XM_40017/notebooks/LEQ.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "46d0dd15",
   "metadata": {},
   "source": [
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/3/39/VU_logo.png/800px-VU_logo.png?20161029201021\" width=\"350\">\n",
    "\n",
    "### Programming large-scale parallel systems\n",
    "\n",
    "# Gaussian elimination"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff0fbd76",
   "metadata": {},
   "source": [
    "## Contents\n",
    "\n",
    "In this notebook, we will learn\n",
    "\n",
    "- How to parallelize Gaussian elimination\n",
    "- How to fix static load imbalance"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "480af594",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Note:</b> Do not forget to execute the cell below before starting this notebook! \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7e93809a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ge_dep_check (generic function with 1 method)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Printf\n",
    "function answer_checker(answer,solution)\n",
    "    if answer == solution\n",
    "        \"🥳 Well done! \"\n",
    "    else\n",
    "        \"It's not correct. Keep trying! 💪\"\n",
    "    end |> println\n",
    "end\n",
    "ge_par_check(answer) = answer_checker(answer, \"a\")\n",
    "ge_dep_check(answer) = answer_checker(answer, \"b\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8dcee319",
   "metadata": {},
   "source": [
    "## Gaussian elimination\n",
    "\n",
    "\n",
    "[Gaussian elimination](https://en.wikipedia.org/wiki/Gaussian_elimination) is a method to solve systems of linear equations, e.g.\n",
    "\n",
    "$$\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "1 & 3 & 1 \\\\\n",
    "1 & 2 & -1 \\\\\n",
    "3 & 11 & 5 \\\\\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "x \\\\\n",
    "y \\\\\n",
    "z  \\\\\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "=\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "9 \\\\\n",
    "1 \\\\\n",
    "35  \\\\\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$\n",
    "\n",
    "The steps of the Gaussian elimination will transform the system into an upper triangular matrix. The system of linear equations can now easily be solved by backward substitution. \n",
    "\n",
    "\n",
    "$$\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "1 & 3 & 1 & 9 \\\\\n",
    "1 & 2 & -1 & 1 \\\\\n",
    "3 & 11 & 5 & 35 \\\\\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "\\rightarrow\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "1 & 3 & 1 & 9 \\\\\n",
    "0 & -1 & -2 & -8 \\\\\n",
    "0 & 2 & 2 & 8 \\\\\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "\\rightarrow\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "1 & 3 & 1 & 9 \\\\\n",
    "0 & 1 & 2 & 8 \\\\\n",
    "0 & 2 & 2 & 8 \\\\\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "\\rightarrow\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "1 & 3 & 1 & 9 \\\\\n",
    "0 & 1 & 2 & 8 \\\\\n",
    "0 & 0 & -2 & -8 \\\\\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "\\rightarrow\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "1 & 3 & 1 & 9 \\\\\n",
    "0 & 1 & 2 & 8 \\\\\n",
    "0 & 0 & 1 & 4 \\\\\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94c10106",
   "metadata": {},
   "source": [
    "### Serial implementation\n",
    "The following algorithm computes the Gaussian elimination on a matrix which represents a system of linear equations.\n",
    "- 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. \n",
    "- The second inner loop beginning in line 8 substracts the rows from one another such that all entries below the diagonal become zero. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e4070214",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gaussian_elimination! (generic function with 1 method)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function gaussian_elimination!(B)\n",
    "    n,m = size(B)\n",
    "    @inbounds for k in 1:n\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",
    "    end\n",
    "    B\n",
    "end"
   ]
  },
  {
   "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 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>.   \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "eb30df0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×4 Matrix{Float64}:\n",
       " 1.0  3.0  1.0  9.0\n",
       " 0.0  1.0  2.0  8.0\n",
       " 0.0  0.0  1.0  4.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": "8d941741",
   "metadata": {},
   "source": [
    "The result is an upper triangular matrix which can be used to solve the system by backward substitution. "
   ]
  },
  {
   "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 k in 1:n\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",
    "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": 5,
   "id": "078e974e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It's not correct. Keep trying! 💪\n"
     ]
    }
   ],
   "source": [
    "answer = \"x\" # replace x with a, b, c, or d \n",
    "ge_par_check(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14d57c52",
   "metadata": {},
   "source": [
    "### Two possible data partitions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c518f863",
   "metadata": {},
   "source": [
    "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. Let's have a look at two different parallelization schemes. \n",
    "\n",
    "1. **Block-wise partitioning**: Each processor gets a block of subsequent rows. \n",
    "2. **Cyclic partitioning**: The rows are cyclicly distributed among the processors. "
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "id": "f06f0869",
   "metadata": {},
   "source": [
    "<div>\n",
    "<img src=\"attachment:g23933.png\"  align=\"left\" width=\"400\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a67e0aad",
   "metadata": {},
   "source": [
    "## What is the work per process at iteration k?\n",
    "To evaluate the efficiency of both partitioning schemes, consider how much work the processors do in the following example. \n",
    "In any iteration k, which part of the matrix is updated in the inner loops? "
   ]
  },
  {
   "attachments": {
    "g26595.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "53a94ed3",
   "metadata": {},
   "source": [
    "<div>\n",
    "<img src=\"attachment:g26595.png\"  align=\"left\" width=\"250\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d083cd53",
   "metadata": {},
   "source": [
    "It is clear from the code that at a given iteration `k`, the matrix is updated from row `k` to `n` and from column `k` to `m`. If we look at how that reflects the distribution of work over the processes, we can see that CPU 1 does not have any work, whereas CPU 2 does a little work and CPU 3 and 4 do a lot of work. Thus, the work load is _imbalanced_ across the different processes. "
   ]
  },
  {
   "attachments": {
    "g26786.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "0d80cd72",
   "metadata": {},
   "source": [
    "<div>\n",
    "<img src=\"attachment:g26786.png\"  align=\"left\" width=\"250\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6409890d",
   "metadata": {},
   "source": [
    "### Load imbalance\n",
    "\n",
    "- CPUs with rows <k are idle during iteration k\n",
    "- Bad load balance means bad speedups, as some CPUs are waiting instead of doing useful work\n",
    "- Solution: cyclic partition  \n",
    "                    \n",
    "### Data dependencies\n",
    "                    \n",
    "<div class=\"alert alert-block alert-success\">\n",
    "<b>Question:</b>  What are the data dependencies of this partitioning?\n",
    "</div>\n",
    "\n",
    "    a) CPUs with rows >k need all rows <=k\n",
    "    b) CPUs with rows >k need part of row k\n",
    "    c) All CPUs need row k \n",
    "    d) CPUs with row k needs all rows >k  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e0565e92",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It's not correct. Keep trying! 💪\n"
     ]
    }
   ],
   "source": [
    "answer = \"x\" # replace x with a, b, c, or d \n",
    "ge_dep_check(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b90252f1",
   "metadata": {},
   "source": [
    "### Cyclic partition\n",
    "\n",
    "In contrast, if we look at how the work is balanced for the same example and cyclic partitioning, we find that the processes have similar work load. "
   ]
  },
  {
   "attachments": {
    "g27009.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "6a4c4051",
   "metadata": {},
   "source": [
    "<div>\n",
    "<img src=\"attachment:g27009.png\"  align=\"left\" width=\"250\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "866824c6",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "Cyclic partitioning tends to work well in problems with predictable load imbalance. It is a form of **static load balancing** which means using a pre-defined load schedule based on prior information about the algorithm (as opposed to **dynamic load balancing** which can schedule loads more flexibly during runtime). The data dependencies are the same as for the 1d block partitioning.\n",
    "\n",
    "At the same time, 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 neighbouring elements."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20982b04",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "The actual implementation of the parallel algorithm is left as an exercise. Implement both 1d block and 1d cyclic partitioning and compare their performance. The implementation is closely related to that of Floyd's algorithm. To test your algorithms, generate input matrices with the function below (a random matrix is not enough, we need a non singular matrix that does not require pivoting). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a65cf8e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tridiagonal_matrix (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function tridiagonal_matrix(n)\n",
    "    C = zeros(n,n)\n",
    "    stencil = [(-1,2,-1),(-1,0,1)]\n",
    "    for i in 1:n\n",
    "        for  (coeff,o) in zip((-1,2,-1),(-1,0,1))\n",
    "            j = i+o\n",
    "            if j in 1:n\n",
    "                C[i,j] = coeff\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    C\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31d8586a",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 5\n",
    "C = tridiagonal_matrix(n)\n",
    "b = ones(n)\n",
    "gaussian_elimination!(C)"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Julia 1.9.1",
   "language": "julia",
   "name": "julia-1.9"
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  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.9.1"
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 "nbformat_minor": 5
}