|
| 1 | +{ |
| 2 | + "cells": [ |
| 3 | + { |
| 4 | + "cell_type": "markdown", |
| 5 | + "metadata": {}, |
| 6 | + "source": [ |
| 7 | + "# Introducing the multidimensional array in NumPy for fast array computations" |
| 8 | + ] |
| 9 | + }, |
| 10 | + { |
| 11 | + "cell_type": "code", |
| 12 | + "execution_count": 1, |
| 13 | + "metadata": {}, |
| 14 | + "outputs": [], |
| 15 | + "source": [ |
| 16 | + "import random\n", |
| 17 | + "import numpy as np" |
| 18 | + ] |
| 19 | + }, |
| 20 | + { |
| 21 | + "cell_type": "code", |
| 22 | + "execution_count": 2, |
| 23 | + "metadata": {}, |
| 24 | + "outputs": [], |
| 25 | + "source": [ |
| 26 | + "n = 1000000\n", |
| 27 | + "x = [random.random() for _ in range(n)]\n", |
| 28 | + "y = [random.random() for _ in range(n)]" |
| 29 | + ] |
| 30 | + }, |
| 31 | + { |
| 32 | + "cell_type": "code", |
| 33 | + "execution_count": 3, |
| 34 | + "metadata": {}, |
| 35 | + "outputs": [ |
| 36 | + { |
| 37 | + "data": { |
| 38 | + "text/plain": [ |
| 39 | + "([0.926, 0.722, 0.962], [0.291, 0.339, 0.819])" |
| 40 | + ] |
| 41 | + }, |
| 42 | + "execution_count": 3, |
| 43 | + "metadata": {}, |
| 44 | + "output_type": "execute_result" |
| 45 | + } |
| 46 | + ], |
| 47 | + "source": [ |
| 48 | + "x[:3], y[:3]" |
| 49 | + ] |
| 50 | + }, |
| 51 | + { |
| 52 | + "cell_type": "code", |
| 53 | + "execution_count": 4, |
| 54 | + "metadata": {}, |
| 55 | + "outputs": [ |
| 56 | + { |
| 57 | + "data": { |
| 58 | + "text/plain": [ |
| 59 | + "[1.217, 1.061, 1.781]" |
| 60 | + ] |
| 61 | + }, |
| 62 | + "execution_count": 4, |
| 63 | + "metadata": {}, |
| 64 | + "output_type": "execute_result" |
| 65 | + } |
| 66 | + ], |
| 67 | + "source": [ |
| 68 | + "z = [x[i] + y[i] for i in range(n)]\n", |
| 69 | + "z[:3]" |
| 70 | + ] |
| 71 | + }, |
| 72 | + { |
| 73 | + "cell_type": "code", |
| 74 | + "execution_count": 5, |
| 75 | + "metadata": {}, |
| 76 | + "outputs": [ |
| 77 | + { |
| 78 | + "name": "stdout", |
| 79 | + "output_type": "stream", |
| 80 | + "text": [ |
| 81 | + "101 ms ± 5.12 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" |
| 82 | + ] |
| 83 | + } |
| 84 | + ], |
| 85 | + "source": [ |
| 86 | + "%timeit [x[i] + y[i] for i in range(n)]" |
| 87 | + ] |
| 88 | + }, |
| 89 | + { |
| 90 | + "cell_type": "code", |
| 91 | + "execution_count": 6, |
| 92 | + "metadata": {}, |
| 93 | + "outputs": [], |
| 94 | + "source": [ |
| 95 | + "xa = np.array(x)\n", |
| 96 | + "ya = np.array(y)" |
| 97 | + ] |
| 98 | + }, |
| 99 | + { |
| 100 | + "cell_type": "code", |
| 101 | + "execution_count": 7, |
| 102 | + "metadata": {}, |
| 103 | + "outputs": [ |
| 104 | + { |
| 105 | + "data": { |
| 106 | + "text/plain": [ |
| 107 | + "array([ 0.926, 0.722, 0.962])" |
| 108 | + ] |
| 109 | + }, |
| 110 | + "execution_count": 7, |
| 111 | + "metadata": {}, |
| 112 | + "output_type": "execute_result" |
| 113 | + } |
| 114 | + ], |
| 115 | + "source": [ |
| 116 | + "xa[:3]" |
| 117 | + ] |
| 118 | + }, |
| 119 | + { |
| 120 | + "cell_type": "code", |
| 121 | + "execution_count": 8, |
| 122 | + "metadata": {}, |
| 123 | + "outputs": [ |
| 124 | + { |
| 125 | + "data": { |
| 126 | + "text/plain": [ |
| 127 | + "array([ 1.217, 1.061, 1.781])" |
| 128 | + ] |
| 129 | + }, |
| 130 | + "execution_count": 8, |
| 131 | + "metadata": {}, |
| 132 | + "output_type": "execute_result" |
| 133 | + } |
| 134 | + ], |
| 135 | + "source": [ |
| 136 | + "za = xa + ya\n", |
| 137 | + "za[:3]" |
| 138 | + ] |
| 139 | + }, |
| 140 | + { |
| 141 | + "cell_type": "code", |
| 142 | + "execution_count": 9, |
| 143 | + "metadata": {}, |
| 144 | + "outputs": [ |
| 145 | + { |
| 146 | + "name": "stdout", |
| 147 | + "output_type": "stream", |
| 148 | + "text": [ |
| 149 | + "1.09 ms ± 37.3 μs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" |
| 150 | + ] |
| 151 | + } |
| 152 | + ], |
| 153 | + "source": [ |
| 154 | + "%timeit xa + ya" |
| 155 | + ] |
| 156 | + }, |
| 157 | + { |
| 158 | + "cell_type": "code", |
| 159 | + "execution_count": 10, |
| 160 | + "metadata": {}, |
| 161 | + "outputs": [ |
| 162 | + { |
| 163 | + "name": "stdout", |
| 164 | + "output_type": "stream", |
| 165 | + "text": [ |
| 166 | + "3.94 ms ± 4.44 μs per loop (mean ± std. dev. of 7 runs\n", |
| 167 | + " 100 loops each)\n" |
| 168 | + ] |
| 169 | + } |
| 170 | + ], |
| 171 | + "source": [ |
| 172 | + "%timeit sum(x) # pure Python" |
| 173 | + ] |
| 174 | + }, |
| 175 | + { |
| 176 | + "cell_type": "code", |
| 177 | + "execution_count": 11, |
| 178 | + "metadata": {}, |
| 179 | + "outputs": [ |
| 180 | + { |
| 181 | + "name": "stdout", |
| 182 | + "output_type": "stream", |
| 183 | + "text": [ |
| 184 | + "298 μs ± 4.62 μs per loop (mean ± std. dev. of 7 runs,\n", |
| 185 | + " 1000 loops each)\n" |
| 186 | + ] |
| 187 | + } |
| 188 | + ], |
| 189 | + "source": [ |
| 190 | + "%timeit np.sum(xa) # NumPy" |
| 191 | + ] |
| 192 | + }, |
| 193 | + { |
| 194 | + "cell_type": "code", |
| 195 | + "execution_count": 12, |
| 196 | + "metadata": {}, |
| 197 | + "outputs": [], |
| 198 | + "source": [ |
| 199 | + "d = [abs(x[i] - y[j])\n", |
| 200 | + " for i in range(1000)\n", |
| 201 | + " for j in range(1000)]" |
| 202 | + ] |
| 203 | + }, |
| 204 | + { |
| 205 | + "cell_type": "code", |
| 206 | + "execution_count": 13, |
| 207 | + "metadata": {}, |
| 208 | + "outputs": [ |
| 209 | + { |
| 210 | + "data": { |
| 211 | + "text/plain": [ |
| 212 | + "[0.635, 0.587, 0.106]" |
| 213 | + ] |
| 214 | + }, |
| 215 | + "execution_count": 13, |
| 216 | + "metadata": {}, |
| 217 | + "output_type": "execute_result" |
| 218 | + } |
| 219 | + ], |
| 220 | + "source": [ |
| 221 | + "d[:3]" |
| 222 | + ] |
| 223 | + }, |
| 224 | + { |
| 225 | + "cell_type": "code", |
| 226 | + "execution_count": 14, |
| 227 | + "metadata": {}, |
| 228 | + "outputs": [], |
| 229 | + "source": [ |
| 230 | + "da = np.abs(xa[:1000, np.newaxis] - ya[:1000])" |
| 231 | + ] |
| 232 | + }, |
| 233 | + { |
| 234 | + "cell_type": "code", |
| 235 | + "execution_count": 15, |
| 236 | + "metadata": {}, |
| 237 | + "outputs": [ |
| 238 | + { |
| 239 | + "data": { |
| 240 | + "text/plain": [ |
| 241 | + "array([[ 0.635, 0.587, ..., 0.849, 0.046],\n", |
| 242 | + " [ 0.431, 0.383, ..., 0.646, 0.158],\n", |
| 243 | + " ...,\n", |
| 244 | + " [ 0.024, 0.024, ..., 0.238, 0.566],\n", |
| 245 | + " [ 0.081, 0.033, ..., 0.295, 0.509]])" |
| 246 | + ] |
| 247 | + }, |
| 248 | + "execution_count": 15, |
| 249 | + "metadata": {}, |
| 250 | + "output_type": "execute_result" |
| 251 | + } |
| 252 | + ], |
| 253 | + "source": [ |
| 254 | + "da" |
| 255 | + ] |
| 256 | + }, |
| 257 | + { |
| 258 | + "cell_type": "code", |
| 259 | + "execution_count": 16, |
| 260 | + "metadata": {}, |
| 261 | + "outputs": [ |
| 262 | + { |
| 263 | + "name": "stdout", |
| 264 | + "output_type": "stream", |
| 265 | + "text": [ |
| 266 | + "134 ms ± 1.79 ms per loop (mean ± std. dev. of 7 runs,\n", |
| 267 | + " 10 loops each)\n", |
| 268 | + " 1000 loops each)\n" |
| 269 | + ] |
| 270 | + } |
| 271 | + ], |
| 272 | + "source": [ |
| 273 | + "%timeit [abs(x[i] - y[j]) \\\n", |
| 274 | + " for i in range(1000) \\\n", |
| 275 | + " for j in range(1000)]" |
| 276 | + ] |
| 277 | + }, |
| 278 | + { |
| 279 | + "cell_type": "code", |
| 280 | + "execution_count": 17, |
| 281 | + "metadata": {}, |
| 282 | + "outputs": [ |
| 283 | + { |
| 284 | + "name": "stdout", |
| 285 | + "output_type": "stream", |
| 286 | + "text": [ |
| 287 | + " 10 loops each)\n", |
| 288 | + "1.54 ms ± 48.9 μs per loop (mean ± std. dev. of 7 runs\n", |
| 289 | + " 1000 loops each)\n" |
| 290 | + ] |
| 291 | + } |
| 292 | + ], |
| 293 | + "source": [ |
| 294 | + "%timeit np.abs(xa[:1000, np.newaxis] - ya[:1000])" |
| 295 | + ] |
| 296 | + } |
| 297 | + ], |
| 298 | + "metadata": {}, |
| 299 | + "nbformat": 4, |
| 300 | + "nbformat_minor": 2 |
| 301 | +} |
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