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Browse files- NumPy_Library_Basics.ipynb +1116 -0
- README.md +29 -0
- numpy.png +0 -0
NumPy_Library_Basics.ipynb
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|
| 1 |
+
{
|
| 2 |
+
"cells": [
|
| 3 |
+
{
|
| 4 |
+
"cell_type": "markdown",
|
| 5 |
+
"metadata": {},
|
| 6 |
+
"source": [
|
| 7 |
+
"### Load in NumPy (remember to pip install numpy first)"
|
| 8 |
+
]
|
| 9 |
+
},
|
| 10 |
+
{
|
| 11 |
+
"cell_type": "code",
|
| 12 |
+
"execution_count": 1,
|
| 13 |
+
"metadata": {},
|
| 14 |
+
"outputs": [],
|
| 15 |
+
"source": [
|
| 16 |
+
"import numpy as np"
|
| 17 |
+
]
|
| 18 |
+
},
|
| 19 |
+
{
|
| 20 |
+
"cell_type": "markdown",
|
| 21 |
+
"metadata": {},
|
| 22 |
+
"source": [
|
| 23 |
+
"### The Basics"
|
| 24 |
+
]
|
| 25 |
+
},
|
| 26 |
+
{
|
| 27 |
+
"cell_type": "code",
|
| 28 |
+
"execution_count": 2,
|
| 29 |
+
"metadata": {},
|
| 30 |
+
"outputs": [
|
| 31 |
+
{
|
| 32 |
+
"name": "stdout",
|
| 33 |
+
"output_type": "stream",
|
| 34 |
+
"text": [
|
| 35 |
+
"[1 2 3]\n"
|
| 36 |
+
]
|
| 37 |
+
}
|
| 38 |
+
],
|
| 39 |
+
"source": [
|
| 40 |
+
"a = np.array([1,2,3], dtype='int32')\n",
|
| 41 |
+
"print(a)"
|
| 42 |
+
]
|
| 43 |
+
},
|
| 44 |
+
{
|
| 45 |
+
"cell_type": "code",
|
| 46 |
+
"execution_count": 3,
|
| 47 |
+
"metadata": {},
|
| 48 |
+
"outputs": [
|
| 49 |
+
{
|
| 50 |
+
"name": "stdout",
|
| 51 |
+
"output_type": "stream",
|
| 52 |
+
"text": [
|
| 53 |
+
"[[9. 8. 7.]\n",
|
| 54 |
+
" [6. 5. 4.]]\n"
|
| 55 |
+
]
|
| 56 |
+
}
|
| 57 |
+
],
|
| 58 |
+
"source": [
|
| 59 |
+
"b = np.array([[9.0,8.0,7.0],[6.0,5.0,4.0]])\n",
|
| 60 |
+
"print(b)"
|
| 61 |
+
]
|
| 62 |
+
},
|
| 63 |
+
{
|
| 64 |
+
"cell_type": "code",
|
| 65 |
+
"execution_count": 4,
|
| 66 |
+
"metadata": {},
|
| 67 |
+
"outputs": [
|
| 68 |
+
{
|
| 69 |
+
"data": {
|
| 70 |
+
"text/plain": [
|
| 71 |
+
"1"
|
| 72 |
+
]
|
| 73 |
+
},
|
| 74 |
+
"execution_count": 4,
|
| 75 |
+
"metadata": {},
|
| 76 |
+
"output_type": "execute_result"
|
| 77 |
+
}
|
| 78 |
+
],
|
| 79 |
+
"source": [
|
| 80 |
+
"# Get Dimension\n",
|
| 81 |
+
"a.ndim"
|
| 82 |
+
]
|
| 83 |
+
},
|
| 84 |
+
{
|
| 85 |
+
"cell_type": "code",
|
| 86 |
+
"execution_count": 5,
|
| 87 |
+
"metadata": {},
|
| 88 |
+
"outputs": [
|
| 89 |
+
{
|
| 90 |
+
"data": {
|
| 91 |
+
"text/plain": [
|
| 92 |
+
"(2, 3)"
|
| 93 |
+
]
|
| 94 |
+
},
|
| 95 |
+
"execution_count": 5,
|
| 96 |
+
"metadata": {},
|
| 97 |
+
"output_type": "execute_result"
|
| 98 |
+
}
|
| 99 |
+
],
|
| 100 |
+
"source": [
|
| 101 |
+
"# Get Shape\n",
|
| 102 |
+
"b.shape"
|
| 103 |
+
]
|
| 104 |
+
},
|
| 105 |
+
{
|
| 106 |
+
"cell_type": "code",
|
| 107 |
+
"execution_count": 6,
|
| 108 |
+
"metadata": {},
|
| 109 |
+
"outputs": [
|
| 110 |
+
{
|
| 111 |
+
"data": {
|
| 112 |
+
"text/plain": [
|
| 113 |
+
"dtype('int32')"
|
| 114 |
+
]
|
| 115 |
+
},
|
| 116 |
+
"execution_count": 6,
|
| 117 |
+
"metadata": {},
|
| 118 |
+
"output_type": "execute_result"
|
| 119 |
+
}
|
| 120 |
+
],
|
| 121 |
+
"source": [
|
| 122 |
+
"# Get Type\n",
|
| 123 |
+
"a.dtype"
|
| 124 |
+
]
|
| 125 |
+
},
|
| 126 |
+
{
|
| 127 |
+
"cell_type": "code",
|
| 128 |
+
"execution_count": 7,
|
| 129 |
+
"metadata": {},
|
| 130 |
+
"outputs": [
|
| 131 |
+
{
|
| 132 |
+
"data": {
|
| 133 |
+
"text/plain": [
|
| 134 |
+
"4"
|
| 135 |
+
]
|
| 136 |
+
},
|
| 137 |
+
"execution_count": 7,
|
| 138 |
+
"metadata": {},
|
| 139 |
+
"output_type": "execute_result"
|
| 140 |
+
}
|
| 141 |
+
],
|
| 142 |
+
"source": [
|
| 143 |
+
"# Get Size\n",
|
| 144 |
+
"a.itemsize"
|
| 145 |
+
]
|
| 146 |
+
},
|
| 147 |
+
{
|
| 148 |
+
"cell_type": "code",
|
| 149 |
+
"execution_count": 8,
|
| 150 |
+
"metadata": {},
|
| 151 |
+
"outputs": [
|
| 152 |
+
{
|
| 153 |
+
"data": {
|
| 154 |
+
"text/plain": [
|
| 155 |
+
"12"
|
| 156 |
+
]
|
| 157 |
+
},
|
| 158 |
+
"execution_count": 8,
|
| 159 |
+
"metadata": {},
|
| 160 |
+
"output_type": "execute_result"
|
| 161 |
+
}
|
| 162 |
+
],
|
| 163 |
+
"source": [
|
| 164 |
+
"# Get total size\n",
|
| 165 |
+
"a.nbytes"
|
| 166 |
+
]
|
| 167 |
+
},
|
| 168 |
+
{
|
| 169 |
+
"cell_type": "code",
|
| 170 |
+
"execution_count": 9,
|
| 171 |
+
"metadata": {},
|
| 172 |
+
"outputs": [
|
| 173 |
+
{
|
| 174 |
+
"data": {
|
| 175 |
+
"text/plain": [
|
| 176 |
+
"3"
|
| 177 |
+
]
|
| 178 |
+
},
|
| 179 |
+
"execution_count": 9,
|
| 180 |
+
"metadata": {},
|
| 181 |
+
"output_type": "execute_result"
|
| 182 |
+
}
|
| 183 |
+
],
|
| 184 |
+
"source": [
|
| 185 |
+
"# Get number of elements\n",
|
| 186 |
+
"a.size"
|
| 187 |
+
]
|
| 188 |
+
},
|
| 189 |
+
{
|
| 190 |
+
"cell_type": "markdown",
|
| 191 |
+
"metadata": {},
|
| 192 |
+
"source": [
|
| 193 |
+
"### Accessing/Changing specific elements, rows, columns, etc"
|
| 194 |
+
]
|
| 195 |
+
},
|
| 196 |
+
{
|
| 197 |
+
"cell_type": "code",
|
| 198 |
+
"execution_count": 10,
|
| 199 |
+
"metadata": {},
|
| 200 |
+
"outputs": [
|
| 201 |
+
{
|
| 202 |
+
"name": "stdout",
|
| 203 |
+
"output_type": "stream",
|
| 204 |
+
"text": [
|
| 205 |
+
"[[ 1 2 3 4 5 6 7]\n",
|
| 206 |
+
" [ 8 9 10 11 12 13 14]]\n"
|
| 207 |
+
]
|
| 208 |
+
}
|
| 209 |
+
],
|
| 210 |
+
"source": [
|
| 211 |
+
"a = np.array([[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]])\n",
|
| 212 |
+
"print(a)"
|
| 213 |
+
]
|
| 214 |
+
},
|
| 215 |
+
{
|
| 216 |
+
"cell_type": "code",
|
| 217 |
+
"execution_count": 11,
|
| 218 |
+
"metadata": {},
|
| 219 |
+
"outputs": [
|
| 220 |
+
{
|
| 221 |
+
"data": {
|
| 222 |
+
"text/plain": [
|
| 223 |
+
"13"
|
| 224 |
+
]
|
| 225 |
+
},
|
| 226 |
+
"execution_count": 11,
|
| 227 |
+
"metadata": {},
|
| 228 |
+
"output_type": "execute_result"
|
| 229 |
+
}
|
| 230 |
+
],
|
| 231 |
+
"source": [
|
| 232 |
+
"# Get a specific element [r, c]\n",
|
| 233 |
+
"a[1, 5]"
|
| 234 |
+
]
|
| 235 |
+
},
|
| 236 |
+
{
|
| 237 |
+
"cell_type": "code",
|
| 238 |
+
"execution_count": 12,
|
| 239 |
+
"metadata": {},
|
| 240 |
+
"outputs": [
|
| 241 |
+
{
|
| 242 |
+
"data": {
|
| 243 |
+
"text/plain": [
|
| 244 |
+
"array([1, 2, 3, 4, 5, 6, 7])"
|
| 245 |
+
]
|
| 246 |
+
},
|
| 247 |
+
"execution_count": 12,
|
| 248 |
+
"metadata": {},
|
| 249 |
+
"output_type": "execute_result"
|
| 250 |
+
}
|
| 251 |
+
],
|
| 252 |
+
"source": [
|
| 253 |
+
"# Get a specific row \n",
|
| 254 |
+
"a[0, :]"
|
| 255 |
+
]
|
| 256 |
+
},
|
| 257 |
+
{
|
| 258 |
+
"cell_type": "code",
|
| 259 |
+
"execution_count": 13,
|
| 260 |
+
"metadata": {},
|
| 261 |
+
"outputs": [
|
| 262 |
+
{
|
| 263 |
+
"data": {
|
| 264 |
+
"text/plain": [
|
| 265 |
+
"array([ 3, 10])"
|
| 266 |
+
]
|
| 267 |
+
},
|
| 268 |
+
"execution_count": 13,
|
| 269 |
+
"metadata": {},
|
| 270 |
+
"output_type": "execute_result"
|
| 271 |
+
}
|
| 272 |
+
],
|
| 273 |
+
"source": [
|
| 274 |
+
"# Get a specific column\n",
|
| 275 |
+
"a[:, 2]"
|
| 276 |
+
]
|
| 277 |
+
},
|
| 278 |
+
{
|
| 279 |
+
"cell_type": "code",
|
| 280 |
+
"execution_count": 14,
|
| 281 |
+
"metadata": {},
|
| 282 |
+
"outputs": [
|
| 283 |
+
{
|
| 284 |
+
"data": {
|
| 285 |
+
"text/plain": [
|
| 286 |
+
"array([2, 4, 6])"
|
| 287 |
+
]
|
| 288 |
+
},
|
| 289 |
+
"execution_count": 14,
|
| 290 |
+
"metadata": {},
|
| 291 |
+
"output_type": "execute_result"
|
| 292 |
+
}
|
| 293 |
+
],
|
| 294 |
+
"source": [
|
| 295 |
+
"# Getting a little more fancy [startindex:endindex:stepsize]\n",
|
| 296 |
+
"a[0, 1:-1:2]"
|
| 297 |
+
]
|
| 298 |
+
},
|
| 299 |
+
{
|
| 300 |
+
"cell_type": "code",
|
| 301 |
+
"execution_count": 15,
|
| 302 |
+
"metadata": {},
|
| 303 |
+
"outputs": [
|
| 304 |
+
{
|
| 305 |
+
"name": "stdout",
|
| 306 |
+
"output_type": "stream",
|
| 307 |
+
"text": [
|
| 308 |
+
"[[ 1 2 1 4 5 6 7]\n",
|
| 309 |
+
" [ 8 9 2 11 12 20 14]]\n"
|
| 310 |
+
]
|
| 311 |
+
}
|
| 312 |
+
],
|
| 313 |
+
"source": [
|
| 314 |
+
"a[1,5] = 20\n",
|
| 315 |
+
"\n",
|
| 316 |
+
"a[:,2] = [1,2]\n",
|
| 317 |
+
"print(a)"
|
| 318 |
+
]
|
| 319 |
+
},
|
| 320 |
+
{
|
| 321 |
+
"cell_type": "markdown",
|
| 322 |
+
"metadata": {},
|
| 323 |
+
"source": [
|
| 324 |
+
"*3-d example"
|
| 325 |
+
]
|
| 326 |
+
},
|
| 327 |
+
{
|
| 328 |
+
"cell_type": "code",
|
| 329 |
+
"execution_count": 16,
|
| 330 |
+
"metadata": {},
|
| 331 |
+
"outputs": [
|
| 332 |
+
{
|
| 333 |
+
"name": "stdout",
|
| 334 |
+
"output_type": "stream",
|
| 335 |
+
"text": [
|
| 336 |
+
"[[[1 2]\n",
|
| 337 |
+
" [3 4]]\n",
|
| 338 |
+
"\n",
|
| 339 |
+
" [[5 6]\n",
|
| 340 |
+
" [7 8]]]\n"
|
| 341 |
+
]
|
| 342 |
+
}
|
| 343 |
+
],
|
| 344 |
+
"source": [
|
| 345 |
+
"b = np.array([[[1,2],[3,4]],[[5,6],[7,8]]])\n",
|
| 346 |
+
"print(b)"
|
| 347 |
+
]
|
| 348 |
+
},
|
| 349 |
+
{
|
| 350 |
+
"cell_type": "code",
|
| 351 |
+
"execution_count": 17,
|
| 352 |
+
"metadata": {},
|
| 353 |
+
"outputs": [
|
| 354 |
+
{
|
| 355 |
+
"data": {
|
| 356 |
+
"text/plain": [
|
| 357 |
+
"4"
|
| 358 |
+
]
|
| 359 |
+
},
|
| 360 |
+
"execution_count": 17,
|
| 361 |
+
"metadata": {},
|
| 362 |
+
"output_type": "execute_result"
|
| 363 |
+
}
|
| 364 |
+
],
|
| 365 |
+
"source": [
|
| 366 |
+
"# Get specific element (work outside in)\n",
|
| 367 |
+
"b[0,1,1]"
|
| 368 |
+
]
|
| 369 |
+
},
|
| 370 |
+
{
|
| 371 |
+
"cell_type": "code",
|
| 372 |
+
"execution_count": 19,
|
| 373 |
+
"metadata": {},
|
| 374 |
+
"outputs": [],
|
| 375 |
+
"source": [
|
| 376 |
+
"# replace \n",
|
| 377 |
+
"b[:,1,:] = [[9,9],[8,8]]"
|
| 378 |
+
]
|
| 379 |
+
},
|
| 380 |
+
{
|
| 381 |
+
"cell_type": "code",
|
| 382 |
+
"execution_count": 20,
|
| 383 |
+
"metadata": {},
|
| 384 |
+
"outputs": [
|
| 385 |
+
{
|
| 386 |
+
"data": {
|
| 387 |
+
"text/plain": [
|
| 388 |
+
"array([[[1, 2],\n",
|
| 389 |
+
" [9, 9]],\n",
|
| 390 |
+
"\n",
|
| 391 |
+
" [[5, 6],\n",
|
| 392 |
+
" [8, 8]]])"
|
| 393 |
+
]
|
| 394 |
+
},
|
| 395 |
+
"execution_count": 20,
|
| 396 |
+
"metadata": {},
|
| 397 |
+
"output_type": "execute_result"
|
| 398 |
+
}
|
| 399 |
+
],
|
| 400 |
+
"source": [
|
| 401 |
+
"b"
|
| 402 |
+
]
|
| 403 |
+
},
|
| 404 |
+
{
|
| 405 |
+
"cell_type": "markdown",
|
| 406 |
+
"metadata": {},
|
| 407 |
+
"source": [
|
| 408 |
+
"### Initializing Different Types of Arrays"
|
| 409 |
+
]
|
| 410 |
+
},
|
| 411 |
+
{
|
| 412 |
+
"cell_type": "code",
|
| 413 |
+
"execution_count": 21,
|
| 414 |
+
"metadata": {},
|
| 415 |
+
"outputs": [
|
| 416 |
+
{
|
| 417 |
+
"data": {
|
| 418 |
+
"text/plain": [
|
| 419 |
+
"array([[0., 0., 0.],\n",
|
| 420 |
+
" [0., 0., 0.]])"
|
| 421 |
+
]
|
| 422 |
+
},
|
| 423 |
+
"execution_count": 21,
|
| 424 |
+
"metadata": {},
|
| 425 |
+
"output_type": "execute_result"
|
| 426 |
+
}
|
| 427 |
+
],
|
| 428 |
+
"source": [
|
| 429 |
+
"# All 0s matrix\n",
|
| 430 |
+
"np.zeros((2,3))"
|
| 431 |
+
]
|
| 432 |
+
},
|
| 433 |
+
{
|
| 434 |
+
"cell_type": "code",
|
| 435 |
+
"execution_count": 22,
|
| 436 |
+
"metadata": {},
|
| 437 |
+
"outputs": [
|
| 438 |
+
{
|
| 439 |
+
"data": {
|
| 440 |
+
"text/plain": [
|
| 441 |
+
"array([[[1, 1],\n",
|
| 442 |
+
" [1, 1]],\n",
|
| 443 |
+
"\n",
|
| 444 |
+
" [[1, 1],\n",
|
| 445 |
+
" [1, 1]],\n",
|
| 446 |
+
"\n",
|
| 447 |
+
" [[1, 1],\n",
|
| 448 |
+
" [1, 1]],\n",
|
| 449 |
+
"\n",
|
| 450 |
+
" [[1, 1],\n",
|
| 451 |
+
" [1, 1]]])"
|
| 452 |
+
]
|
| 453 |
+
},
|
| 454 |
+
"execution_count": 22,
|
| 455 |
+
"metadata": {},
|
| 456 |
+
"output_type": "execute_result"
|
| 457 |
+
}
|
| 458 |
+
],
|
| 459 |
+
"source": [
|
| 460 |
+
"# All 1s matrix\n",
|
| 461 |
+
"np.ones((4,2,2), dtype='int32')"
|
| 462 |
+
]
|
| 463 |
+
},
|
| 464 |
+
{
|
| 465 |
+
"cell_type": "code",
|
| 466 |
+
"execution_count": 23,
|
| 467 |
+
"metadata": {},
|
| 468 |
+
"outputs": [
|
| 469 |
+
{
|
| 470 |
+
"data": {
|
| 471 |
+
"text/plain": [
|
| 472 |
+
"array([[99, 99],\n",
|
| 473 |
+
" [99, 99]])"
|
| 474 |
+
]
|
| 475 |
+
},
|
| 476 |
+
"execution_count": 23,
|
| 477 |
+
"metadata": {},
|
| 478 |
+
"output_type": "execute_result"
|
| 479 |
+
}
|
| 480 |
+
],
|
| 481 |
+
"source": [
|
| 482 |
+
"# Any other number\n",
|
| 483 |
+
"np.full((2,2), 99)"
|
| 484 |
+
]
|
| 485 |
+
},
|
| 486 |
+
{
|
| 487 |
+
"cell_type": "code",
|
| 488 |
+
"execution_count": 24,
|
| 489 |
+
"metadata": {},
|
| 490 |
+
"outputs": [
|
| 491 |
+
{
|
| 492 |
+
"data": {
|
| 493 |
+
"text/plain": [
|
| 494 |
+
"array([[4, 4, 4, 4, 4, 4, 4],\n",
|
| 495 |
+
" [4, 4, 4, 4, 4, 4, 4]])"
|
| 496 |
+
]
|
| 497 |
+
},
|
| 498 |
+
"execution_count": 24,
|
| 499 |
+
"metadata": {},
|
| 500 |
+
"output_type": "execute_result"
|
| 501 |
+
}
|
| 502 |
+
],
|
| 503 |
+
"source": [
|
| 504 |
+
"# Any other number (full_like)\n",
|
| 505 |
+
"np.full_like(a, 4)"
|
| 506 |
+
]
|
| 507 |
+
},
|
| 508 |
+
{
|
| 509 |
+
"cell_type": "code",
|
| 510 |
+
"execution_count": 25,
|
| 511 |
+
"metadata": {},
|
| 512 |
+
"outputs": [
|
| 513 |
+
{
|
| 514 |
+
"data": {
|
| 515 |
+
"text/plain": [
|
| 516 |
+
"array([[0.24480678, 0.71347348],\n",
|
| 517 |
+
" [0.56163517, 0.80732991],\n",
|
| 518 |
+
" [0.72750015, 0.65200353],\n",
|
| 519 |
+
" [0.13660036, 0.92045687]])"
|
| 520 |
+
]
|
| 521 |
+
},
|
| 522 |
+
"execution_count": 25,
|
| 523 |
+
"metadata": {},
|
| 524 |
+
"output_type": "execute_result"
|
| 525 |
+
}
|
| 526 |
+
],
|
| 527 |
+
"source": [
|
| 528 |
+
"# Random decimal numbers\n",
|
| 529 |
+
"np.random.rand(4,2)"
|
| 530 |
+
]
|
| 531 |
+
},
|
| 532 |
+
{
|
| 533 |
+
"cell_type": "code",
|
| 534 |
+
"execution_count": 26,
|
| 535 |
+
"metadata": {},
|
| 536 |
+
"outputs": [
|
| 537 |
+
{
|
| 538 |
+
"data": {
|
| 539 |
+
"text/plain": [
|
| 540 |
+
"array([[-4, 2, 6],\n",
|
| 541 |
+
" [ 6, -4, -3],\n",
|
| 542 |
+
" [ 3, 2, 4]])"
|
| 543 |
+
]
|
| 544 |
+
},
|
| 545 |
+
"execution_count": 26,
|
| 546 |
+
"metadata": {},
|
| 547 |
+
"output_type": "execute_result"
|
| 548 |
+
}
|
| 549 |
+
],
|
| 550 |
+
"source": [
|
| 551 |
+
"# Random Integer values\n",
|
| 552 |
+
"np.random.randint(-4,8, size=(3,3))"
|
| 553 |
+
]
|
| 554 |
+
},
|
| 555 |
+
{
|
| 556 |
+
"cell_type": "code",
|
| 557 |
+
"execution_count": 27,
|
| 558 |
+
"metadata": {},
|
| 559 |
+
"outputs": [
|
| 560 |
+
{
|
| 561 |
+
"data": {
|
| 562 |
+
"text/plain": [
|
| 563 |
+
"array([[1., 0., 0., 0., 0.],\n",
|
| 564 |
+
" [0., 1., 0., 0., 0.],\n",
|
| 565 |
+
" [0., 0., 1., 0., 0.],\n",
|
| 566 |
+
" [0., 0., 0., 1., 0.],\n",
|
| 567 |
+
" [0., 0., 0., 0., 1.]])"
|
| 568 |
+
]
|
| 569 |
+
},
|
| 570 |
+
"execution_count": 27,
|
| 571 |
+
"metadata": {},
|
| 572 |
+
"output_type": "execute_result"
|
| 573 |
+
}
|
| 574 |
+
],
|
| 575 |
+
"source": [
|
| 576 |
+
"# The identity matrix\n",
|
| 577 |
+
"np.identity(5)"
|
| 578 |
+
]
|
| 579 |
+
},
|
| 580 |
+
{
|
| 581 |
+
"cell_type": "code",
|
| 582 |
+
"execution_count": 28,
|
| 583 |
+
"metadata": {},
|
| 584 |
+
"outputs": [
|
| 585 |
+
{
|
| 586 |
+
"name": "stdout",
|
| 587 |
+
"output_type": "stream",
|
| 588 |
+
"text": [
|
| 589 |
+
"[[1 2 3]\n",
|
| 590 |
+
" [1 2 3]\n",
|
| 591 |
+
" [1 2 3]]\n"
|
| 592 |
+
]
|
| 593 |
+
}
|
| 594 |
+
],
|
| 595 |
+
"source": [
|
| 596 |
+
"# Repeat an array\n",
|
| 597 |
+
"arr = np.array([[1,2,3]])\n",
|
| 598 |
+
"r1 = np.repeat(arr,3, axis=0)\n",
|
| 599 |
+
"print(r1)"
|
| 600 |
+
]
|
| 601 |
+
},
|
| 602 |
+
{
|
| 603 |
+
"cell_type": "code",
|
| 604 |
+
"execution_count": 29,
|
| 605 |
+
"metadata": {},
|
| 606 |
+
"outputs": [
|
| 607 |
+
{
|
| 608 |
+
"name": "stdout",
|
| 609 |
+
"output_type": "stream",
|
| 610 |
+
"text": [
|
| 611 |
+
"[[1. 1. 1. 1. 1.]\n",
|
| 612 |
+
" [1. 1. 1. 1. 1.]\n",
|
| 613 |
+
" [1. 1. 1. 1. 1.]\n",
|
| 614 |
+
" [1. 1. 1. 1. 1.]\n",
|
| 615 |
+
" [1. 1. 1. 1. 1.]]\n",
|
| 616 |
+
"[[0. 0. 0.]\n",
|
| 617 |
+
" [0. 9. 0.]\n",
|
| 618 |
+
" [0. 0. 0.]]\n",
|
| 619 |
+
"[[1. 1. 1. 1. 1.]\n",
|
| 620 |
+
" [1. 0. 0. 0. 1.]\n",
|
| 621 |
+
" [1. 0. 9. 0. 1.]\n",
|
| 622 |
+
" [1. 0. 0. 0. 1.]\n",
|
| 623 |
+
" [1. 1. 1. 1. 1.]]\n"
|
| 624 |
+
]
|
| 625 |
+
}
|
| 626 |
+
],
|
| 627 |
+
"source": [
|
| 628 |
+
"output = np.ones((5,5))\n",
|
| 629 |
+
"print(output)\n",
|
| 630 |
+
"\n",
|
| 631 |
+
"z = np.zeros((3,3))\n",
|
| 632 |
+
"z[1,1] = 9\n",
|
| 633 |
+
"print(z)\n",
|
| 634 |
+
"\n",
|
| 635 |
+
"output[1:-1,1:-1] = z\n",
|
| 636 |
+
"print(output)"
|
| 637 |
+
]
|
| 638 |
+
},
|
| 639 |
+
{
|
| 640 |
+
"cell_type": "markdown",
|
| 641 |
+
"metadata": {},
|
| 642 |
+
"source": [
|
| 643 |
+
"##### Be careful when copying arrays!!!"
|
| 644 |
+
]
|
| 645 |
+
},
|
| 646 |
+
{
|
| 647 |
+
"cell_type": "code",
|
| 648 |
+
"execution_count": 30,
|
| 649 |
+
"metadata": {},
|
| 650 |
+
"outputs": [
|
| 651 |
+
{
|
| 652 |
+
"name": "stdout",
|
| 653 |
+
"output_type": "stream",
|
| 654 |
+
"text": [
|
| 655 |
+
"[1 2 3]\n"
|
| 656 |
+
]
|
| 657 |
+
}
|
| 658 |
+
],
|
| 659 |
+
"source": [
|
| 660 |
+
"a = np.array([1,2,3])\n",
|
| 661 |
+
"b = a.copy()\n",
|
| 662 |
+
"b[0] = 100\n",
|
| 663 |
+
"\n",
|
| 664 |
+
"print(a)"
|
| 665 |
+
]
|
| 666 |
+
},
|
| 667 |
+
{
|
| 668 |
+
"cell_type": "markdown",
|
| 669 |
+
"metadata": {},
|
| 670 |
+
"source": [
|
| 671 |
+
"### Mathematics"
|
| 672 |
+
]
|
| 673 |
+
},
|
| 674 |
+
{
|
| 675 |
+
"cell_type": "code",
|
| 676 |
+
"execution_count": 31,
|
| 677 |
+
"metadata": {},
|
| 678 |
+
"outputs": [
|
| 679 |
+
{
|
| 680 |
+
"name": "stdout",
|
| 681 |
+
"output_type": "stream",
|
| 682 |
+
"text": [
|
| 683 |
+
"[1 2 3 4]\n"
|
| 684 |
+
]
|
| 685 |
+
}
|
| 686 |
+
],
|
| 687 |
+
"source": [
|
| 688 |
+
"a = np.array([1,2,3,4])\n",
|
| 689 |
+
"print(a)"
|
| 690 |
+
]
|
| 691 |
+
},
|
| 692 |
+
{
|
| 693 |
+
"cell_type": "code",
|
| 694 |
+
"execution_count": 32,
|
| 695 |
+
"metadata": {},
|
| 696 |
+
"outputs": [
|
| 697 |
+
{
|
| 698 |
+
"data": {
|
| 699 |
+
"text/plain": [
|
| 700 |
+
"array([3, 4, 5, 6])"
|
| 701 |
+
]
|
| 702 |
+
},
|
| 703 |
+
"execution_count": 32,
|
| 704 |
+
"metadata": {},
|
| 705 |
+
"output_type": "execute_result"
|
| 706 |
+
}
|
| 707 |
+
],
|
| 708 |
+
"source": [
|
| 709 |
+
"a + 2"
|
| 710 |
+
]
|
| 711 |
+
},
|
| 712 |
+
{
|
| 713 |
+
"cell_type": "code",
|
| 714 |
+
"execution_count": 33,
|
| 715 |
+
"metadata": {},
|
| 716 |
+
"outputs": [
|
| 717 |
+
{
|
| 718 |
+
"data": {
|
| 719 |
+
"text/plain": [
|
| 720 |
+
"array([-1, 0, 1, 2])"
|
| 721 |
+
]
|
| 722 |
+
},
|
| 723 |
+
"execution_count": 33,
|
| 724 |
+
"metadata": {},
|
| 725 |
+
"output_type": "execute_result"
|
| 726 |
+
}
|
| 727 |
+
],
|
| 728 |
+
"source": [
|
| 729 |
+
"a - 2"
|
| 730 |
+
]
|
| 731 |
+
},
|
| 732 |
+
{
|
| 733 |
+
"cell_type": "code",
|
| 734 |
+
"execution_count": 34,
|
| 735 |
+
"metadata": {},
|
| 736 |
+
"outputs": [
|
| 737 |
+
{
|
| 738 |
+
"data": {
|
| 739 |
+
"text/plain": [
|
| 740 |
+
"array([2, 4, 6, 8])"
|
| 741 |
+
]
|
| 742 |
+
},
|
| 743 |
+
"execution_count": 34,
|
| 744 |
+
"metadata": {},
|
| 745 |
+
"output_type": "execute_result"
|
| 746 |
+
}
|
| 747 |
+
],
|
| 748 |
+
"source": [
|
| 749 |
+
"a * 2"
|
| 750 |
+
]
|
| 751 |
+
},
|
| 752 |
+
{
|
| 753 |
+
"cell_type": "code",
|
| 754 |
+
"execution_count": 35,
|
| 755 |
+
"metadata": {},
|
| 756 |
+
"outputs": [
|
| 757 |
+
{
|
| 758 |
+
"data": {
|
| 759 |
+
"text/plain": [
|
| 760 |
+
"array([0.5, 1. , 1.5, 2. ])"
|
| 761 |
+
]
|
| 762 |
+
},
|
| 763 |
+
"execution_count": 35,
|
| 764 |
+
"metadata": {},
|
| 765 |
+
"output_type": "execute_result"
|
| 766 |
+
}
|
| 767 |
+
],
|
| 768 |
+
"source": [
|
| 769 |
+
"a / 2"
|
| 770 |
+
]
|
| 771 |
+
},
|
| 772 |
+
{
|
| 773 |
+
"cell_type": "code",
|
| 774 |
+
"execution_count": 36,
|
| 775 |
+
"metadata": {},
|
| 776 |
+
"outputs": [
|
| 777 |
+
{
|
| 778 |
+
"data": {
|
| 779 |
+
"text/plain": [
|
| 780 |
+
"array([2, 2, 4, 4])"
|
| 781 |
+
]
|
| 782 |
+
},
|
| 783 |
+
"execution_count": 36,
|
| 784 |
+
"metadata": {},
|
| 785 |
+
"output_type": "execute_result"
|
| 786 |
+
}
|
| 787 |
+
],
|
| 788 |
+
"source": [
|
| 789 |
+
"b = np.array([1,0,1,0])\n",
|
| 790 |
+
"a + b"
|
| 791 |
+
]
|
| 792 |
+
},
|
| 793 |
+
{
|
| 794 |
+
"cell_type": "code",
|
| 795 |
+
"execution_count": 37,
|
| 796 |
+
"metadata": {},
|
| 797 |
+
"outputs": [
|
| 798 |
+
{
|
| 799 |
+
"data": {
|
| 800 |
+
"text/plain": [
|
| 801 |
+
"array([ 1, 4, 9, 16])"
|
| 802 |
+
]
|
| 803 |
+
},
|
| 804 |
+
"execution_count": 37,
|
| 805 |
+
"metadata": {},
|
| 806 |
+
"output_type": "execute_result"
|
| 807 |
+
}
|
| 808 |
+
],
|
| 809 |
+
"source": [
|
| 810 |
+
"a ** 2"
|
| 811 |
+
]
|
| 812 |
+
},
|
| 813 |
+
{
|
| 814 |
+
"cell_type": "code",
|
| 815 |
+
"execution_count": 38,
|
| 816 |
+
"metadata": {},
|
| 817 |
+
"outputs": [
|
| 818 |
+
{
|
| 819 |
+
"data": {
|
| 820 |
+
"text/plain": [
|
| 821 |
+
"array([ 0.54030231, -0.41614684, -0.9899925 , -0.65364362])"
|
| 822 |
+
]
|
| 823 |
+
},
|
| 824 |
+
"execution_count": 38,
|
| 825 |
+
"metadata": {},
|
| 826 |
+
"output_type": "execute_result"
|
| 827 |
+
}
|
| 828 |
+
],
|
| 829 |
+
"source": [
|
| 830 |
+
"# Take the sin\n",
|
| 831 |
+
"np.cos(a)\n",
|
| 832 |
+
"\n"
|
| 833 |
+
]
|
| 834 |
+
},
|
| 835 |
+
{
|
| 836 |
+
"cell_type": "markdown",
|
| 837 |
+
"metadata": {},
|
| 838 |
+
"source": [
|
| 839 |
+
"##### Linear Algebra"
|
| 840 |
+
]
|
| 841 |
+
},
|
| 842 |
+
{
|
| 843 |
+
"cell_type": "code",
|
| 844 |
+
"execution_count": 40,
|
| 845 |
+
"metadata": {},
|
| 846 |
+
"outputs": [
|
| 847 |
+
{
|
| 848 |
+
"name": "stdout",
|
| 849 |
+
"output_type": "stream",
|
| 850 |
+
"text": [
|
| 851 |
+
"[[1. 1. 1.]\n",
|
| 852 |
+
" [1. 1. 1.]]\n",
|
| 853 |
+
"[[2 2]\n",
|
| 854 |
+
" [2 2]\n",
|
| 855 |
+
" [2 2]]\n"
|
| 856 |
+
]
|
| 857 |
+
},
|
| 858 |
+
{
|
| 859 |
+
"data": {
|
| 860 |
+
"text/plain": [
|
| 861 |
+
"array([[6., 6.],\n",
|
| 862 |
+
" [6., 6.]])"
|
| 863 |
+
]
|
| 864 |
+
},
|
| 865 |
+
"execution_count": 40,
|
| 866 |
+
"metadata": {},
|
| 867 |
+
"output_type": "execute_result"
|
| 868 |
+
}
|
| 869 |
+
],
|
| 870 |
+
"source": [
|
| 871 |
+
"a = np.ones((2,3))\n",
|
| 872 |
+
"print(a)\n",
|
| 873 |
+
"\n",
|
| 874 |
+
"b = np.full((3,2), 2)\n",
|
| 875 |
+
"print(b)\n",
|
| 876 |
+
"\n",
|
| 877 |
+
"np.matmul(a,b)"
|
| 878 |
+
]
|
| 879 |
+
},
|
| 880 |
+
{
|
| 881 |
+
"cell_type": "code",
|
| 882 |
+
"execution_count": 41,
|
| 883 |
+
"metadata": {},
|
| 884 |
+
"outputs": [
|
| 885 |
+
{
|
| 886 |
+
"data": {
|
| 887 |
+
"text/plain": [
|
| 888 |
+
"1.0"
|
| 889 |
+
]
|
| 890 |
+
},
|
| 891 |
+
"execution_count": 41,
|
| 892 |
+
"metadata": {},
|
| 893 |
+
"output_type": "execute_result"
|
| 894 |
+
}
|
| 895 |
+
],
|
| 896 |
+
"source": [
|
| 897 |
+
"# Find the determinant\n",
|
| 898 |
+
"c = np.identity(3)\n",
|
| 899 |
+
"np.linalg.det(c)"
|
| 900 |
+
]
|
| 901 |
+
},
|
| 902 |
+
{
|
| 903 |
+
"cell_type": "markdown",
|
| 904 |
+
"metadata": {},
|
| 905 |
+
"source": [
|
| 906 |
+
"##### Statistics"
|
| 907 |
+
]
|
| 908 |
+
},
|
| 909 |
+
{
|
| 910 |
+
"cell_type": "code",
|
| 911 |
+
"execution_count": 43,
|
| 912 |
+
"metadata": {},
|
| 913 |
+
"outputs": [
|
| 914 |
+
{
|
| 915 |
+
"data": {
|
| 916 |
+
"text/plain": [
|
| 917 |
+
"array([[1, 2, 3],\n",
|
| 918 |
+
" [4, 5, 6]])"
|
| 919 |
+
]
|
| 920 |
+
},
|
| 921 |
+
"execution_count": 43,
|
| 922 |
+
"metadata": {},
|
| 923 |
+
"output_type": "execute_result"
|
| 924 |
+
}
|
| 925 |
+
],
|
| 926 |
+
"source": [
|
| 927 |
+
"stats = np.array([[1,2,3],[4,5,6]])\n",
|
| 928 |
+
"stats"
|
| 929 |
+
]
|
| 930 |
+
},
|
| 931 |
+
{
|
| 932 |
+
"cell_type": "code",
|
| 933 |
+
"execution_count": 44,
|
| 934 |
+
"metadata": {},
|
| 935 |
+
"outputs": [
|
| 936 |
+
{
|
| 937 |
+
"data": {
|
| 938 |
+
"text/plain": [
|
| 939 |
+
"1"
|
| 940 |
+
]
|
| 941 |
+
},
|
| 942 |
+
"execution_count": 44,
|
| 943 |
+
"metadata": {},
|
| 944 |
+
"output_type": "execute_result"
|
| 945 |
+
}
|
| 946 |
+
],
|
| 947 |
+
"source": [
|
| 948 |
+
"np.min(stats)"
|
| 949 |
+
]
|
| 950 |
+
},
|
| 951 |
+
{
|
| 952 |
+
"cell_type": "code",
|
| 953 |
+
"execution_count": 45,
|
| 954 |
+
"metadata": {},
|
| 955 |
+
"outputs": [
|
| 956 |
+
{
|
| 957 |
+
"data": {
|
| 958 |
+
"text/plain": [
|
| 959 |
+
"array([3, 6])"
|
| 960 |
+
]
|
| 961 |
+
},
|
| 962 |
+
"execution_count": 45,
|
| 963 |
+
"metadata": {},
|
| 964 |
+
"output_type": "execute_result"
|
| 965 |
+
}
|
| 966 |
+
],
|
| 967 |
+
"source": [
|
| 968 |
+
"np.max(stats, axis=1)"
|
| 969 |
+
]
|
| 970 |
+
},
|
| 971 |
+
{
|
| 972 |
+
"cell_type": "code",
|
| 973 |
+
"execution_count": 46,
|
| 974 |
+
"metadata": {},
|
| 975 |
+
"outputs": [
|
| 976 |
+
{
|
| 977 |
+
"data": {
|
| 978 |
+
"text/plain": [
|
| 979 |
+
"array([5, 7, 9])"
|
| 980 |
+
]
|
| 981 |
+
},
|
| 982 |
+
"execution_count": 46,
|
| 983 |
+
"metadata": {},
|
| 984 |
+
"output_type": "execute_result"
|
| 985 |
+
}
|
| 986 |
+
],
|
| 987 |
+
"source": [
|
| 988 |
+
"np.sum(stats, axis=0)"
|
| 989 |
+
]
|
| 990 |
+
},
|
| 991 |
+
{
|
| 992 |
+
"cell_type": "markdown",
|
| 993 |
+
"metadata": {},
|
| 994 |
+
"source": [
|
| 995 |
+
"### Reorganizing Arrays"
|
| 996 |
+
]
|
| 997 |
+
},
|
| 998 |
+
{
|
| 999 |
+
"cell_type": "code",
|
| 1000 |
+
"execution_count": 49,
|
| 1001 |
+
"metadata": {},
|
| 1002 |
+
"outputs": [
|
| 1003 |
+
{
|
| 1004 |
+
"name": "stdout",
|
| 1005 |
+
"output_type": "stream",
|
| 1006 |
+
"text": [
|
| 1007 |
+
"[[1 2 3 4]\n",
|
| 1008 |
+
" [5 6 7 8]]\n",
|
| 1009 |
+
"[[1]\n",
|
| 1010 |
+
" [2]\n",
|
| 1011 |
+
" [3]\n",
|
| 1012 |
+
" [4]\n",
|
| 1013 |
+
" [5]\n",
|
| 1014 |
+
" [6]\n",
|
| 1015 |
+
" [7]\n",
|
| 1016 |
+
" [8]]\n"
|
| 1017 |
+
]
|
| 1018 |
+
}
|
| 1019 |
+
],
|
| 1020 |
+
"source": [
|
| 1021 |
+
"before = np.array([[1,2,3,4],[5,6,7,8]])\n",
|
| 1022 |
+
"print(before)\n",
|
| 1023 |
+
"\n",
|
| 1024 |
+
"after = before.reshape((8,1))\n",
|
| 1025 |
+
"print(after)"
|
| 1026 |
+
]
|
| 1027 |
+
},
|
| 1028 |
+
{
|
| 1029 |
+
"cell_type": "code",
|
| 1030 |
+
"execution_count": 50,
|
| 1031 |
+
"metadata": {},
|
| 1032 |
+
"outputs": [
|
| 1033 |
+
{
|
| 1034 |
+
"data": {
|
| 1035 |
+
"text/plain": [
|
| 1036 |
+
"array([[1, 2, 3, 4],\n",
|
| 1037 |
+
" [5, 6, 7, 8],\n",
|
| 1038 |
+
" [1, 2, 3, 4],\n",
|
| 1039 |
+
" [5, 6, 7, 8]])"
|
| 1040 |
+
]
|
| 1041 |
+
},
|
| 1042 |
+
"execution_count": 50,
|
| 1043 |
+
"metadata": {},
|
| 1044 |
+
"output_type": "execute_result"
|
| 1045 |
+
}
|
| 1046 |
+
],
|
| 1047 |
+
"source": [
|
| 1048 |
+
"# Vertically stacking vectors\n",
|
| 1049 |
+
"v1 = np.array([1,2,3,4])\n",
|
| 1050 |
+
"v2 = np.array([5,6,7,8])\n",
|
| 1051 |
+
"\n",
|
| 1052 |
+
"np.vstack([v1,v2,v1,v2])"
|
| 1053 |
+
]
|
| 1054 |
+
},
|
| 1055 |
+
{
|
| 1056 |
+
"cell_type": "code",
|
| 1057 |
+
"execution_count": 51,
|
| 1058 |
+
"metadata": {},
|
| 1059 |
+
"outputs": [
|
| 1060 |
+
{
|
| 1061 |
+
"data": {
|
| 1062 |
+
"text/plain": [
|
| 1063 |
+
"array([[1., 1., 1., 1., 0., 0.],\n",
|
| 1064 |
+
" [1., 1., 1., 1., 0., 0.]])"
|
| 1065 |
+
]
|
| 1066 |
+
},
|
| 1067 |
+
"execution_count": 51,
|
| 1068 |
+
"metadata": {},
|
| 1069 |
+
"output_type": "execute_result"
|
| 1070 |
+
}
|
| 1071 |
+
],
|
| 1072 |
+
"source": [
|
| 1073 |
+
"# Horizontal stack\n",
|
| 1074 |
+
"h1 = np.ones((2,4))\n",
|
| 1075 |
+
"h2 = np.zeros((2,2))\n",
|
| 1076 |
+
"\n",
|
| 1077 |
+
"np.hstack((h1,h2))"
|
| 1078 |
+
]
|
| 1079 |
+
},
|
| 1080 |
+
{
|
| 1081 |
+
"cell_type": "code",
|
| 1082 |
+
"execution_count": null,
|
| 1083 |
+
"metadata": {},
|
| 1084 |
+
"outputs": [],
|
| 1085 |
+
"source": []
|
| 1086 |
+
},
|
| 1087 |
+
{
|
| 1088 |
+
"cell_type": "code",
|
| 1089 |
+
"execution_count": null,
|
| 1090 |
+
"metadata": {},
|
| 1091 |
+
"outputs": [],
|
| 1092 |
+
"source": []
|
| 1093 |
+
}
|
| 1094 |
+
],
|
| 1095 |
+
"metadata": {
|
| 1096 |
+
"kernelspec": {
|
| 1097 |
+
"display_name": "Python 3 (ipykernel)",
|
| 1098 |
+
"language": "python",
|
| 1099 |
+
"name": "python3"
|
| 1100 |
+
},
|
| 1101 |
+
"language_info": {
|
| 1102 |
+
"codemirror_mode": {
|
| 1103 |
+
"name": "ipython",
|
| 1104 |
+
"version": 3
|
| 1105 |
+
},
|
| 1106 |
+
"file_extension": ".py",
|
| 1107 |
+
"mimetype": "text/x-python",
|
| 1108 |
+
"name": "python",
|
| 1109 |
+
"nbconvert_exporter": "python",
|
| 1110 |
+
"pygments_lexer": "ipython3",
|
| 1111 |
+
"version": "3.10.9"
|
| 1112 |
+
}
|
| 1113 |
+
},
|
| 1114 |
+
"nbformat": 4,
|
| 1115 |
+
"nbformat_minor": 2
|
| 1116 |
+
}
|
README.md
ADDED
|
@@ -0,0 +1,29 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
# Numpy_Basics
|
| 2 |
+

|
| 3 |
+
<h2>What is NumPy?</h2>
|
| 4 |
+
<p>NumPy is a Python library used for working with arrays.
|
| 5 |
+
|
| 6 |
+
It also has functions for working in domain of linear algebra, fourier transform, and matrices.
|
| 7 |
+
|
| 8 |
+
NumPy was created in 2005 by Travis Oliphant. It is an open source project and you can use it freely.
|
| 9 |
+
|
| 10 |
+
NumPy stands for Numerical Python.</p>
|
| 11 |
+
--------------------------------------------------------------------------------------------------------------------------------------------------
|
| 12 |
+
<h2>Why Use NumPy?</h2>
|
| 13 |
+
<p>In Python we have lists that serve the purpose of arrays, but they are slow to process.
|
| 14 |
+
|
| 15 |
+
NumPy aims to provide an array object that is up to 50x faster than traditional Python lists.
|
| 16 |
+
|
| 17 |
+
The array object in NumPy is called ndarray, it provides a lot of supporting functions that make working with ndarray very easy.
|
| 18 |
+
|
| 19 |
+
Arrays are very frequently used in data science, where speed and resources are very important.</p>
|
| 20 |
+
--------------------------------------------------------------------------------------------------------------------------------------------------
|
| 21 |
+
<h2>Why is NumPy Faster Than Lists?</h2>
|
| 22 |
+
<p>NumPy arrays are stored at one continuous place in memory unlike lists, so processes can access and manipulate them very efficiently.
|
| 23 |
+
|
| 24 |
+
This behavior is called locality of reference in computer science.
|
| 25 |
+
|
| 26 |
+
This is the main reason why NumPy is faster than lists. Also it is optimized to work with latest CPU architectures.</p>
|
| 27 |
+
--------------------------------------------------------------------------------------------------------------------------------------------------
|
| 28 |
+
<h2>Which Language is NumPy written in?</h2>
|
| 29 |
+
<p>NumPy is a Python library and is written partially in Python, but most of the parts that require fast computation are written in C or C++.</p>
|
numpy.png
ADDED
|