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This commit is contained in:
Francesc Verdugo
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5b47a090a5
@ -13,7 +13,7 @@
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "b4fef0c2",
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"id": "b4d5f1a1",
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"metadata": {},
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"outputs": [],
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"source": [
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@ -22,23 +22,14 @@
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"execution_count": null,
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"id": "2f8ba040",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"alg_2_deps_check (generic function with 1 method)"
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]
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},
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"execution_count": 14,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"using Distributed\n",
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"using BenchmarkTools\n",
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"using Printf\n",
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"if procs() == workers()\n",
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" addprocs(4)\n",
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"end\n",
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@ -72,8 +63,7 @@
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"\n",
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"- Parallelize a simple algorithm\n",
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"- Study the performance of different parallelization strategies\n",
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"- Implement them using Julia\n",
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"- Learn concepts such as communication overhead and parallel speedup. "
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"- Implement them using Julia"
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]
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},
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{
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@ -103,7 +93,7 @@
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},
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{
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"cell_type": "markdown",
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"id": "4cb6e98f",
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"id": "a358ee60",
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"metadata": {},
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"source": [
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"### Goals\n",
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@ -167,7 +157,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"execution_count": null,
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"id": "af8dfb37",
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"metadata": {},
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"outputs": [],
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@ -208,12 +198,11 @@
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "899235d1",
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"id": "725387f6",
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"metadata": {},
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"outputs": [],
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"source": [
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"using LinearAlgebra\n",
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"using BenchmarkTools\n",
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"N = 1000\n",
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"A = rand(N,N)\n",
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"B = rand(N,N)\n",
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@ -290,7 +279,7 @@
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"source": [
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"### Data dependencies\n",
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"\n",
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"Moving data through the network is expensive and reducing data movement is one of the key points in distributed algorithm. To this end, we determine which is the minimum data needed by a worker to perform its computations.\n",
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"Moving data through the network is expensive and reducing data movement is one of the key points in a distributed algorithm. To this end, we determine which is the minimum data needed by a worker to perform its computations.\n",
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"\n",
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"In algorithm 1, each worker computes only an entry of the result matrix C."
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]
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@ -312,7 +301,7 @@
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},
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{
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"cell_type": "markdown",
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"id": "28c04679",
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"id": "be3c4a01",
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"metadata": {},
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"source": [
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"<div class=\"alert alert-block alert-success\">\n",
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@ -328,7 +317,7 @@
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "d350220b",
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"id": "a8b7d1e1",
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"metadata": {},
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"outputs": [],
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"source": [
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@ -463,7 +452,7 @@
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},
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{
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"cell_type": "markdown",
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"id": "7192ee22",
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"id": "b8eb224d",
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"metadata": {},
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"source": [
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"### Experimental speedup\n",
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@ -474,7 +463,7 @@
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "8fd20dac",
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"id": "cc698aa8",
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"metadata": {},
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"outputs": [],
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"source": [
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@ -493,7 +482,7 @@
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},
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{
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"cell_type": "markdown",
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"id": "044c4d97",
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"id": "dac6a50b",
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"metadata": {},
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"source": [
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"### Communication overhead\n",
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@ -507,14 +496,14 @@
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"3. The worker sends back the result of C[i,j] to the master process\n",
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"\n",
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"<div class=\"alert alert-block alert-success\">\n",
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"<b>Question:</b> How many scalars are communicated from an to a worker? Assume that matrices A, B, and C are N by N matrices.\n",
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"<b>Question:</b> How many scalars are communicated from and to a worker? Assume that matrices A, B, and C are N by N matrices.\n",
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"</div>\n"
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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": "b05e43f9",
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"id": "e78cbc7b",
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"metadata": {},
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"outputs": [],
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"source": [
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@ -523,7 +512,7 @@
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},
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{
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"cell_type": "markdown",
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"id": "e661d4f9",
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"id": "b27a4d3f",
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"metadata": {},
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"source": [
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"<div class=\"alert alert-block alert-success\">\n",
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@ -534,7 +523,7 @@
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "2f60d9fc",
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"id": "fcc9b903",
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"metadata": {},
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"outputs": [],
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"source": [
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@ -543,7 +532,7 @@
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},
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{
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"cell_type": "markdown",
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"id": "55eb3ff5",
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"id": "d4c301de",
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"metadata": {},
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"source": [
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"From these results we can conclude:\n",
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@ -696,7 +685,7 @@
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},
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{
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"cell_type": "markdown",
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"id": "c13dd6af",
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"id": "8de835b9",
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"metadata": {},
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"source": [
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"Test it using next cell"
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},
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{
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"cell_type": "markdown",
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"id": "e8553faa",
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"id": "f1f30faf",
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"metadata": {},
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"source": [
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"### Experimental speedup"
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "b3c3ffb7",
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"id": "fe42f069",
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"metadata": {},
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"outputs": [],
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"source": [
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@ -781,7 +770,7 @@
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},
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{
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"cell_type": "markdown",
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"id": "1c54b0ae",
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"id": "a2038e04",
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"metadata": {},
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"source": [
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"The communication and computation cost are still of the same order of magnitude even though we have increased the grain size. "
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},
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{
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"cell_type": "markdown",
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"id": "63f5e59f",
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"id": "71088fb9",
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"metadata": {},
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"source": [
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"## Parallel algorithm 3\n",
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}
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},
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"cell_type": "markdown",
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"id": "0c38af09",
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"id": "f1b8c712",
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"metadata": {},
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"source": [
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"<div>\n",
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},
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{
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"cell_type": "markdown",
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"id": "db099c49",
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"id": "4d456fed",
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"metadata": {},
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"source": [
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"### Data dependencies"
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},
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{
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"cell_type": "markdown",
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"id": "b5290fcf",
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"id": "67b65ea6",
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"metadata": {},
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"source": [
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"<div class=\"alert alert-block alert-success\">\n",
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@ -833,7 +822,7 @@
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "ac898985",
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"id": "2825385a",
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"metadata": {},
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"outputs": [],
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"source": [
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},
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{
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"cell_type": "markdown",
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"id": "4f8dbc8c",
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"id": "429faa32",
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"metadata": {},
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"source": [
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"### Implementation\n",
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"\n",
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"These are the main steps of the implementation of algorithm 2:\n",
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"These are the main steps of the implementation of algorithm 3:\n",
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"\n",
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"1. The worker receives the corresponding rows A[rows,:] and matrix B from the master process\n",
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"2. The worker computes the product of A[rows,:] times B\n",
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@ -861,7 +850,7 @@
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}
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},
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"cell_type": "markdown",
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"id": "188ce727",
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"id": "c14ebcb3",
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"metadata": {},
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"source": [
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"<div>\n",
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@ -871,7 +860,7 @@
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},
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{
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"cell_type": "markdown",
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"id": "e5e4eafa",
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"id": "7d7952c1",
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"metadata": {},
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"source": [
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"The implementation of this variant is let as an exercise (see below)."
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},
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{
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"cell_type": "markdown",
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"id": "dce52b5b",
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"id": "0323d6d8",
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"metadata": {},
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"source": [
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"### Communication overhead\n",
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "d6dbbf50",
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"id": "50b8bf53",
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"metadata": {},
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"outputs": [],
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"source": [
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@ -903,7 +892,7 @@
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},
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{
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"cell_type": "markdown",
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"id": "ba449065",
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"id": "3f0d99e6",
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"metadata": {},
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"source": [
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"In this case, the ratio between communication and computation is O(P/N). If the matrix size N is much larger than the number of workers P, then the communication overhead O(P/N) would be negligible. This opens the door to an scalable implementation."
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},
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{
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"cell_type": "markdown",
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"id": "706cb6ea",
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"id": "7bb65f2e",
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"metadata": {},
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"source": [
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"## Summary\n",
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},
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{
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"cell_type": "markdown",
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"id": "8a1048b3",
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"id": "8b83e744",
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"metadata": {},
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"source": [
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"## Exercises"
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},
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{
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"cell_type": "markdown",
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"id": "3e3a0c49",
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"id": "a628a1df",
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"metadata": {},
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"source": [
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"### Implementation of algorithm 3\n",
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "c2941c87",
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"id": "8e50b923",
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"metadata": {},
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"outputs": [],
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"source": [
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},
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{
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"cell_type": "markdown",
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"id": "9810107f",
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"id": "4506dcfb",
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"metadata": {},
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"source": [
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"Use test-driven development to implement the algorithm. Use this test:"
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "d2df240f",
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"id": "28cde36a",
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"metadata": {},
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"outputs": [],
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"source": [
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},
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{
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"cell_type": "markdown",
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"id": "968d8237",
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"id": "03952b0b",
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"metadata": {},
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"source": [
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"Measure the performance of your implementation by running next cell. Do you get close to the optimal speedup?"
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "c0d43911",
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"id": "b3aa2b7c",
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"metadata": {},
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"outputs": [],
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"source": [
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"execution_count": null,
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"id": "023b20d1",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"matmul_dist_1_v2! (generic function with 1 method)"
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]
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},
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"execution_count": 10,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"function matmul_dist_1_v2!(C, A, B)\n",
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" m = size(C,1)\n",
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"execution_count": null,
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"id": "c1d3595b",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
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]
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},
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"using Test\n",
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"N = 50\n",
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},
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{
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"cell_type": "markdown",
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"id": "b49ee366",
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"id": "ab609c18",
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"metadata": {},
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"source": [
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"Run the next cell to check the performance of this implementation. Note that we are far away from the optimal speed up. Why? To answer this question compute the theoretical communication over computation ratio for this implementation and reason about the obtained result. Hint: the number of times a worker is spawned in this implementation is N^3/P on average."
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"id": "9a4c526c",
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"execution_count": null,
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"id": "d7d31710",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Speedup = 0.0012612337176382187\n",
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"Optimal speedup = 4\n",
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"Efficiency = 0.03153084294095547%\n"
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]
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}
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],
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"outputs": [],
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"source": [
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"N = 100\n",
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"A = rand(N,N)\n",
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "4f2d0d9b",
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"id": "cd31d955",
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"metadata": {},
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"outputs": [],
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"source": []
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