
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"z \\\\\n",
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"\\end{matrix}\n",
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"\\right]\n",
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"=\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"9 \\\\\n",
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"1 \\\\\n",
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"35 \\\\\n",
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"\\end{matrix}\n",
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"\\right]\\longrightarrow\n",
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"A^*=\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"1 & 3 & 1 & 9 \\\\\n",
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"1 & 2 & -1 & 1 \\\\\n",
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"3 & 11 & 5 & 35\\\\\n",
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"\\end{matrix}\n",
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"\\right].\n",
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"$$\n",
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"\n",
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"With this new notation, the goal of Gaussian elimination is to find the augmented matrix containing $U$ and $c$, namely $U^*= [U c]$, given the augmented matrix $A^* = [A b]$. These are $A^*$ and $U^*$ in our example:\n",
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"\n",
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"$$\n",
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"A^*=\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"1 & 3 & 1 & 9 \\\\\n",
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"1 & 2 & -1 & 1 \\\\\n",
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"3 & 11 & 5 & 35\\\\\n",
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"\\end{matrix}\n",
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"\\right]\\longrightarrow\n",
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"U^*=\n",
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"\\left[\n",
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"\\begin{matrix}\n",
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"1 & 3 & 1 & 9 \\\\\n",
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"0 & 1 & 2 & 8\\\\\n",
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"0 & 0 & 1 & 4\\\\\n",
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"\\end{matrix}\n",
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"\\right].\n",
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"$$\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "94c10106",
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"metadata": {},
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"source": [
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"### Serial implementation\n",
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"\n",
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"\n",
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"The following algorithm computes the Gaussian elimination on a given augmented matrix `B`, representing a system of linear equations. The result is given by overwriting `B`, avoiding the allocation of an additional matrix.\n",
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"\n",
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"- The outer loop is a loop over rows.\n",
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"- The first inner loop in line 4 divides the current row by the value of the diagonal entry, thus transforming the diagonal to contain only ones. Note that we skip the first entries in the row, as we know that these values are zero at this point. The cells updated in this loop at iteration $k$ are depicted in red in the figure below.\n",
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"- The second inner loop beginning in line 8 subtracts the rows from one another such that all entries below the diagonal become zero. The entries updated in this loop are depicted in blue in the figure below."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "e4070214",
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"metadata": {},
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"outputs": [],
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"source": [
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"function gaussian_elimination!(B)\n",
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" n,m = size(B)\n",
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" @inbounds for k in 1:n\n",
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" for t in (k+1):m\n",
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" B[k,t] = B[k,t]/B[k,k]\n",
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" end\n",
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" B[k,k] = 1\n",
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" for i in (k+1):n \n",
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" for j in (k+1):m\n",
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" B[i,j] = B[i,j] - B[i,k]*B[k,j]\n",
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" end\n",
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" B[i,k] = 0\n",
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" end\n",
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" end\n",
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" B\n",
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"end"
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]
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},
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{
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"attachments": {
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"g27851.png": {
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"image/png": 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"
|
|
}
|
|
},
|
|
"cell_type": "markdown",
|
|
"id": "cc6ce65e",
|
|
"metadata": {},
|
|
"source": [
|
|
"<div>\n",
|
|
"<img src=\"attachment:g27851.png\" align=\"left\" width=\"300\"/>\n",
|
|
"</div>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "3763b000",
|
|
"metadata": {},
|
|
"source": [
|
|
"<div class=\"alert alert-block alert-info\">\n",
|
|
"<b>Note:</b> This algorithm is not correct for all nonsingular matrices: if any diagonal element <code>B[k,k]</code> is zero, the computation in the first inner loop fails. To get around this problem, another step can be added to the algorithm that swaps the rows until the diagonal entry of the current row is not zero. This process of finding a nonzero value is called <b>pivoting</b>. We are not going to consider pivoting here for simplicity. \n",
|
|
"</div>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "fbb3d1eb",
|
|
"metadata": {},
|
|
"source": [
|
|
"You can verify that the algorithm computes the upper triangular matrix correctly for the example in the introduction by running the following code cell. "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "eb30df0d",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"A = Float64[1 3 1; 1 2 -1; 3 11 5]\n",
|
|
"b = Float64[9,1,35]\n",
|
|
"B = [A b]\n",
|
|
"gaussian_elimination!(B)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "a7d6f90a",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Complexity of the algorithm\n",
|
|
"\n",
|
|
"The number of operations of the algorithm is $O(N^3)$, where $N$ is the number of unknowns in the system. Intuitively, this makes sense as there are three nested loops. However, the length of the loops is not equal to $N$. In any case, it can be proven that the total number of operations is still $O(N^3)$. The actual proof is a bit challenging and it is not discussed here."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "39f2e8ef",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Parallelization\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "1b1a6469",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Where can we extract parallelism?\n",
|
|
"\n",
|
|
"```julia\n",
|
|
"n,m = size(B)\n",
|
|
"for t in (k+1):m\n",
|
|
" B[k,t] = B[k,t]/B[k,k]\n",
|
|
"end\n",
|
|
"B[k,k] = 1\n",
|
|
"for i in (k+1):n \n",
|
|
" for j in (k+1):m\n",
|
|
" B[i,j] = B[i,j] - B[i,k]*B[k,j]\n",
|
|
" end\n",
|
|
" B[i,k] = 0\n",
|
|
"end\n",
|
|
"```"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "e52c4b38",
|
|
"metadata": {},
|
|
"source": [
|
|
"<div class=\"alert alert-block alert-success\">\n",
|
|
"<b>Question:</b> Which of the loops can be parallelized?\n",
|
|
"</div>\n",
|
|
"\n",
|
|
" a) the inner loops, but not the outer loop\n",
|
|
" b) the outer loop, but not the inner loops\n",
|
|
" c) all loops\n",
|
|
" d) only the first inner loop"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "078e974e",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"answer = \"x\" # replace x with a, b, c, or d \n",
|
|
"ge_par_check(answer)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "1169c86e",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"ge_par_why()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
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"id": "74491f64",
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"metadata": {},
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"source": [
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"### Data partition\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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"\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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]
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},
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{
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"attachments": {
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"g31767.png": {
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"image/png": 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"
|
|
}
|
|
},
|
|
"cell_type": "markdown",
|
|
"id": "7460b0af",
|
|
"metadata": {},
|
|
"source": [
|
|
"<div>\n",
|
|
"<img src=\"attachment:g31767.png\" align=\"left\" width=\"250\"/>\n",
|
|
"</div>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "3ebddda1",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Load imbalance\n",
|
|
"\n",
|
|
"Each CPU will be on charge of updating the entries stored locally. However, this algorithm is a bit different than the previous ones. At iteration $k$ only a subset of the entries in the matrix `B` are updated, i.e. only the entries in the bottom right block `B[k:end,k:end]` are updated. This block is illustrated in a darker color in the next figure for $k=6$. "
|
|
]
|
|
},
|
|
{
|
|
"attachments": {
|
|
"fig-asp-data-updated-2.png": {
|
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"image/png": 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"
|
|
}
|
|
},
|
|
"cell_type": "markdown",
|
|
"id": "d083cd53",
|
|
"metadata": {},
|
|
"source": [
|
|
"<div>\n",
|
|
"<img src=\"attachment:fig-asp-data-updated-2.png\" align=\"left\" width=\"250\"/>\n",
|
|
"</div>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "e341fda6",
|
|
"metadata": {},
|
|
"source": [
|
|
"In this particular example CPU 1 will not have any work to do at iteration $k=6$ and it will be waiting, while other CPUs are computing. In general, CPUs containing rows previous to row $k$ will have less work to do than CPUs containing rows after row $k$. This will worsen as the value of $k$ increases. At some point, only the last CPU will have work to do and the others will idle. \n",
|
|
"\n",
|
|
"<div class=\"alert alert-block alert-info\">\n",
|
|
"<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",
|
|
"</div>\n",
|
|
"\n",
|
|
"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"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "51498a44",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Fixing load imbalance\n",
|
|
"\n",
|
|
"In this application, is relatively easy to fix the load imbalance problem. We know in advance which data is going to be processes at each CPU and we can design a more clever data partition.\n",
|
|
"\n",
|
|
"We can consider row-wise cyclic partition to fix the problem. See figure below. In this case, the CPUs will have less work as the value of $k$ increases, but amount of work will be better distributed than with the previous row block partition."
|
|
]
|
|
},
|
|
{
|
|
"attachments": {
|
|
"fig-asp-data-updated-cyclic.png": {
|
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"image/png": 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"
|
|
}
|
|
},
|
|
"cell_type": "markdown",
|
|
"id": "b90252f1",
|
|
"metadata": {},
|
|
"source": [
|
|
"<div>\n",
|
|
"<img src=\"attachment:fig-asp-data-updated-cyclic.png\" align=\"left\" width=\"250\"/>\n",
|
|
"</div>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "1c9e4c8a",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Static vs dynamic load balancing\n",
|
|
"\n",
|
|
"Load balancing is the process of distributing work to processors uniformly with the aim to efficiently exploit a parallel system. There are two key forms of load balancing: Static and dynamic load balancing.\n",
|
|
"\n",
|
|
"- **Static load balancing** the work distribution strategy is based on prior information of the algorithm and it does not depend on runtime values.\n",
|
|
"- **Dynamic load balancing** the work distribution strategy is based on runtime values.\n",
|
|
"\n",
|
|
"Static load balancing is often used in algorithms for which the load distribution is known in advance and it does not depend on runtime values. On the other hand, dynamic load balancing is often needed in problems in which the work distribution cannot be predicted in advance and depends on runtime values.\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"<div class=\"alert alert-block alert-success\">\n",
|
|
"<b>Question:</b> Using a cyclic partition for Gaussian elimination, is a form of static or dynamic load balancing?\n",
|
|
"</div>\n",
|
|
"\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "a6741a25",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"ge_lb_answer()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "e151fb8d",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Data dependencies\n",
|
|
"\n",
|
|
"Using a cyclic partition, we managed to distribute the work uniformly. But we still need to study the data dependencies in order to implement this algorithm in parallel efficiently.\n",
|
|
"\n",
|
|
"Look again to the algorithm\n",
|
|
"\n",
|
|
"```julia\n",
|
|
"n,m = size(B)\n",
|
|
"for t in (k+1):m\n",
|
|
" B[k,t] = B[k,t]/B[k,k]\n",
|
|
"end\n",
|
|
"B[k,k] = 1\n",
|
|
"for i in (k+1):n \n",
|
|
" for j in (k+1):m\n",
|
|
" B[i,j] = B[i,j] - B[i,k]*B[k,j]\n",
|
|
" end\n",
|
|
" B[i,k] = 0\n",
|
|
"end\n",
|
|
"```\n",
|
|
"\n",
|
|
"Note that all updates on the loop over i and j we do the following: \n",
|
|
"\n",
|
|
"```julia\n",
|
|
"B[i,j] = B[i,j] - B[i,k]*B[k,j]\n",
|
|
"```\n",
|
|
"\n",
|
|
"As we are using row-wise partitions, the CPU that updates `B[i,j]` will also have entry `B[i,k]` in memory (both are in the same row). However, `B[k,j]` is in another row and it might be located on another processor. We might need to communicate `B[k,j]` for `j=(k+1):m`. This corresponds to the cells marked in red in the figure below. These red entries are the data dependencies of this algorithm. The owner of these entries has to send them to the other processors. This is very similar to the communication pattern seen in previous notebook for Floyd's algorithm. There is a key difference however. In the current case, we do not need to send the full row, only the entries beyond column $k$ (the red cells in the figure).\n"
|
|
]
|
|
},
|
|
{
|
|
"attachments": {
|
|
"g27851.png": {
|
|
"image/png": 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"
|
|
}
|
|
},
|
|
"cell_type": "markdown",
|
|
"id": "0050b6c4",
|
|
"metadata": {},
|
|
"source": [
|
|
"<div>\n",
|
|
"<img src=\"attachment:g27851.png\" align=\"left\" width=\"300\"/>\n",
|
|
"</div>"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "cf189776",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Parallel implementation\n",
|
|
"\n",
|
|
"\n",
|
|
"At iteration $k$,\n",
|
|
"\n",
|
|
"1. The CPU owning row $k$ does the loop over $t$ to update row $k$.\n",
|
|
"2. The CPU owning row $k$ sets $B_{kk} = 1$.\n",
|
|
"2. This CPU sends the red cells in figure above to the other processors.\n",
|
|
"3. All processors receive the updated values in row $k$ and do the loop over i and j locally (blue cells).\n",
|
|
"\n",
|
|
"\n",
|
|
"As you probably see, the parallel implementation of this method is closely related to Floyd's algorithm. But there are some differences. \n",
|
|
"\n",
|
|
"1. The process that owns row $k$ updates its values before sending them.\n",
|
|
"2. We do not send the full row $k$, only the entries beyond column $k$.\n",
|
|
"3. We need a cyclic partition to balance the load properly.\n",
|
|
"\n",
|
|
"A key similarity between the two algorithms, however, is that they both suffer from synchronization problems. We need to make sure that the rows arrive in the right order. The strategies discussed for Floyd's algorithm also apply in this current case.\n",
|
|
"\n",
|
|
"The actual implementation of the parallel algorithm is left as an open exercise."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "866824c6",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Conclusion\n",
|
|
"\n",
|
|
"\n",
|
|
"We studied the parallelization of an algorithm that leads to load imbalance. We fixed the problem using a cyclic partition. This is a form of static load balancing since we were able to distribute the load in advance without using runtime values. This is opposed to dynamic load balancing which can schedule loads flexibly during runtime. Note however that cyclic partitioning is not suitable for all communication patterns. For example, it can lead to a large communication overhead in the parallel Jacobi method, since the computation of each value depends on its neighboring elements.\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "f60d9ea0",
|
|
"metadata": {},
|
|
"source": [
|
|
"# License\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"This notebook is part of the course [Programming Large Scale Parallel Systems](https://www.francescverdugo.com/XM_40017) at Vrije Universiteit Amsterdam and may be used under a [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/) license."
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Julia 1.9.0",
|
|
"language": "julia",
|
|
"name": "julia-1.9"
|
|
},
|
|
"language_info": {
|
|
"file_extension": ".jl",
|
|
"mimetype": "application/julia",
|
|
"name": "julia",
|
|
"version": "1.9.0"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|