{ "cells": [ { "cell_type": "markdown", "id": "46d0dd15", "metadata": {}, "source": [ "\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 the data partition can create (or solve) load imbalances" ] }, { "cell_type": "markdown", "id": "8dcee319", "metadata": {}, "source": [ "## Gaussian elimination\n", "\n", "[Gaussian elimination](https://en.wikipedia.org/wiki/Gaussian_elimination) is provably one of the first algorithms you have learned to solve linear equations like this one:\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", "\n", "The value of $x$, $y$, and $z$ can be found by creating an *augmented matrix* and applying Gaussian elimination to it:\n", "\n", "$$\n", "\\left[\n", "\\begin{matrix}\n", "1 & 3 & 1 & 9 \\\\\n", "1 & 2 & -1 & 1 \\\\\n", "3 & 11 & 5 & 35 \\\\\n", "\\end{matrix}\n", "\\right]\n", "\\rightarrow\n", "\\left[\n", "\\begin{matrix}\n", "1 & 3 & 1 & 9 \\\\\n", "0 & -1 & -2 & -8 \\\\\n", "0 & 2 & 2 & 8 \\\\\n", "\\end{matrix}\n", "\\right]\n", "\\rightarrow\n", "\\left[\n", "\\begin{matrix}\n", "1 & 3 & 1 & 9 \\\\\n", "0 & 1 & 2 & 8 \\\\\n", "0 & 0 & 1 & 4 \\\\\n", "\\end{matrix}\n", "\\right]\n", "$$\n", "\n", "The result is an upper diagonal matrix with ones on the diagonal. From this matrix the values $x$, $y$, and $z$ can be found via [backward substitution](https://en.wikipedia.org/wiki/Triangular_matrix).\n", "\n" ] }, { "cell_type": "markdown", "id": "94c10106", "metadata": {}, "source": [ "### Serial implementation\n", "\n", "Gaussian elimination can be implemented as shown in the following function. Note that the result is overwritten in-place on the input matrix." ] }, { "cell_type": "code", "execution_count": 70, "id": "e4070214", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "gaussian_elimination! (generic function with 2 methods)" ] }, "execution_count": 70, "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": "cb7f89e5", "metadata": {}, "source": [ "Let us test the function with the example above:" ] }, { "cell_type": "code", "execution_count": 68, "id": "eb30df0d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3×4 Matrix{Float64}:\n", " 1.0 3.0 1.0 9.0\n", " 1.0 2.0 -1.0 1.0\n", " 3.0 11.0 5.0 35.0" ] }, "execution_count": 68, "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]" ] }, { "cell_type": "code", "execution_count": 71, "id": "52bfada2", "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": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gaussian_elimination!(B)" ] }, { "cell_type": "markdown", "id": "563aa0d0", "metadata": {}, "source": [ "We get the same result as shown before (as expected)." ] }, { "cell_type": "markdown", "id": "39f2e8ef", "metadata": {}, "source": [ "## Parallelization\n", "\n", "Gaussian elimination is expensive and thus it makes sense to try to seed-up this computation by using several processors. It requires $(2n^3)/3$ operation, where $n$ is the number of rows in the input matrix. Thus, the time complexity is $O(n^3)$, which rapidly grows with $n$.\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", "```\n", "\n", "- The loop over k cannot be parallelized (the state of B at iteration k depends on the state at iteration k-1)\n", "- Loops over t, i, and j can be parallelized\n", "- BUT the loop over t needs to be done before loop over i and j" ] }, { "cell_type": "markdown", "id": "a67e0aad", "metadata": {}, "source": [ "### Data partition\n", "\n", "Let us start considering a simple 1D block partition. We assume that each process contains only a portion of the input matrix consisting in a block of consecutive rows. In this algorithm, the data stored in a process does not correspond with the data updated at a given iteration over the outer loop over k. The data updated is only a subset of the data stored, which leads to load imbalances (as we will see in a second).\n", "\n", "Consider next figure. Let's find out which is the data updated and the data used by CPU 3 at iteration $k$.\n" ] }, { "attachments": { "g20491.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "6d8b79ba", "metadata": {}, "source": [ "
\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "edb211d0", "metadata": {}, "source": [ "By looking into the code above, you can see that `B[i,j]` is updated at iteration k, if and only if i and j are greater or equal than k. Thus, from all entries owned by CPU3, only the ones fulfilling this condition will be updated. See the entries highlighted in the next figure." ] }, { "attachments": { "g20853.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "f18f33da", "metadata": {}, "source": [ "
\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "1eced940", "metadata": {}, "source": [ "### Data dependencies\n", "\n", "At iteration k, CPU3 needs part of row k to update its entries. The process owning row k needs to broadcast this entries to all other processes that require them. This communication pattern is almost identical to the one previously studied in Floyd's algorithm." ] }, { "attachments": { "g21211.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "410eb1ba", "metadata": {}, "source": [ "
\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "d04f70fa", "metadata": {}, "source": [ "### Load imbalance\n", "\n", "Do all processes process the same amount of data at a given iteration? This answer is no. To understand this let us find out the data updated by CPU1 in the figure below. At iteration k, CPU 1 has not data to process since k is larger than all row ids that CPU 1 owns. This is in contrast to CPU 2 and CPU 3 which have data to process. As a result, CPU 1 is idle (doing nothing), which is waisting computational resources that could be otherwise used." ] }, { "attachments": { "g23603.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "3988b2ae", "metadata": {}, "source": [ "
\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "c1957040", "metadata": {}, "source": [ "### Addressing the load imbalance\n", "\n", "For this algorithm, a cyclic distribution mitigates the load imbalance.\n", "\n", "- Cyclic partitions are often useful in algorithms with *predictable* load imbalance\n", "- A cyclic partition is a form of *static* load balancing\n", "- Cyclic partition are not suitable for all communication patters. E.g., algorithms that require communication between nearest-neighbors like Jacobi." ] }, { "attachments": { "g23933.png": { "image/png": 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AQC0pvgAAAACoJcUXAAAAALWk+AIAAACglhRfAAAAANSS4gsAAACAWlJ8AQAAAFBLii8AAAAAaknxBQAAAEAtKb4AAAAAqCXFFwAAAAC1pPgCAAAAoJYUXwAAAADUkuILAAAAgFpSfAEAAABQS4ovAAAAAGpJ8QUAAABALSm+AAAAAKglxRcAAAAAtaT4AgAAAKCWFF8AAAAA1JLiCwAAAIBaUnwBAAAAUEuKLwAAAABqSfEFAAAAQC0pvgAAAACoJcUXAAAAALWk+AIAAACglpq//uC+u7eLPC+ryPI/Gh99Z3zxn/aoOsZWPb3utPwbX3xZ3PffM6qO0tfCucfFyIYZWbOV5hk+8fBQrF4+OU/5jsfHfjGDWZZVHaWvdatOye/46v7x6APbVx2lr3n3Hx2NRiPZO169fLtYv+7ULNV8ERGjI6dnN33sxdEeHKg6Sl+rlr8tv/vrL4rlC59XdZS+fvq9I+OpNRuTncFutxdjo2ckOYM//9G0qiNAXw//eFqS74djo2dkX75m72i2GlVH6Wvt8MmN/7p131g4d6eqo/T18x/NifGxXrL7+ul1O8TGp09Lcl9vtmnj6dnNn9gnhiYPVh2lr+Glb8nvuW2PWLNit6qj9HXf3a+L5YvWJDuDZVnG2OgZSe6/zTY+/Y7865/ZL6bPnFJ1lL6WPnZ89sM7d4jOWJpn+PB9rVix8HnJzmBEuh3NfXdvt8WzLKJMr+UCAFI2HJHNqjoEz0XliogwewDAb60ZEd+PeGpSljVfXJZDaX6VBQCoXJY9WZZl+/6IweVVZ+E560cRm3bIsrE/LMup3lsBgL6ybGNZlt2HIqZs2PzCMCli3fcipr6k0mQAQMJW3B2x/WsjYqzqJDyntSOWfzNi9qurDgIApOqpn0VMfWVErN/8P7ffEDF1fZWRAIDUzV4bSi+qN/bLWQQA2IopGyJifUTE/wXLiFV2Az9mHAAAAABJRU5ErkJggg==" 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