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1-numpy_tutorial.ipynb 165 kB

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  1. {
  2. "cells": [
  3. {
  4. "cell_type": "markdown",
  5. "metadata": {},
  6. "source": [
  7. "# Numpy - 多维数据的数组"
  8. ]
  9. },
  10. {
  11. "cell_type": "markdown",
  12. "metadata": {},
  13. "source": [
  14. "NumPy是Python中科学计算的基本软件包。它是一个Python库,提供多维数组对象、各种派生类(如掩码数组和矩阵)和各种例程,用于对数组进行快速操作,包括数学、逻辑、形状操作、排序、选择、I/O、离散傅立叶变换、基本线性代数、基本统计操作、随机模拟等等。Numpy作为Python数据计算的基础广泛应用到数据处理、信号处理、机器学习等领域。"
  15. ]
  16. },
  17. {
  18. "cell_type": "code",
  19. "execution_count": 1,
  20. "metadata": {},
  21. "outputs": [],
  22. "source": [
  23. "# 这一行的作用会在课程4中回答\n",
  24. "%matplotlib inline\n",
  25. "import matplotlib.pyplot as plt"
  26. ]
  27. },
  28. {
  29. "cell_type": "markdown",
  30. "metadata": {},
  31. "source": [
  32. "## 1. 简介"
  33. ]
  34. },
  35. {
  36. "cell_type": "markdown",
  37. "metadata": {},
  38. "source": [
  39. "这个`numpy`包(模块)用在几乎所有使用Python的数值计算中。他是一个为Python提供高性能向量,矩阵和高维数据结构的模块。它是用C和Fortran语言实现的,因此当计算向量化数据(用向量和矩阵表示)时,性能非常的好。\n",
  40. "\n",
  41. "为了使用`numpy`模块,你先要像下面的例子一样导入这个模块:"
  42. ]
  43. },
  44. {
  45. "cell_type": "code",
  46. "execution_count": 3,
  47. "metadata": {},
  48. "outputs": [],
  49. "source": [
  50. "# 不建议用这种方式导入库\n",
  51. "from numpy import *"
  52. ]
  53. },
  54. {
  55. "cell_type": "code",
  56. "execution_count": 2,
  57. "metadata": {},
  58. "outputs": [],
  59. "source": [
  60. "import numpy as np"
  61. ]
  62. },
  63. {
  64. "cell_type": "markdown",
  65. "metadata": {},
  66. "source": [
  67. "在`numpy`模块中,用于向量,矩阵和高维数据集的术语是*数组*。\n",
  68. "\n",
  69. "**建议大家使用第二种导入方法** `import numpy as np`\n"
  70. ]
  71. },
  72. {
  73. "cell_type": "markdown",
  74. "metadata": {},
  75. "source": [
  76. "## 2. 创建`numpy`数组"
  77. ]
  78. },
  79. {
  80. "cell_type": "markdown",
  81. "metadata": {},
  82. "source": [
  83. "有很多种方法去初始化新的numpy数组, 例如从\n",
  84. "\n",
  85. "* Python列表或元组\n",
  86. "* 使用专门用来创建numpy arrays的函数,例如 `arange`, `linspace`等\n",
  87. "* 从文件中读取数据"
  88. ]
  89. },
  90. {
  91. "cell_type": "markdown",
  92. "metadata": {},
  93. "source": [
  94. "### 2.1 从列表中"
  95. ]
  96. },
  97. {
  98. "cell_type": "markdown",
  99. "metadata": {},
  100. "source": [
  101. "例如,为了从Python列表创建新的向量和矩阵我们可以用`numpy.array`函数。\n"
  102. ]
  103. },
  104. {
  105. "cell_type": "code",
  106. "execution_count": 4,
  107. "metadata": {},
  108. "outputs": [
  109. {
  110. "name": "stdout",
  111. "output_type": "stream",
  112. "text": [
  113. "[1, 2, 3, 4]\n"
  114. ]
  115. },
  116. {
  117. "data": {
  118. "text/plain": [
  119. "array([1, 2, 3, 4])"
  120. ]
  121. },
  122. "execution_count": 4,
  123. "metadata": {},
  124. "output_type": "execute_result"
  125. }
  126. ],
  127. "source": [
  128. "import numpy as np\n",
  129. "\n",
  130. "a = [1, 2, 3, 4]\n",
  131. "print(a)\n",
  132. "\n",
  133. "# a vector: the argument to the array function is a Python list\n",
  134. "v = np.array(a)\n",
  135. "\n",
  136. "v"
  137. ]
  138. },
  139. {
  140. "cell_type": "code",
  141. "execution_count": 6,
  142. "metadata": {},
  143. "outputs": [
  144. {
  145. "name": "stdout",
  146. "output_type": "stream",
  147. "text": [
  148. "[[1 2]\n",
  149. " [3 4]\n",
  150. " [5 6]]\n",
  151. "\n",
  152. "(3, 2)\n"
  153. ]
  154. }
  155. ],
  156. "source": [
  157. "# 矩阵:数组函数的参数是一个嵌套的Python列表\n",
  158. "M = np.array([[1, 2], [3, 4], [5, 6]])\n",
  159. "\n",
  160. "print(M)\n",
  161. "print()\n",
  162. "print(M.shape)"
  163. ]
  164. },
  165. {
  166. "cell_type": "code",
  167. "execution_count": 8,
  168. "metadata": {},
  169. "outputs": [
  170. {
  171. "name": "stdout",
  172. "output_type": "stream",
  173. "text": [
  174. "[[[ 1 2]\n",
  175. " [ 3 4]\n",
  176. " [ 5 6]]\n",
  177. "\n",
  178. " [[ 3 4]\n",
  179. " [ 5 6]\n",
  180. " [ 7 8]]\n",
  181. "\n",
  182. " [[ 5 6]\n",
  183. " [ 7 8]\n",
  184. " [ 9 10]]\n",
  185. "\n",
  186. " [[ 7 8]\n",
  187. " [ 9 10]\n",
  188. " [11 12]]]\n",
  189. "\n",
  190. "(4, 3, 2)\n"
  191. ]
  192. }
  193. ],
  194. "source": [
  195. "M = np.array([[[1,2], [3,4], [5,6]], \\\n",
  196. " [[3,4], [5,6], [7,8]], \\\n",
  197. " [[5,6], [7,8], [9,10]], \\\n",
  198. " [[7,8], [9,10], [11,12]]])\n",
  199. "print(M)\n",
  200. "print()\n",
  201. "print(M.shape)"
  202. ]
  203. },
  204. {
  205. "cell_type": "markdown",
  206. "metadata": {},
  207. "source": [
  208. "`v`和`M`两个都是属于`numpy`模块提供的`ndarray`类型。"
  209. ]
  210. },
  211. {
  212. "cell_type": "code",
  213. "execution_count": 9,
  214. "metadata": {},
  215. "outputs": [
  216. {
  217. "data": {
  218. "text/plain": [
  219. "(numpy.ndarray, numpy.ndarray)"
  220. ]
  221. },
  222. "execution_count": 9,
  223. "metadata": {},
  224. "output_type": "execute_result"
  225. }
  226. ],
  227. "source": [
  228. "type(v), type(M)"
  229. ]
  230. },
  231. {
  232. "cell_type": "markdown",
  233. "metadata": {},
  234. "source": [
  235. "`v`和`M`之间的区别仅在于他们的形状。我们可以用属性函数`ndarray.shape`得到数组形状的信息。"
  236. ]
  237. },
  238. {
  239. "cell_type": "code",
  240. "execution_count": 10,
  241. "metadata": {},
  242. "outputs": [
  243. {
  244. "data": {
  245. "text/plain": [
  246. "(4,)"
  247. ]
  248. },
  249. "execution_count": 10,
  250. "metadata": {},
  251. "output_type": "execute_result"
  252. }
  253. ],
  254. "source": [
  255. "v.shape"
  256. ]
  257. },
  258. {
  259. "cell_type": "code",
  260. "execution_count": 11,
  261. "metadata": {},
  262. "outputs": [
  263. {
  264. "data": {
  265. "text/plain": [
  266. "(4, 3, 2)"
  267. ]
  268. },
  269. "execution_count": 11,
  270. "metadata": {},
  271. "output_type": "execute_result"
  272. }
  273. ],
  274. "source": [
  275. "M.shape"
  276. ]
  277. },
  278. {
  279. "cell_type": "markdown",
  280. "metadata": {},
  281. "source": [
  282. "通过属性函数`ndarray.size`我们可以得到数组中元素的个数"
  283. ]
  284. },
  285. {
  286. "cell_type": "code",
  287. "execution_count": 12,
  288. "metadata": {},
  289. "outputs": [
  290. {
  291. "data": {
  292. "text/plain": [
  293. "24"
  294. ]
  295. },
  296. "execution_count": 12,
  297. "metadata": {},
  298. "output_type": "execute_result"
  299. }
  300. ],
  301. "source": [
  302. "M.size"
  303. ]
  304. },
  305. {
  306. "cell_type": "markdown",
  307. "metadata": {},
  308. "source": [
  309. "同样,我们可以用函数`numpy.shape`和`numpy.size`"
  310. ]
  311. },
  312. {
  313. "cell_type": "code",
  314. "execution_count": 13,
  315. "metadata": {},
  316. "outputs": [
  317. {
  318. "data": {
  319. "text/plain": [
  320. "(4, 3, 2)"
  321. ]
  322. },
  323. "execution_count": 13,
  324. "metadata": {},
  325. "output_type": "execute_result"
  326. }
  327. ],
  328. "source": [
  329. "np.shape(M)"
  330. ]
  331. },
  332. {
  333. "cell_type": "code",
  334. "execution_count": 14,
  335. "metadata": {},
  336. "outputs": [
  337. {
  338. "data": {
  339. "text/plain": [
  340. "24"
  341. ]
  342. },
  343. "execution_count": 14,
  344. "metadata": {},
  345. "output_type": "execute_result"
  346. }
  347. ],
  348. "source": [
  349. "np.size(M)"
  350. ]
  351. },
  352. {
  353. "cell_type": "markdown",
  354. "metadata": {},
  355. "source": [
  356. "到目前为止`numpy.ndarray`看起来非常像Python列表(或嵌套列表)。为什么不简单地使用Python列表来进行计算,而不是创建一个新的数组类型?\n",
  357. "\n",
  358. "下面有几个原因:\n",
  359. "\n",
  360. "* Python列表非常普遍。它们可以包含任何类型的对象。它们是动态类型的。它们不支持矩阵和点乘等数学函数。由于动态类型的关系,为Python列表实现这类函数的效率不是很高。\n",
  361. "* Numpy数组是**静态类型的**和**同构的**。元素的类型是在创建数组时确定的。\n",
  362. "* Numpy数组是内存高效的。\n",
  363. "* 由于是静态类型,数学函数的快速实现,比如“numpy”数组的乘法和加法可以用编译语言实现(使用C和Fortran).\n",
  364. "\n",
  365. "利用`ndarray`的属性函数`dtype`(数据类型),我们可以看出数组的数据是那种类型。\n"
  366. ]
  367. },
  368. {
  369. "cell_type": "code",
  370. "execution_count": 15,
  371. "metadata": {},
  372. "outputs": [
  373. {
  374. "data": {
  375. "text/plain": [
  376. "dtype('int64')"
  377. ]
  378. },
  379. "execution_count": 15,
  380. "metadata": {},
  381. "output_type": "execute_result"
  382. }
  383. ],
  384. "source": [
  385. "M.dtype"
  386. ]
  387. },
  388. {
  389. "cell_type": "markdown",
  390. "metadata": {},
  391. "source": [
  392. "如果我们试图给一个numpy数组中的元素赋一个错误类型的值,我们会得到一个错误:"
  393. ]
  394. },
  395. {
  396. "cell_type": "code",
  397. "execution_count": 17,
  398. "metadata": {},
  399. "outputs": [
  400. {
  401. "ename": "ValueError",
  402. "evalue": "invalid literal for int() with base 10: 'hello'",
  403. "output_type": "error",
  404. "traceback": [
  405. "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
  406. "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
  407. "\u001b[0;32m<ipython-input-17-3eecc5e8509b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mM\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m\"hello\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
  408. "\u001b[0;31mValueError\u001b[0m: invalid literal for int() with base 10: 'hello'"
  409. ]
  410. }
  411. ],
  412. "source": [
  413. "M[0,0,0] = \"hello\""
  414. ]
  415. },
  416. {
  417. "cell_type": "markdown",
  418. "metadata": {},
  419. "source": [
  420. "如果我们想的话,我们可以利用`dtype`关键字参数显式地定义我们创建的数组数据类型:"
  421. ]
  422. },
  423. {
  424. "cell_type": "code",
  425. "execution_count": 18,
  426. "metadata": {},
  427. "outputs": [
  428. {
  429. "data": {
  430. "text/plain": [
  431. "array([[1.+0.j, 2.+0.j],\n",
  432. " [3.+0.j, 4.+0.j]])"
  433. ]
  434. },
  435. "execution_count": 18,
  436. "metadata": {},
  437. "output_type": "execute_result"
  438. }
  439. ],
  440. "source": [
  441. "M = np.array([[1, 2], [3, 4]], dtype=complex)\n",
  442. "\n",
  443. "M"
  444. ]
  445. },
  446. {
  447. "cell_type": "markdown",
  448. "metadata": {},
  449. "source": [
  450. "常规可以伴随`dtype`使用的数据类型是:`int`, `float`, `complex`, `bool`, `object`等\n",
  451. "\n",
  452. "我们也可以显式地定义数据类型的大小,例如:`int64`, `int16`, `float128`, `complex128`。"
  453. ]
  454. },
  455. {
  456. "cell_type": "markdown",
  457. "metadata": {},
  458. "source": [
  459. "### 2.2 使用数组生成函数"
  460. ]
  461. },
  462. {
  463. "cell_type": "markdown",
  464. "metadata": {},
  465. "source": [
  466. "对于较大的数组,使用显式的Python列表人为地初始化数据是不切实际的。除此之外我们可以用`numpy`的很多函数得到不同类型的数组。有一些常用的分别是:"
  467. ]
  468. },
  469. {
  470. "cell_type": "markdown",
  471. "metadata": {},
  472. "source": [
  473. "#### arange"
  474. ]
  475. },
  476. {
  477. "cell_type": "code",
  478. "execution_count": 19,
  479. "metadata": {},
  480. "outputs": [
  481. {
  482. "name": "stdout",
  483. "output_type": "stream",
  484. "text": [
  485. "[0 1 2 3 4 5 6 7 8 9]\n",
  486. "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n"
  487. ]
  488. }
  489. ],
  490. "source": [
  491. "# 创建一个范围\n",
  492. "\n",
  493. "x = np.arange(0, 10, 1) # 参数:start, stop, step: \n",
  494. "y = range(0, 10, 1)\n",
  495. "print(x)\n",
  496. "print(list(y))"
  497. ]
  498. },
  499. {
  500. "cell_type": "code",
  501. "execution_count": 20,
  502. "metadata": {},
  503. "outputs": [
  504. {
  505. "data": {
  506. "text/plain": [
  507. "array([-1.00000000e+00, -9.00000000e-01, -8.00000000e-01, -7.00000000e-01,\n",
  508. " -6.00000000e-01, -5.00000000e-01, -4.00000000e-01, -3.00000000e-01,\n",
  509. " -2.00000000e-01, -1.00000000e-01, -2.22044605e-16, 1.00000000e-01,\n",
  510. " 2.00000000e-01, 3.00000000e-01, 4.00000000e-01, 5.00000000e-01,\n",
  511. " 6.00000000e-01, 7.00000000e-01, 8.00000000e-01, 9.00000000e-01])"
  512. ]
  513. },
  514. "execution_count": 20,
  515. "metadata": {},
  516. "output_type": "execute_result"
  517. }
  518. ],
  519. "source": [
  520. "x = np.arange(-1, 1, 0.1)\n",
  521. "\n",
  522. "x"
  523. ]
  524. },
  525. {
  526. "cell_type": "markdown",
  527. "metadata": {},
  528. "source": [
  529. "#### linspace and logspace"
  530. ]
  531. },
  532. {
  533. "cell_type": "code",
  534. "execution_count": 21,
  535. "metadata": {},
  536. "outputs": [
  537. {
  538. "data": {
  539. "text/plain": [
  540. "array([ 0. , 2.5, 5. , 7.5, 10. ])"
  541. ]
  542. },
  543. "execution_count": 21,
  544. "metadata": {},
  545. "output_type": "execute_result"
  546. }
  547. ],
  548. "source": [
  549. "# 使用linspace两边的端点也被包含进去\n",
  550. "np.linspace(0, 10, 5)"
  551. ]
  552. },
  553. {
  554. "cell_type": "code",
  555. "execution_count": 23,
  556. "metadata": {},
  557. "outputs": [
  558. {
  559. "data": {
  560. "text/plain": [
  561. "array([1.00000000e+00, 3.03773178e+00, 9.22781435e+00, 2.80316249e+01,\n",
  562. " 8.51525577e+01, 2.58670631e+02, 7.85771994e+02, 2.38696456e+03,\n",
  563. " 7.25095809e+03, 2.20264658e+04])"
  564. ]
  565. },
  566. "execution_count": 23,
  567. "metadata": {},
  568. "output_type": "execute_result"
  569. }
  570. ],
  571. "source": [
  572. "np.logspace(0, 10, 10, base=np.e)"
  573. ]
  574. },
  575. {
  576. "cell_type": "markdown",
  577. "metadata": {},
  578. "source": [
  579. "#### mgrid"
  580. ]
  581. },
  582. {
  583. "cell_type": "code",
  584. "execution_count": 24,
  585. "metadata": {},
  586. "outputs": [],
  587. "source": [
  588. "y, x = np.mgrid[0:5, 0:5] # 和MATLAB中的meshgrid类似"
  589. ]
  590. },
  591. {
  592. "cell_type": "code",
  593. "execution_count": 25,
  594. "metadata": {},
  595. "outputs": [
  596. {
  597. "data": {
  598. "text/plain": [
  599. "array([[0, 1, 2, 3, 4],\n",
  600. " [0, 1, 2, 3, 4],\n",
  601. " [0, 1, 2, 3, 4],\n",
  602. " [0, 1, 2, 3, 4],\n",
  603. " [0, 1, 2, 3, 4]])"
  604. ]
  605. },
  606. "execution_count": 25,
  607. "metadata": {},
  608. "output_type": "execute_result"
  609. }
  610. ],
  611. "source": [
  612. "x"
  613. ]
  614. },
  615. {
  616. "cell_type": "code",
  617. "execution_count": 26,
  618. "metadata": {},
  619. "outputs": [
  620. {
  621. "data": {
  622. "text/plain": [
  623. "array([[0, 0, 0, 0, 0],\n",
  624. " [1, 1, 1, 1, 1],\n",
  625. " [2, 2, 2, 2, 2],\n",
  626. " [3, 3, 3, 3, 3],\n",
  627. " [4, 4, 4, 4, 4]])"
  628. ]
  629. },
  630. "execution_count": 26,
  631. "metadata": {},
  632. "output_type": "execute_result"
  633. }
  634. ],
  635. "source": [
  636. "y"
  637. ]
  638. },
  639. {
  640. "cell_type": "markdown",
  641. "metadata": {},
  642. "source": [
  643. "#### random data"
  644. ]
  645. },
  646. {
  647. "cell_type": "code",
  648. "execution_count": 27,
  649. "metadata": {},
  650. "outputs": [],
  651. "source": [
  652. "from numpy import random"
  653. ]
  654. },
  655. {
  656. "cell_type": "code",
  657. "execution_count": 29,
  658. "metadata": {},
  659. "outputs": [
  660. {
  661. "data": {
  662. "text/plain": [
  663. "array([[[0.05939386, 0.11090236],\n",
  664. " [0.79171356, 0.9035595 ],\n",
  665. " [0.91073118, 0.44563208],\n",
  666. " [0.04466834, 0.5628772 ]],\n",
  667. "\n",
  668. " [[0.4416194 , 0.91226087],\n",
  669. " [0.168705 , 0.00683321],\n",
  670. " [0.41202402, 0.29339536],\n",
  671. " [0.96726694, 0.95870147]],\n",
  672. "\n",
  673. " [[0.70866367, 0.34569454],\n",
  674. " [0.49093219, 0.41306501],\n",
  675. " [0.01983635, 0.20873294],\n",
  676. " [0.20396734, 0.40334421]],\n",
  677. "\n",
  678. " [[0.50604792, 0.06472671],\n",
  679. " [0.31110672, 0.24701568],\n",
  680. " [0.24144453, 0.90806792],\n",
  681. " [0.04381394, 0.84682658]],\n",
  682. "\n",
  683. " [[0.61750894, 0.92342968],\n",
  684. " [0.55962797, 0.20718725],\n",
  685. " [0.54104153, 0.88491054],\n",
  686. " [0.80989667, 0.47680582]]])"
  687. ]
  688. },
  689. "execution_count": 29,
  690. "metadata": {},
  691. "output_type": "execute_result"
  692. }
  693. ],
  694. "source": [
  695. "# 均匀随机数在[0,1)区间\n",
  696. "random.rand(5,4,2)"
  697. ]
  698. },
  699. {
  700. "cell_type": "code",
  701. "execution_count": 30,
  702. "metadata": {},
  703. "outputs": [
  704. {
  705. "data": {
  706. "text/plain": [
  707. "array([[ 0.11502391, -0.92395205, 0.68163698, -1.79088946, 0.14831216],\n",
  708. " [ 0.78671373, -0.56667653, 0.7015141 , -0.06435951, -1.19476965],\n",
  709. " [ 0.87780154, -0.46150288, -0.34295011, -0.37943472, 0.40605553],\n",
  710. " [ 1.71869392, 1.89791292, 1.27828548, 0.09929399, 0.91991364],\n",
  711. " [-0.2730765 , -0.39200219, -0.03646926, -1.9063281 , 1.1373957 ]])"
  712. ]
  713. },
  714. "execution_count": 30,
  715. "metadata": {},
  716. "output_type": "execute_result"
  717. }
  718. ],
  719. "source": [
  720. "# 标准正态分布随机数\n",
  721. "random.randn(5,5)"
  722. ]
  723. },
  724. {
  725. "cell_type": "markdown",
  726. "metadata": {},
  727. "source": [
  728. "#### diag"
  729. ]
  730. },
  731. {
  732. "cell_type": "code",
  733. "execution_count": 31,
  734. "metadata": {},
  735. "outputs": [
  736. {
  737. "data": {
  738. "text/plain": [
  739. "array([[1, 0, 0],\n",
  740. " [0, 2, 0],\n",
  741. " [0, 0, 3]])"
  742. ]
  743. },
  744. "execution_count": 31,
  745. "metadata": {},
  746. "output_type": "execute_result"
  747. }
  748. ],
  749. "source": [
  750. "# 一个对角矩阵\n",
  751. "np.diag([1,2,3])"
  752. ]
  753. },
  754. {
  755. "cell_type": "code",
  756. "execution_count": 33,
  757. "metadata": {},
  758. "outputs": [
  759. {
  760. "data": {
  761. "text/plain": [
  762. "array([[0, 0, 0, 0],\n",
  763. " [1, 0, 0, 0],\n",
  764. " [0, 2, 0, 0],\n",
  765. " [0, 0, 3, 0]])"
  766. ]
  767. },
  768. "execution_count": 33,
  769. "metadata": {},
  770. "output_type": "execute_result"
  771. }
  772. ],
  773. "source": [
  774. "# 从主对角线偏移的对角线\n",
  775. "np.diag([1,2,3], k=-1) "
  776. ]
  777. },
  778. {
  779. "cell_type": "markdown",
  780. "metadata": {},
  781. "source": [
  782. "#### zeros and ones"
  783. ]
  784. },
  785. {
  786. "cell_type": "code",
  787. "execution_count": 34,
  788. "metadata": {},
  789. "outputs": [
  790. {
  791. "data": {
  792. "text/plain": [
  793. "array([[0., 0., 0.],\n",
  794. " [0., 0., 0.],\n",
  795. " [0., 0., 0.]])"
  796. ]
  797. },
  798. "execution_count": 34,
  799. "metadata": {},
  800. "output_type": "execute_result"
  801. }
  802. ],
  803. "source": [
  804. "np.zeros((3,3))"
  805. ]
  806. },
  807. {
  808. "cell_type": "code",
  809. "execution_count": 35,
  810. "metadata": {},
  811. "outputs": [
  812. {
  813. "data": {
  814. "text/plain": [
  815. "array([[1., 1., 1.],\n",
  816. " [1., 1., 1.],\n",
  817. " [1., 1., 1.]])"
  818. ]
  819. },
  820. "execution_count": 35,
  821. "metadata": {},
  822. "output_type": "execute_result"
  823. }
  824. ],
  825. "source": [
  826. "np.ones((3,3))"
  827. ]
  828. },
  829. {
  830. "cell_type": "markdown",
  831. "metadata": {},
  832. "source": [
  833. "## 3. 文件 I/O"
  834. ]
  835. },
  836. {
  837. "cell_type": "markdown",
  838. "metadata": {},
  839. "source": [
  840. "### 3.1 逗号分隔值 (CSV)"
  841. ]
  842. },
  843. {
  844. "cell_type": "markdown",
  845. "metadata": {},
  846. "source": [
  847. "对于数据文件来说一种非常常见的文件格式是逗号分割值(CSV),或者有关的格式例如TSV(制表符分隔的值)。为了从这些文件中读取数据到Numpy数组中,我们可以用`numpy.genfromtxt`函数。例如:"
  848. ]
  849. },
  850. {
  851. "cell_type": "code",
  852. "execution_count": 36,
  853. "metadata": {},
  854. "outputs": [
  855. {
  856. "name": "stdout",
  857. "output_type": "stream",
  858. "text": [
  859. "1800 1 1 -6.1 -6.1 -6.1 1\r\n",
  860. "1800 1 2 -15.4 -15.4 -15.4 1\r\n",
  861. "1800 1 3 -15.0 -15.0 -15.0 1\r\n",
  862. "1800 1 4 -19.3 -19.3 -19.3 1\r\n",
  863. "1800 1 5 -16.8 -16.8 -16.8 1\r\n",
  864. "1800 1 6 -11.4 -11.4 -11.4 1\r\n",
  865. "1800 1 7 -7.6 -7.6 -7.6 1\r\n",
  866. "1800 1 8 -7.1 -7.1 -7.1 1\r\n",
  867. "1800 1 9 -10.1 -10.1 -10.1 1\r\n",
  868. "1800 1 10 -9.5 -9.5 -9.5 1\r\n"
  869. ]
  870. }
  871. ],
  872. "source": [
  873. "!head stockholm_td_adj.dat"
  874. ]
  875. },
  876. {
  877. "cell_type": "code",
  878. "execution_count": 38,
  879. "metadata": {},
  880. "outputs": [],
  881. "source": [
  882. "import numpy as np\n",
  883. "data = np.genfromtxt('stockholm_td_adj.dat')"
  884. ]
  885. },
  886. {
  887. "cell_type": "code",
  888. "execution_count": 39,
  889. "metadata": {},
  890. "outputs": [
  891. {
  892. "data": {
  893. "text/plain": [
  894. "(77431, 7)"
  895. ]
  896. },
  897. "execution_count": 39,
  898. "metadata": {},
  899. "output_type": "execute_result"
  900. }
  901. ],
  902. "source": [
  903. "data.shape"
  904. ]
  905. },
  906. {
  907. "cell_type": "code",
  908. "execution_count": 40,
  909. "metadata": {},
  910. "outputs": [
  911. {
  912. "data": {
  913. 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\n",
  914. "text/plain": [
  915. "<Figure size 1008x288 with 1 Axes>"
  916. ]
  917. },
  918. "metadata": {
  919. "needs_background": "light"
  920. },
  921. "output_type": "display_data"
  922. }
  923. ],
  924. "source": [
  925. "%matplotlib inline\n",
  926. "import matplotlib.pyplot as plt\n",
  927. "\n",
  928. "fig, ax = plt.subplots(figsize=(14,4))\n",
  929. "ax.plot(data[:,0]+data[:,1]/12.0+data[:,2]/365, data[:,5])\n",
  930. "ax.axis('tight')\n",
  931. "ax.set_title('tempeatures in Stockholm')\n",
  932. "ax.set_xlabel('year')\n",
  933. "ax.set_ylabel('temperature (C)');"
  934. ]
  935. },
  936. {
  937. "cell_type": "markdown",
  938. "metadata": {},
  939. "source": [
  940. "使用`numpy.savetxt`我们可以将一个Numpy数组以CSV格式存入:"
  941. ]
  942. },
  943. {
  944. "cell_type": "code",
  945. "execution_count": 41,
  946. "metadata": {},
  947. "outputs": [
  948. {
  949. "data": {
  950. "text/plain": [
  951. "array([[0.23335391, 0.0986599 , 0.0572248 ],\n",
  952. " [0.69544933, 0.53988449, 0.70582772],\n",
  953. " [0.74875206, 0.09427575, 0.7859238 ]])"
  954. ]
  955. },
  956. "execution_count": 41,
  957. "metadata": {},
  958. "output_type": "execute_result"
  959. }
  960. ],
  961. "source": [
  962. "M = np.random.rand(3,3)\n",
  963. "\n",
  964. "M"
  965. ]
  966. },
  967. {
  968. "cell_type": "code",
  969. "execution_count": 42,
  970. "metadata": {},
  971. "outputs": [],
  972. "source": [
  973. "np.savetxt(\"random-matrix.csv\", M)"
  974. ]
  975. },
  976. {
  977. "cell_type": "code",
  978. "execution_count": 43,
  979. "metadata": {},
  980. "outputs": [
  981. {
  982. "name": "stdout",
  983. "output_type": "stream",
  984. "text": [
  985. "2.333539099227897040e-01 9.865990104831434682e-02 5.722480315676647944e-02\r\n",
  986. "6.954493301173710895e-01 5.398844914884662893e-01 7.058277231806755481e-01\r\n",
  987. "7.487520572646998440e-01 9.427574847574227146e-02 7.859238035716934467e-01\r\n"
  988. ]
  989. }
  990. ],
  991. "source": [
  992. "!cat random-matrix.csv"
  993. ]
  994. },
  995. {
  996. "cell_type": "code",
  997. "execution_count": 44,
  998. "metadata": {},
  999. "outputs": [
  1000. {
  1001. "name": "stdout",
  1002. "output_type": "stream",
  1003. "text": [
  1004. "0.23335 0.09866 0.05722\r\n",
  1005. "0.69545 0.53988 0.70583\r\n",
  1006. "0.74875 0.09428 0.78592\r\n"
  1007. ]
  1008. }
  1009. ],
  1010. "source": [
  1011. "np.savetxt(\"random-matrix.csv\", M, fmt='%.5f') # fmt 确定格式\n",
  1012. "\n",
  1013. "!cat random-matrix.csv"
  1014. ]
  1015. },
  1016. {
  1017. "cell_type": "markdown",
  1018. "metadata": {},
  1019. "source": [
  1020. "### 3.2 numpy 的本地文件格式"
  1021. ]
  1022. },
  1023. {
  1024. "cell_type": "markdown",
  1025. "metadata": {},
  1026. "source": [
  1027. "当存储和读取numpy数组时非常有用。利用函数`numpy.save`和`numpy.load`:"
  1028. ]
  1029. },
  1030. {
  1031. "cell_type": "code",
  1032. "execution_count": 45,
  1033. "metadata": {},
  1034. "outputs": [
  1035. {
  1036. "name": "stdout",
  1037. "output_type": "stream",
  1038. "text": [
  1039. "random-matrix.npy: data\r\n"
  1040. ]
  1041. }
  1042. ],
  1043. "source": [
  1044. "np.save(\"random-matrix.npy\", M)\n",
  1045. "\n",
  1046. "!file random-matrix.npy"
  1047. ]
  1048. },
  1049. {
  1050. "cell_type": "code",
  1051. "execution_count": 46,
  1052. "metadata": {},
  1053. "outputs": [
  1054. {
  1055. "data": {
  1056. "text/plain": [
  1057. "array([[0.23335391, 0.0986599 , 0.0572248 ],\n",
  1058. " [0.69544933, 0.53988449, 0.70582772],\n",
  1059. " [0.74875206, 0.09427575, 0.7859238 ]])"
  1060. ]
  1061. },
  1062. "execution_count": 46,
  1063. "metadata": {},
  1064. "output_type": "execute_result"
  1065. }
  1066. ],
  1067. "source": [
  1068. "np.load(\"random-matrix.npy\")"
  1069. ]
  1070. },
  1071. {
  1072. "cell_type": "markdown",
  1073. "metadata": {},
  1074. "source": [
  1075. "## 4. 更多Numpy数组的性质"
  1076. ]
  1077. },
  1078. {
  1079. "cell_type": "code",
  1080. "execution_count": 47,
  1081. "metadata": {},
  1082. "outputs": [
  1083. {
  1084. "name": "stdout",
  1085. "output_type": "stream",
  1086. "text": [
  1087. "int64\n",
  1088. "8\n"
  1089. ]
  1090. }
  1091. ],
  1092. "source": [
  1093. "M = np.array([[1, 2], [3, 4], [5, 6]])\n",
  1094. "\n",
  1095. "print(M.dtype)\n",
  1096. "print(M.itemsize) # 每个元素的字节数\n"
  1097. ]
  1098. },
  1099. {
  1100. "cell_type": "code",
  1101. "execution_count": 48,
  1102. "metadata": {},
  1103. "outputs": [
  1104. {
  1105. "data": {
  1106. "text/plain": [
  1107. "48"
  1108. ]
  1109. },
  1110. "execution_count": 48,
  1111. "metadata": {},
  1112. "output_type": "execute_result"
  1113. }
  1114. ],
  1115. "source": [
  1116. "M.nbytes # 字节数"
  1117. ]
  1118. },
  1119. {
  1120. "cell_type": "code",
  1121. "execution_count": 49,
  1122. "metadata": {},
  1123. "outputs": [
  1124. {
  1125. "data": {
  1126. "text/plain": [
  1127. "2"
  1128. ]
  1129. },
  1130. "execution_count": 49,
  1131. "metadata": {},
  1132. "output_type": "execute_result"
  1133. }
  1134. ],
  1135. "source": [
  1136. "M.ndim # 维度"
  1137. ]
  1138. },
  1139. {
  1140. "cell_type": "markdown",
  1141. "metadata": {},
  1142. "source": [
  1143. "## 5. 操作数组"
  1144. ]
  1145. },
  1146. {
  1147. "cell_type": "markdown",
  1148. "metadata": {},
  1149. "source": [
  1150. "### 5.1 索引"
  1151. ]
  1152. },
  1153. {
  1154. "cell_type": "markdown",
  1155. "metadata": {},
  1156. "source": [
  1157. "我们可以用方括号和下标索引元素:"
  1158. ]
  1159. },
  1160. {
  1161. "cell_type": "code",
  1162. "execution_count": 50,
  1163. "metadata": {},
  1164. "outputs": [
  1165. {
  1166. "data": {
  1167. "text/plain": [
  1168. "1"
  1169. ]
  1170. },
  1171. "execution_count": 50,
  1172. "metadata": {},
  1173. "output_type": "execute_result"
  1174. }
  1175. ],
  1176. "source": [
  1177. "v = np.array([1, 2, 3, 4, 5])\n",
  1178. "# v 是一个向量,仅仅只有一维,取一个索引\n",
  1179. "v[0]"
  1180. ]
  1181. },
  1182. {
  1183. "cell_type": "code",
  1184. "execution_count": 51,
  1185. "metadata": {},
  1186. "outputs": [
  1187. {
  1188. "name": "stdout",
  1189. "output_type": "stream",
  1190. "text": [
  1191. "4\n",
  1192. "4\n",
  1193. "[3 4]\n"
  1194. ]
  1195. }
  1196. ],
  1197. "source": [
  1198. "\n",
  1199. "# M 是一个矩阵或者是一个二维的数组,取两个索引 \n",
  1200. "print(M[1,1])\n",
  1201. "print(M[1][1])\n",
  1202. "print(M[1])"
  1203. ]
  1204. },
  1205. {
  1206. "cell_type": "markdown",
  1207. "metadata": {},
  1208. "source": [
  1209. "如果我们省略了一个多维数组的索引,它将会返回整行(或者,总的来说,一个 N-1 维的数组)"
  1210. ]
  1211. },
  1212. {
  1213. "cell_type": "code",
  1214. "execution_count": 52,
  1215. "metadata": {},
  1216. "outputs": [
  1217. {
  1218. "data": {
  1219. "text/plain": [
  1220. "array([[1, 2],\n",
  1221. " [3, 4],\n",
  1222. " [5, 6]])"
  1223. ]
  1224. },
  1225. "execution_count": 52,
  1226. "metadata": {},
  1227. "output_type": "execute_result"
  1228. }
  1229. ],
  1230. "source": [
  1231. "M"
  1232. ]
  1233. },
  1234. {
  1235. "cell_type": "code",
  1236. "execution_count": 53,
  1237. "metadata": {},
  1238. "outputs": [
  1239. {
  1240. "data": {
  1241. "text/plain": [
  1242. "array([3, 4])"
  1243. ]
  1244. },
  1245. "execution_count": 53,
  1246. "metadata": {},
  1247. "output_type": "execute_result"
  1248. }
  1249. ],
  1250. "source": [
  1251. "M[1]"
  1252. ]
  1253. },
  1254. {
  1255. "cell_type": "markdown",
  1256. "metadata": {},
  1257. "source": [
  1258. "相同的事情可以利用`:`而不是索引来实现:"
  1259. ]
  1260. },
  1261. {
  1262. "cell_type": "code",
  1263. "execution_count": 54,
  1264. "metadata": {},
  1265. "outputs": [
  1266. {
  1267. "data": {
  1268. "text/plain": [
  1269. "array([3, 4])"
  1270. ]
  1271. },
  1272. "execution_count": 54,
  1273. "metadata": {},
  1274. "output_type": "execute_result"
  1275. }
  1276. ],
  1277. "source": [
  1278. "M[1,:] # 行 1"
  1279. ]
  1280. },
  1281. {
  1282. "cell_type": "code",
  1283. "execution_count": 55,
  1284. "metadata": {},
  1285. "outputs": [
  1286. {
  1287. "data": {
  1288. "text/plain": [
  1289. "array([2, 4, 6])"
  1290. ]
  1291. },
  1292. "execution_count": 55,
  1293. "metadata": {},
  1294. "output_type": "execute_result"
  1295. }
  1296. ],
  1297. "source": [
  1298. "M[:,1] # 列 1"
  1299. ]
  1300. },
  1301. {
  1302. "cell_type": "markdown",
  1303. "metadata": {},
  1304. "source": [
  1305. "我们可以用索引赋新的值给数组中的元素:"
  1306. ]
  1307. },
  1308. {
  1309. "cell_type": "code",
  1310. "execution_count": 56,
  1311. "metadata": {},
  1312. "outputs": [],
  1313. "source": [
  1314. "M[0,0] = 1"
  1315. ]
  1316. },
  1317. {
  1318. "cell_type": "code",
  1319. "execution_count": 57,
  1320. "metadata": {},
  1321. "outputs": [
  1322. {
  1323. "data": {
  1324. "text/plain": [
  1325. "array([[1, 2],\n",
  1326. " [3, 4],\n",
  1327. " [5, 6]])"
  1328. ]
  1329. },
  1330. "execution_count": 57,
  1331. "metadata": {},
  1332. "output_type": "execute_result"
  1333. }
  1334. ],
  1335. "source": [
  1336. "M"
  1337. ]
  1338. },
  1339. {
  1340. "cell_type": "code",
  1341. "execution_count": 58,
  1342. "metadata": {},
  1343. "outputs": [],
  1344. "source": [
  1345. "# 对行和列也同样有用\n",
  1346. "M[1,:] = 0\n",
  1347. "M[:,1] = -1"
  1348. ]
  1349. },
  1350. {
  1351. "cell_type": "code",
  1352. "execution_count": 59,
  1353. "metadata": {},
  1354. "outputs": [
  1355. {
  1356. "data": {
  1357. "text/plain": [
  1358. "array([[ 1, -1],\n",
  1359. " [ 0, -1],\n",
  1360. " [ 5, -1]])"
  1361. ]
  1362. },
  1363. "execution_count": 59,
  1364. "metadata": {},
  1365. "output_type": "execute_result"
  1366. }
  1367. ],
  1368. "source": [
  1369. "M"
  1370. ]
  1371. },
  1372. {
  1373. "cell_type": "markdown",
  1374. "metadata": {},
  1375. "source": [
  1376. "### 5.2 切片索引"
  1377. ]
  1378. },
  1379. {
  1380. "cell_type": "markdown",
  1381. "metadata": {},
  1382. "source": [
  1383. "切片索引是语法`M[lower:upper:step]`的技术名称,用于提取数组的一部分:"
  1384. ]
  1385. },
  1386. {
  1387. "cell_type": "code",
  1388. "execution_count": 60,
  1389. "metadata": {},
  1390. "outputs": [
  1391. {
  1392. "data": {
  1393. "text/plain": [
  1394. "array([1, 2, 3, 4, 5])"
  1395. ]
  1396. },
  1397. "execution_count": 60,
  1398. "metadata": {},
  1399. "output_type": "execute_result"
  1400. }
  1401. ],
  1402. "source": [
  1403. "A = np.array([1,2,3,4,5])\n",
  1404. "A"
  1405. ]
  1406. },
  1407. {
  1408. "cell_type": "code",
  1409. "execution_count": 61,
  1410. "metadata": {},
  1411. "outputs": [
  1412. {
  1413. "data": {
  1414. "text/plain": [
  1415. "array([2, 3])"
  1416. ]
  1417. },
  1418. "execution_count": 61,
  1419. "metadata": {},
  1420. "output_type": "execute_result"
  1421. }
  1422. ],
  1423. "source": [
  1424. "A[1:3]"
  1425. ]
  1426. },
  1427. {
  1428. "cell_type": "markdown",
  1429. "metadata": {},
  1430. "source": [
  1431. "切片索引是*可变的*: 如果它们被分配了一个新值,那么从其中提取切片的原始数组将被修改:\n"
  1432. ]
  1433. },
  1434. {
  1435. "cell_type": "code",
  1436. "execution_count": 62,
  1437. "metadata": {},
  1438. "outputs": [
  1439. {
  1440. "data": {
  1441. "text/plain": [
  1442. "array([ 1, -2, -3, 4, 5])"
  1443. ]
  1444. },
  1445. "execution_count": 62,
  1446. "metadata": {},
  1447. "output_type": "execute_result"
  1448. }
  1449. ],
  1450. "source": [
  1451. "A[1:3] = [-2,-3] # auto convert type\n",
  1452. "A[1:3] = np.array([-2, -3]) \n",
  1453. "\n",
  1454. "A"
  1455. ]
  1456. },
  1457. {
  1458. "cell_type": "markdown",
  1459. "metadata": {},
  1460. "source": [
  1461. "我们可以省略`M[lower:upper:step]`中任意的三个值\n",
  1462. "We can omit any of the three parameters in `M[lower:upper:step]`:"
  1463. ]
  1464. },
  1465. {
  1466. "cell_type": "code",
  1467. "execution_count": 63,
  1468. "metadata": {},
  1469. "outputs": [
  1470. {
  1471. "data": {
  1472. "text/plain": [
  1473. "array([ 1, -2, -3, 4, 5])"
  1474. ]
  1475. },
  1476. "execution_count": 63,
  1477. "metadata": {},
  1478. "output_type": "execute_result"
  1479. }
  1480. ],
  1481. "source": [
  1482. "A[::] # lower, upper, step 都取默认值"
  1483. ]
  1484. },
  1485. {
  1486. "cell_type": "code",
  1487. "execution_count": 64,
  1488. "metadata": {},
  1489. "outputs": [
  1490. {
  1491. "data": {
  1492. "text/plain": [
  1493. "array([ 1, -2, -3, 4, 5])"
  1494. ]
  1495. },
  1496. "execution_count": 64,
  1497. "metadata": {},
  1498. "output_type": "execute_result"
  1499. }
  1500. ],
  1501. "source": [
  1502. "A[:]"
  1503. ]
  1504. },
  1505. {
  1506. "cell_type": "code",
  1507. "execution_count": 65,
  1508. "metadata": {},
  1509. "outputs": [
  1510. {
  1511. "data": {
  1512. "text/plain": [
  1513. "array([ 1, -3, 5])"
  1514. ]
  1515. },
  1516. "execution_count": 65,
  1517. "metadata": {},
  1518. "output_type": "execute_result"
  1519. }
  1520. ],
  1521. "source": [
  1522. "A[::2] # step is 2, lower and upper 代表数组的开始和结束"
  1523. ]
  1524. },
  1525. {
  1526. "cell_type": "code",
  1527. "execution_count": 66,
  1528. "metadata": {},
  1529. "outputs": [
  1530. {
  1531. "data": {
  1532. "text/plain": [
  1533. "array([ 1, -2, -3])"
  1534. ]
  1535. },
  1536. "execution_count": 66,
  1537. "metadata": {},
  1538. "output_type": "execute_result"
  1539. }
  1540. ],
  1541. "source": [
  1542. "A[:3] # 前3个元素"
  1543. ]
  1544. },
  1545. {
  1546. "cell_type": "code",
  1547. "execution_count": 67,
  1548. "metadata": {},
  1549. "outputs": [
  1550. {
  1551. "data": {
  1552. "text/plain": [
  1553. "array([4, 5])"
  1554. ]
  1555. },
  1556. "execution_count": 67,
  1557. "metadata": {},
  1558. "output_type": "execute_result"
  1559. }
  1560. ],
  1561. "source": [
  1562. "A[3:] # 从索引3开始的元素"
  1563. ]
  1564. },
  1565. {
  1566. "cell_type": "markdown",
  1567. "metadata": {},
  1568. "source": [
  1569. "负索引计数从数组的结束(正索引从开始):"
  1570. ]
  1571. },
  1572. {
  1573. "cell_type": "code",
  1574. "execution_count": 68,
  1575. "metadata": {},
  1576. "outputs": [],
  1577. "source": [
  1578. "A = np.array([1,2,3,4,5])"
  1579. ]
  1580. },
  1581. {
  1582. "cell_type": "code",
  1583. "execution_count": 69,
  1584. "metadata": {},
  1585. "outputs": [
  1586. {
  1587. "data": {
  1588. "text/plain": [
  1589. "5"
  1590. ]
  1591. },
  1592. "execution_count": 69,
  1593. "metadata": {},
  1594. "output_type": "execute_result"
  1595. }
  1596. ],
  1597. "source": [
  1598. "A[-1] # 数组中最后一个元素"
  1599. ]
  1600. },
  1601. {
  1602. "cell_type": "code",
  1603. "execution_count": 70,
  1604. "metadata": {},
  1605. "outputs": [
  1606. {
  1607. "data": {
  1608. "text/plain": [
  1609. "array([3, 4, 5])"
  1610. ]
  1611. },
  1612. "execution_count": 70,
  1613. "metadata": {},
  1614. "output_type": "execute_result"
  1615. }
  1616. ],
  1617. "source": [
  1618. "A[-3:] # 最后三个元素"
  1619. ]
  1620. },
  1621. {
  1622. "cell_type": "markdown",
  1623. "metadata": {},
  1624. "source": [
  1625. "索引切片的工作方式与多维数组完全相同:"
  1626. ]
  1627. },
  1628. {
  1629. "cell_type": "code",
  1630. "execution_count": 71,
  1631. "metadata": {},
  1632. "outputs": [
  1633. {
  1634. "data": {
  1635. "text/plain": [
  1636. "array([[ 0, 1, 2, 3, 4],\n",
  1637. " [10, 11, 12, 13, 14],\n",
  1638. " [20, 21, 22, 23, 24],\n",
  1639. " [30, 31, 32, 33, 34],\n",
  1640. " [40, 41, 42, 43, 44]])"
  1641. ]
  1642. },
  1643. "execution_count": 71,
  1644. "metadata": {},
  1645. "output_type": "execute_result"
  1646. }
  1647. ],
  1648. "source": [
  1649. "A = np.array([[n+m*10 for n in range(5)] for m in range(5)])\n",
  1650. "\n",
  1651. "A"
  1652. ]
  1653. },
  1654. {
  1655. "cell_type": "code",
  1656. "execution_count": 72,
  1657. "metadata": {},
  1658. "outputs": [
  1659. {
  1660. "data": {
  1661. "text/plain": [
  1662. "array([[11, 12, 13],\n",
  1663. " [21, 22, 23],\n",
  1664. " [31, 32, 33]])"
  1665. ]
  1666. },
  1667. "execution_count": 72,
  1668. "metadata": {},
  1669. "output_type": "execute_result"
  1670. }
  1671. ],
  1672. "source": [
  1673. "# 原始数组中的一个块\n",
  1674. "A[1:4, 1:4]"
  1675. ]
  1676. },
  1677. {
  1678. "cell_type": "code",
  1679. "execution_count": 66,
  1680. "metadata": {},
  1681. "outputs": [
  1682. {
  1683. "data": {
  1684. "text/plain": [
  1685. "array([[ 0, 2, 4],\n",
  1686. " [20, 22, 24],\n",
  1687. " [40, 42, 44]])"
  1688. ]
  1689. },
  1690. "execution_count": 66,
  1691. "metadata": {},
  1692. "output_type": "execute_result"
  1693. }
  1694. ],
  1695. "source": [
  1696. "# 步长\n",
  1697. "A[::2, ::2]"
  1698. ]
  1699. },
  1700. {
  1701. "cell_type": "markdown",
  1702. "metadata": {},
  1703. "source": [
  1704. "### 5.3 花式索引"
  1705. ]
  1706. },
  1707. {
  1708. "cell_type": "markdown",
  1709. "metadata": {},
  1710. "source": [
  1711. "Fancy索引是一个名称时,一个数组或列表被使用在一个索引:"
  1712. ]
  1713. },
  1714. {
  1715. "cell_type": "code",
  1716. "execution_count": 74,
  1717. "metadata": {},
  1718. "outputs": [
  1719. {
  1720. "name": "stdout",
  1721. "output_type": "stream",
  1722. "text": [
  1723. "[[10 11 12 13 14]\n",
  1724. " [20 21 22 23 24]\n",
  1725. " [30 31 32 33 34]]\n",
  1726. "[[ 0 1 2 3 4]\n",
  1727. " [10 11 12 13 14]\n",
  1728. " [20 21 22 23 24]\n",
  1729. " [30 31 32 33 34]\n",
  1730. " [40 41 42 43 44]]\n"
  1731. ]
  1732. }
  1733. ],
  1734. "source": [
  1735. "A = np.array([[n+m*10 for n in range(5)] for m in range(5)])\n",
  1736. "\n",
  1737. "row_indices = [1, 2, 3]\n",
  1738. "print(A[row_indices])\n",
  1739. "print(A)"
  1740. ]
  1741. },
  1742. {
  1743. "cell_type": "code",
  1744. "execution_count": 75,
  1745. "metadata": {},
  1746. "outputs": [
  1747. {
  1748. "data": {
  1749. "text/plain": [
  1750. "array([11, 21, 34])"
  1751. ]
  1752. },
  1753. "execution_count": 75,
  1754. "metadata": {},
  1755. "output_type": "execute_result"
  1756. }
  1757. ],
  1758. "source": [
  1759. "col_indices = [1, 1, -1] # 索引-1 代表最后一个元素\n",
  1760. "A[row_indices, col_indices]"
  1761. ]
  1762. },
  1763. {
  1764. "cell_type": "markdown",
  1765. "metadata": {},
  1766. "source": [
  1767. "我们也可以使用索引掩码:如果索引掩码是一个数据类型`bool`的Numpy数组,那么一个元素被选择(True)或不(False)取决于索引掩码在每个元素位置的值:"
  1768. ]
  1769. },
  1770. {
  1771. "cell_type": "code",
  1772. "execution_count": 77,
  1773. "metadata": {},
  1774. "outputs": [
  1775. {
  1776. "data": {
  1777. "text/plain": [
  1778. "array([0, 1, 2, 3, 4])"
  1779. ]
  1780. },
  1781. "execution_count": 77,
  1782. "metadata": {},
  1783. "output_type": "execute_result"
  1784. }
  1785. ],
  1786. "source": [
  1787. "B = np.array([n for n in range(5)])\n",
  1788. "B"
  1789. ]
  1790. },
  1791. {
  1792. "cell_type": "code",
  1793. "execution_count": 79,
  1794. "metadata": {},
  1795. "outputs": [
  1796. {
  1797. "data": {
  1798. "text/plain": [
  1799. "array([0, 2])"
  1800. ]
  1801. },
  1802. "execution_count": 79,
  1803. "metadata": {},
  1804. "output_type": "execute_result"
  1805. }
  1806. ],
  1807. "source": [
  1808. "row_mask = np.array([True, False, True, False, False])\n",
  1809. "B[row_mask]"
  1810. ]
  1811. },
  1812. {
  1813. "cell_type": "code",
  1814. "execution_count": 81,
  1815. "metadata": {},
  1816. "outputs": [
  1817. {
  1818. "data": {
  1819. "text/plain": [
  1820. "array([0, 2])"
  1821. ]
  1822. },
  1823. "execution_count": 81,
  1824. "metadata": {},
  1825. "output_type": "execute_result"
  1826. }
  1827. ],
  1828. "source": [
  1829. "# 相同的事情\n",
  1830. "row_mask = np.array([1,0,1,0,0], dtype=bool)\n",
  1831. "B[row_mask]"
  1832. ]
  1833. },
  1834. {
  1835. "cell_type": "markdown",
  1836. "metadata": {},
  1837. "source": [
  1838. "这个特性对于有条件地从数组中选择元素非常有用,例如使用比较运算符:"
  1839. ]
  1840. },
  1841. {
  1842. "cell_type": "code",
  1843. "execution_count": 82,
  1844. "metadata": {},
  1845. "outputs": [
  1846. {
  1847. "data": {
  1848. "text/plain": [
  1849. "array([0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5, 5. , 5.5, 6. ,\n",
  1850. " 6.5, 7. , 7.5, 8. , 8.5, 9. , 9.5])"
  1851. ]
  1852. },
  1853. "execution_count": 82,
  1854. "metadata": {},
  1855. "output_type": "execute_result"
  1856. }
  1857. ],
  1858. "source": [
  1859. "x = np.arange(0, 10, 0.5)\n",
  1860. "x"
  1861. ]
  1862. },
  1863. {
  1864. "cell_type": "code",
  1865. "execution_count": 84,
  1866. "metadata": {},
  1867. "outputs": [
  1868. {
  1869. "data": {
  1870. "text/plain": [
  1871. "array([False, False, False, False, False, False, False, False, False,\n",
  1872. " False, False, True, True, True, True, False, False, False,\n",
  1873. " False, False])"
  1874. ]
  1875. },
  1876. "execution_count": 84,
  1877. "metadata": {},
  1878. "output_type": "execute_result"
  1879. }
  1880. ],
  1881. "source": [
  1882. "mask = (5 < x) * (x < 7.5)\n",
  1883. "\n",
  1884. "mask"
  1885. ]
  1886. },
  1887. {
  1888. "cell_type": "code",
  1889. "execution_count": 85,
  1890. "metadata": {},
  1891. "outputs": [
  1892. {
  1893. "data": {
  1894. "text/plain": [
  1895. "array([5.5, 6. , 6.5, 7. ])"
  1896. ]
  1897. },
  1898. "execution_count": 85,
  1899. "metadata": {},
  1900. "output_type": "execute_result"
  1901. }
  1902. ],
  1903. "source": [
  1904. "x[mask]"
  1905. ]
  1906. },
  1907. {
  1908. "cell_type": "code",
  1909. "execution_count": 86,
  1910. "metadata": {},
  1911. "outputs": [
  1912. {
  1913. "data": {
  1914. "text/plain": [
  1915. "array([3.5, 4. , 4.5, 5. , 5.5])"
  1916. ]
  1917. },
  1918. "execution_count": 86,
  1919. "metadata": {},
  1920. "output_type": "execute_result"
  1921. }
  1922. ],
  1923. "source": [
  1924. "x[(3<x) * (x<6)]"
  1925. ]
  1926. },
  1927. {
  1928. "cell_type": "markdown",
  1929. "metadata": {},
  1930. "source": [
  1931. "## 6. 用于从数组中提取数据和创建数组的函数"
  1932. ]
  1933. },
  1934. {
  1935. "cell_type": "markdown",
  1936. "metadata": {},
  1937. "source": [
  1938. "### 6.1 where"
  1939. ]
  1940. },
  1941. {
  1942. "cell_type": "markdown",
  1943. "metadata": {},
  1944. "source": [
  1945. "索引掩码可以使用`where`函数转换为位置索引"
  1946. ]
  1947. },
  1948. {
  1949. "cell_type": "code",
  1950. "execution_count": 88,
  1951. "metadata": {},
  1952. "outputs": [
  1953. {
  1954. "data": {
  1955. "text/plain": [
  1956. "(array([11, 12, 13, 14]),)"
  1957. ]
  1958. },
  1959. "execution_count": 88,
  1960. "metadata": {},
  1961. "output_type": "execute_result"
  1962. }
  1963. ],
  1964. "source": [
  1965. "x = np.arange(0, 10, 0.5)\n",
  1966. "mask = (5 < x) * (x < 7.5)\n",
  1967. "\n",
  1968. "indices = np.where(mask)\n",
  1969. "\n",
  1970. "indices"
  1971. ]
  1972. },
  1973. {
  1974. "cell_type": "code",
  1975. "execution_count": 89,
  1976. "metadata": {},
  1977. "outputs": [
  1978. {
  1979. "data": {
  1980. "text/plain": [
  1981. "array([5.5, 6. , 6.5, 7. ])"
  1982. ]
  1983. },
  1984. "execution_count": 89,
  1985. "metadata": {},
  1986. "output_type": "execute_result"
  1987. }
  1988. ],
  1989. "source": [
  1990. "x[indices] # 这个索引等同于花式索引x[mask]"
  1991. ]
  1992. },
  1993. {
  1994. "cell_type": "markdown",
  1995. "metadata": {},
  1996. "source": [
  1997. "### 6.2 diag"
  1998. ]
  1999. },
  2000. {
  2001. "cell_type": "markdown",
  2002. "metadata": {},
  2003. "source": [
  2004. "使用diag函数,我们还可以提取一个数组的对角线和亚对角线:"
  2005. ]
  2006. },
  2007. {
  2008. "cell_type": "code",
  2009. "execution_count": 90,
  2010. "metadata": {},
  2011. "outputs": [
  2012. {
  2013. "data": {
  2014. "text/plain": [
  2015. "array([ 0, 11, 22, 33, 44])"
  2016. ]
  2017. },
  2018. "execution_count": 90,
  2019. "metadata": {},
  2020. "output_type": "execute_result"
  2021. }
  2022. ],
  2023. "source": [
  2024. "np.diag(A)"
  2025. ]
  2026. },
  2027. {
  2028. "cell_type": "code",
  2029. "execution_count": 91,
  2030. "metadata": {},
  2031. "outputs": [
  2032. {
  2033. "data": {
  2034. "text/plain": [
  2035. "array([10, 21, 32, 43])"
  2036. ]
  2037. },
  2038. "execution_count": 91,
  2039. "metadata": {},
  2040. "output_type": "execute_result"
  2041. }
  2042. ],
  2043. "source": [
  2044. "np.diag(A, -1)"
  2045. ]
  2046. },
  2047. {
  2048. "cell_type": "markdown",
  2049. "metadata": {},
  2050. "source": [
  2051. "## 7. 线性代数"
  2052. ]
  2053. },
  2054. {
  2055. "cell_type": "markdown",
  2056. "metadata": {},
  2057. "source": [
  2058. "向量化代码是使用Python/Numpy编写高效数值计算的关键。这意味着尽可能多的程序应该用矩阵和向量运算来表示,比如矩阵-矩阵乘法。"
  2059. ]
  2060. },
  2061. {
  2062. "cell_type": "markdown",
  2063. "metadata": {},
  2064. "source": [
  2065. "### 7.1 Scalar-array 操作"
  2066. ]
  2067. },
  2068. {
  2069. "cell_type": "markdown",
  2070. "metadata": {},
  2071. "source": [
  2072. "我们可以使用常用的算术运算符来对标量数组进行乘、加、减和除运算。"
  2073. ]
  2074. },
  2075. {
  2076. "cell_type": "code",
  2077. "execution_count": 96,
  2078. "metadata": {},
  2079. "outputs": [],
  2080. "source": [
  2081. "import numpy as np\n",
  2082. "\n",
  2083. "v1 = np.arange(0, 5)"
  2084. ]
  2085. },
  2086. {
  2087. "cell_type": "code",
  2088. "execution_count": 97,
  2089. "metadata": {},
  2090. "outputs": [
  2091. {
  2092. "data": {
  2093. "text/plain": [
  2094. "array([0, 2, 4, 6, 8])"
  2095. ]
  2096. },
  2097. "execution_count": 97,
  2098. "metadata": {},
  2099. "output_type": "execute_result"
  2100. }
  2101. ],
  2102. "source": [
  2103. "v1 * 2"
  2104. ]
  2105. },
  2106. {
  2107. "cell_type": "code",
  2108. "execution_count": 42,
  2109. "metadata": {},
  2110. "outputs": [
  2111. {
  2112. "data": {
  2113. "text/plain": [
  2114. "array([2, 3, 4, 5, 6])"
  2115. ]
  2116. },
  2117. "execution_count": 42,
  2118. "metadata": {},
  2119. "output_type": "execute_result"
  2120. }
  2121. ],
  2122. "source": [
  2123. "v1 + 2"
  2124. ]
  2125. },
  2126. {
  2127. "cell_type": "code",
  2128. "execution_count": 98,
  2129. "metadata": {},
  2130. "outputs": [
  2131. {
  2132. "data": {
  2133. "text/plain": [
  2134. "(array([[ 0, 2, 4, 6, 8],\n",
  2135. " [20, 22, 24, 26, 28],\n",
  2136. " [40, 42, 44, 46, 48],\n",
  2137. " [60, 62, 64, 66, 68],\n",
  2138. " [80, 82, 84, 86, 88]]),\n",
  2139. " array([[ 2, 3, 4, 5, 6],\n",
  2140. " [12, 13, 14, 15, 16],\n",
  2141. " [22, 23, 24, 25, 26],\n",
  2142. " [32, 33, 34, 35, 36],\n",
  2143. " [42, 43, 44, 45, 46]]))"
  2144. ]
  2145. },
  2146. "execution_count": 98,
  2147. "metadata": {},
  2148. "output_type": "execute_result"
  2149. }
  2150. ],
  2151. "source": [
  2152. "A = np.array([[n+m*10 for n in range(5)] for m in range(5)])\n",
  2153. "\n",
  2154. "A * 2, A + 2"
  2155. ]
  2156. },
  2157. {
  2158. "cell_type": "markdown",
  2159. "metadata": {},
  2160. "source": [
  2161. "### 7.2 数组间的元素操作"
  2162. ]
  2163. },
  2164. {
  2165. "cell_type": "markdown",
  2166. "metadata": {},
  2167. "source": [
  2168. "当我们对数组进行加法、减法、乘法和除法时,默认的行为是**element-wise**操作:"
  2169. ]
  2170. },
  2171. {
  2172. "cell_type": "code",
  2173. "execution_count": 99,
  2174. "metadata": {},
  2175. "outputs": [
  2176. {
  2177. "data": {
  2178. "text/plain": [
  2179. "array([[0.4704086 , 0.04100762, 0.31167633],\n",
  2180. " [0.66134738, 0.47887988, 0.09973749]])"
  2181. ]
  2182. },
  2183. "execution_count": 99,
  2184. "metadata": {},
  2185. "output_type": "execute_result"
  2186. }
  2187. ],
  2188. "source": [
  2189. "A = np.random.rand(2, 3)\n",
  2190. "\n",
  2191. "A * A # element-wise 乘法"
  2192. ]
  2193. },
  2194. {
  2195. "cell_type": "code",
  2196. "execution_count": 106,
  2197. "metadata": {},
  2198. "outputs": [
  2199. {
  2200. "data": {
  2201. "text/plain": [
  2202. "array([1., 4.])"
  2203. ]
  2204. },
  2205. "execution_count": 106,
  2206. "metadata": {},
  2207. "output_type": "execute_result"
  2208. }
  2209. ],
  2210. "source": [
  2211. "v1 = np.array([1.0, 2.0])\n",
  2212. "v1 * v1"
  2213. ]
  2214. },
  2215. {
  2216. "cell_type": "markdown",
  2217. "metadata": {},
  2218. "source": [
  2219. "如果我们用兼容的形状进行数组的乘法,我们会得到每一行的对位相乘结果:"
  2220. ]
  2221. },
  2222. {
  2223. "cell_type": "code",
  2224. "execution_count": 107,
  2225. "metadata": {},
  2226. "outputs": [
  2227. {
  2228. "data": {
  2229. "text/plain": [
  2230. "((2, 3), (2,))"
  2231. ]
  2232. },
  2233. "execution_count": 107,
  2234. "metadata": {},
  2235. "output_type": "execute_result"
  2236. }
  2237. ],
  2238. "source": [
  2239. "A.shape, v1.shape"
  2240. ]
  2241. },
  2242. {
  2243. "cell_type": "code",
  2244. "execution_count": 108,
  2245. "metadata": {},
  2246. "outputs": [
  2247. {
  2248. "ename": "ValueError",
  2249. "evalue": "operands could not be broadcast together with shapes (2,3) (2,) ",
  2250. "output_type": "error",
  2251. "traceback": [
  2252. "\u001b[0;31m-----------------------------------------------------------\u001b[0m",
  2253. "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
  2254. "\u001b[0;32m<ipython-input-108-1af134c5c5d0>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mA\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mv1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
  2255. "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (2,3) (2,) "
  2256. ]
  2257. }
  2258. ],
  2259. "source": [
  2260. "A * v1"
  2261. ]
  2262. },
  2263. {
  2264. "cell_type": "markdown",
  2265. "metadata": {},
  2266. "source": [
  2267. "### 7.4 矩阵代数"
  2268. ]
  2269. },
  2270. {
  2271. "cell_type": "markdown",
  2272. "metadata": {},
  2273. "source": [
  2274. "那么矩阵的乘法呢?有两种方法。我们可以使用点函数,它对两个参数应用矩阵-矩阵、矩阵-向量或内向量乘法"
  2275. ]
  2276. },
  2277. {
  2278. "cell_type": "code",
  2279. "execution_count": 124,
  2280. "metadata": {},
  2281. "outputs": [
  2282. {
  2283. "data": {
  2284. "text/plain": [
  2285. "array([[0.93919112, 1.70487505, 1.76705439, 1.3495362 , 1.46609022],\n",
  2286. " [0.8343938 , 1.88658078, 1.31805554, 1.24245149, 0.96131716],\n",
  2287. " [0.79755253, 1.70825859, 1.44585397, 1.04582713, 1.1244295 ],\n",
  2288. " [0.11333111, 0.60861172, 0.48009346, 0.70933735, 0.57239177],\n",
  2289. " [0.58048796, 1.28344711, 1.36267101, 1.10752867, 1.27728192]])"
  2290. ]
  2291. },
  2292. "execution_count": 124,
  2293. "metadata": {},
  2294. "output_type": "execute_result"
  2295. }
  2296. ],
  2297. "source": [
  2298. "A = np.random.rand(5, 5)\n",
  2299. "v1 = np.random.rand(5, 1)\n",
  2300. "\n",
  2301. "np.dot(A, A)"
  2302. ]
  2303. },
  2304. {
  2305. "cell_type": "code",
  2306. "execution_count": 125,
  2307. "metadata": {},
  2308. "outputs": [
  2309. {
  2310. "data": {
  2311. "text/plain": [
  2312. "array([[1.05508837],\n",
  2313. " [1.01103735],\n",
  2314. " [0.88771095],\n",
  2315. " [0.34107892],\n",
  2316. " [0.78814586]])"
  2317. ]
  2318. },
  2319. "execution_count": 125,
  2320. "metadata": {},
  2321. "output_type": "execute_result"
  2322. }
  2323. ],
  2324. "source": [
  2325. "np.dot(A, v1)"
  2326. ]
  2327. },
  2328. {
  2329. "cell_type": "code",
  2330. "execution_count": 126,
  2331. "metadata": {},
  2332. "outputs": [
  2333. {
  2334. "data": {
  2335. "text/plain": [
  2336. "array([[1.08640806]])"
  2337. ]
  2338. },
  2339. "execution_count": 126,
  2340. "metadata": {},
  2341. "output_type": "execute_result"
  2342. }
  2343. ],
  2344. "source": [
  2345. "np.dot(v1.T, v1)"
  2346. ]
  2347. },
  2348. {
  2349. "cell_type": "markdown",
  2350. "metadata": {},
  2351. "source": [
  2352. "另外,我们可以将数组对象投到`matrix`类型上。这将改变标准算术运算符`+, -, *` 的行为,以使用矩阵代数。"
  2353. ]
  2354. },
  2355. {
  2356. "cell_type": "code",
  2357. "execution_count": 127,
  2358. "metadata": {},
  2359. "outputs": [],
  2360. "source": [
  2361. "M = np.matrix(A)\n",
  2362. "v = np.matrix(v1).T # make it a column vector"
  2363. ]
  2364. },
  2365. {
  2366. "cell_type": "code",
  2367. "execution_count": 128,
  2368. "metadata": {},
  2369. "outputs": [
  2370. {
  2371. "data": {
  2372. "text/plain": [
  2373. "matrix([[0.65312574, 0.36553623, 0.01310058, 0.18549019, 0.70117034]])"
  2374. ]
  2375. },
  2376. "execution_count": 128,
  2377. "metadata": {},
  2378. "output_type": "execute_result"
  2379. }
  2380. ],
  2381. "source": [
  2382. "v"
  2383. ]
  2384. },
  2385. {
  2386. "cell_type": "code",
  2387. "execution_count": 129,
  2388. "metadata": {},
  2389. "outputs": [
  2390. {
  2391. "data": {
  2392. "text/plain": [
  2393. "matrix([[0.93919112, 1.70487505, 1.76705439, 1.3495362 , 1.46609022],\n",
  2394. " [0.8343938 , 1.88658078, 1.31805554, 1.24245149, 0.96131716],\n",
  2395. " [0.79755253, 1.70825859, 1.44585397, 1.04582713, 1.1244295 ],\n",
  2396. " [0.11333111, 0.60861172, 0.48009346, 0.70933735, 0.57239177],\n",
  2397. " [0.58048796, 1.28344711, 1.36267101, 1.10752867, 1.27728192]])"
  2398. ]
  2399. },
  2400. "execution_count": 129,
  2401. "metadata": {},
  2402. "output_type": "execute_result"
  2403. }
  2404. ],
  2405. "source": [
  2406. "M * M"
  2407. ]
  2408. },
  2409. {
  2410. "cell_type": "code",
  2411. "execution_count": 131,
  2412. "metadata": {},
  2413. "outputs": [
  2414. {
  2415. "data": {
  2416. "text/plain": [
  2417. "matrix([[1.05508837],\n",
  2418. " [1.01103735],\n",
  2419. " [0.88771095],\n",
  2420. " [0.34107892],\n",
  2421. " [0.78814586]])"
  2422. ]
  2423. },
  2424. "execution_count": 131,
  2425. "metadata": {},
  2426. "output_type": "execute_result"
  2427. }
  2428. ],
  2429. "source": [
  2430. "M * v.T"
  2431. ]
  2432. },
  2433. {
  2434. "cell_type": "code",
  2435. "execution_count": 133,
  2436. "metadata": {},
  2437. "outputs": [
  2438. {
  2439. "data": {
  2440. "text/plain": [
  2441. "matrix([[1.08640806]])"
  2442. ]
  2443. },
  2444. "execution_count": 133,
  2445. "metadata": {},
  2446. "output_type": "execute_result"
  2447. }
  2448. ],
  2449. "source": [
  2450. "# 內积\n",
  2451. "v * v.T"
  2452. ]
  2453. },
  2454. {
  2455. "cell_type": "code",
  2456. "execution_count": 19,
  2457. "metadata": {},
  2458. "outputs": [
  2459. {
  2460. "data": {
  2461. "text/plain": [
  2462. "matrix([[5.346923 ],\n",
  2463. " [7.32008278],\n",
  2464. " [9.66667311],\n",
  2465. " [6.19229347],\n",
  2466. " [8.84861051]])"
  2467. ]
  2468. },
  2469. "execution_count": 19,
  2470. "metadata": {},
  2471. "output_type": "execute_result"
  2472. }
  2473. ],
  2474. "source": [
  2475. "# 对于矩阵对象,适用标准的矩阵代数\n",
  2476. "v + M*v"
  2477. ]
  2478. },
  2479. {
  2480. "cell_type": "markdown",
  2481. "metadata": {},
  2482. "source": [
  2483. "如果我们尝试用不相配的矩阵形状加,减或者乘我们会得到错误:"
  2484. ]
  2485. },
  2486. {
  2487. "cell_type": "code",
  2488. "execution_count": 134,
  2489. "metadata": {},
  2490. "outputs": [],
  2491. "source": [
  2492. "v = np.matrix([1,2,3,4,5,6]).T"
  2493. ]
  2494. },
  2495. {
  2496. "cell_type": "code",
  2497. "execution_count": 135,
  2498. "metadata": {},
  2499. "outputs": [
  2500. {
  2501. "data": {
  2502. "text/plain": [
  2503. "((5, 5), (6, 1))"
  2504. ]
  2505. },
  2506. "execution_count": 135,
  2507. "metadata": {},
  2508. "output_type": "execute_result"
  2509. }
  2510. ],
  2511. "source": [
  2512. "np.shape(M), np.shape(v)"
  2513. ]
  2514. },
  2515. {
  2516. "cell_type": "code",
  2517. "execution_count": 136,
  2518. "metadata": {},
  2519. "outputs": [
  2520. {
  2521. "ename": "ValueError",
  2522. "evalue": "shapes (5,5) and (6,1) not aligned: 5 (dim 1) != 6 (dim 0)",
  2523. "output_type": "error",
  2524. "traceback": [
  2525. "\u001b[0;31m-----------------------------------------------------------\u001b[0m",
  2526. "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
  2527. "\u001b[0;32m<ipython-input-136-e8f88679fe45>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mM\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
  2528. "\u001b[0;32m~/virtualenv/dl/lib/python3.6/site-packages/numpy/matrixlib/defmatrix.py\u001b[0m in \u001b[0;36m__mul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m 218\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndarray\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 219\u001b[0m \u001b[0;31m# This promotes 1-D vectors to row vectors\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 220\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mN\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0masmatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 221\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misscalar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mother\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'__rmul__'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 222\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mN\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mother\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
  2529. "\u001b[0;32m<__array_function__ internals>\u001b[0m in \u001b[0;36mdot\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
  2530. "\u001b[0;31mValueError\u001b[0m: shapes (5,5) and (6,1) not aligned: 5 (dim 1) != 6 (dim 0)"
  2531. ]
  2532. }
  2533. ],
  2534. "source": [
  2535. "M * v"
  2536. ]
  2537. },
  2538. {
  2539. "cell_type": "markdown",
  2540. "metadata": {},
  2541. "source": [
  2542. "同样了解相关的函数:`inner`, `outer`, `cross`, `kron`, `tensordot`。例如用`help(kron)`。"
  2543. ]
  2544. },
  2545. {
  2546. "cell_type": "markdown",
  2547. "metadata": {},
  2548. "source": [
  2549. "### 7.5 数组/矩阵转换"
  2550. ]
  2551. },
  2552. {
  2553. "cell_type": "markdown",
  2554. "metadata": {},
  2555. "source": [
  2556. "同样我们也用`.T`对矩阵目标`v`进行转置。我们也可以利用`transpose`函数去实现同样的事情。\n",
  2557. "\n",
  2558. "变换矩阵对象的其他数学函数有:"
  2559. ]
  2560. },
  2561. {
  2562. "cell_type": "code",
  2563. "execution_count": 137,
  2564. "metadata": {},
  2565. "outputs": [
  2566. {
  2567. "name": "stdout",
  2568. "output_type": "stream",
  2569. "text": [
  2570. "[[0.59227725 0.17647736 0.32760242 0.94853282]\n",
  2571. " [0.47433311 0.96295875 0.53835066 0.65341328]\n",
  2572. " [0.31043303 0.91920326 0.11855559 0.96115268]]\n",
  2573. "[[0.59227725 0.47433311 0.31043303]\n",
  2574. " [0.17647736 0.96295875 0.91920326]\n",
  2575. " [0.32760242 0.53835066 0.11855559]\n",
  2576. " [0.94853282 0.65341328 0.96115268]]\n"
  2577. ]
  2578. }
  2579. ],
  2580. "source": [
  2581. "A = np.random.rand(3,4)\n",
  2582. "print(A)\n",
  2583. "print(A.T)"
  2584. ]
  2585. },
  2586. {
  2587. "cell_type": "code",
  2588. "execution_count": 138,
  2589. "metadata": {},
  2590. "outputs": [
  2591. {
  2592. "data": {
  2593. "text/plain": [
  2594. "matrix([[0.+1.j, 0.+2.j],\n",
  2595. " [0.+3.j, 0.+4.j]])"
  2596. ]
  2597. },
  2598. "execution_count": 138,
  2599. "metadata": {},
  2600. "output_type": "execute_result"
  2601. }
  2602. ],
  2603. "source": [
  2604. "C = np.matrix([[1j, 2j], [3j, 4j]])\n",
  2605. "C"
  2606. ]
  2607. },
  2608. {
  2609. "cell_type": "code",
  2610. "execution_count": 139,
  2611. "metadata": {},
  2612. "outputs": [
  2613. {
  2614. "data": {
  2615. "text/plain": [
  2616. "matrix([[0.-1.j, 0.-2.j],\n",
  2617. " [0.-3.j, 0.-4.j]])"
  2618. ]
  2619. },
  2620. "execution_count": 139,
  2621. "metadata": {},
  2622. "output_type": "execute_result"
  2623. }
  2624. ],
  2625. "source": [
  2626. "np.conjugate(C)"
  2627. ]
  2628. },
  2629. {
  2630. "cell_type": "markdown",
  2631. "metadata": {},
  2632. "source": [
  2633. "厄米共轭:转置+共轭"
  2634. ]
  2635. },
  2636. {
  2637. "cell_type": "code",
  2638. "execution_count": 140,
  2639. "metadata": {},
  2640. "outputs": [
  2641. {
  2642. "data": {
  2643. "text/plain": [
  2644. "matrix([[0.-1.j, 0.-3.j],\n",
  2645. " [0.-2.j, 0.-4.j]])"
  2646. ]
  2647. },
  2648. "execution_count": 140,
  2649. "metadata": {},
  2650. "output_type": "execute_result"
  2651. }
  2652. ],
  2653. "source": [
  2654. "C.H"
  2655. ]
  2656. },
  2657. {
  2658. "cell_type": "markdown",
  2659. "metadata": {},
  2660. "source": [
  2661. "我们可以将复数数组的实部和虚部提取出来并用`real`和`imag`来表示:"
  2662. ]
  2663. },
  2664. {
  2665. "cell_type": "code",
  2666. "execution_count": 141,
  2667. "metadata": {},
  2668. "outputs": [
  2669. {
  2670. "data": {
  2671. "text/plain": [
  2672. "matrix([[0., 0.],\n",
  2673. " [0., 0.]])"
  2674. ]
  2675. },
  2676. "execution_count": 141,
  2677. "metadata": {},
  2678. "output_type": "execute_result"
  2679. }
  2680. ],
  2681. "source": [
  2682. "np.real(C) # same as: C.real"
  2683. ]
  2684. },
  2685. {
  2686. "cell_type": "code",
  2687. "execution_count": 142,
  2688. "metadata": {},
  2689. "outputs": [
  2690. {
  2691. "data": {
  2692. "text/plain": [
  2693. "matrix([[1., 2.],\n",
  2694. " [3., 4.]])"
  2695. ]
  2696. },
  2697. "execution_count": 142,
  2698. "metadata": {},
  2699. "output_type": "execute_result"
  2700. }
  2701. ],
  2702. "source": [
  2703. "np.imag(C) # same as: C.imag"
  2704. ]
  2705. },
  2706. {
  2707. "cell_type": "markdown",
  2708. "metadata": {},
  2709. "source": [
  2710. "或者说复数和绝对值"
  2711. ]
  2712. },
  2713. {
  2714. "cell_type": "code",
  2715. "execution_count": 143,
  2716. "metadata": {},
  2717. "outputs": [
  2718. {
  2719. "data": {
  2720. "text/plain": [
  2721. "matrix([[0.78539816, 1.10714872],\n",
  2722. " [1.24904577, 1.32581766]])"
  2723. ]
  2724. },
  2725. "execution_count": 143,
  2726. "metadata": {},
  2727. "output_type": "execute_result"
  2728. }
  2729. ],
  2730. "source": [
  2731. "np.angle(C+1) # heads up MATLAB Users, angle is used instead of arg"
  2732. ]
  2733. },
  2734. {
  2735. "cell_type": "code",
  2736. "execution_count": 144,
  2737. "metadata": {},
  2738. "outputs": [
  2739. {
  2740. "data": {
  2741. "text/plain": [
  2742. "matrix([[1., 2.],\n",
  2743. " [3., 4.]])"
  2744. ]
  2745. },
  2746. "execution_count": 144,
  2747. "metadata": {},
  2748. "output_type": "execute_result"
  2749. }
  2750. ],
  2751. "source": [
  2752. "np.abs(C)"
  2753. ]
  2754. },
  2755. {
  2756. "cell_type": "markdown",
  2757. "metadata": {},
  2758. "source": [
  2759. "### 7.6 矩阵计算"
  2760. ]
  2761. },
  2762. {
  2763. "cell_type": "markdown",
  2764. "metadata": {},
  2765. "source": [
  2766. "#### 求逆"
  2767. ]
  2768. },
  2769. {
  2770. "cell_type": "code",
  2771. "execution_count": 145,
  2772. "metadata": {},
  2773. "outputs": [
  2774. {
  2775. "data": {
  2776. "text/plain": [
  2777. "matrix([[0.+2.j , 0.-1.j ],\n",
  2778. " [0.-1.5j, 0.+0.5j]])"
  2779. ]
  2780. },
  2781. "execution_count": 145,
  2782. "metadata": {},
  2783. "output_type": "execute_result"
  2784. }
  2785. ],
  2786. "source": [
  2787. "np.linalg.inv(C) # equivalent to C.I "
  2788. ]
  2789. },
  2790. {
  2791. "cell_type": "code",
  2792. "execution_count": 146,
  2793. "metadata": {},
  2794. "outputs": [
  2795. {
  2796. "data": {
  2797. "text/plain": [
  2798. "matrix([[1.00000000e+00+0.j, 0.00000000e+00+0.j],\n",
  2799. " [1.11022302e-16+0.j, 1.00000000e+00+0.j]])"
  2800. ]
  2801. },
  2802. "execution_count": 146,
  2803. "metadata": {},
  2804. "output_type": "execute_result"
  2805. }
  2806. ],
  2807. "source": [
  2808. "C.I * C"
  2809. ]
  2810. },
  2811. {
  2812. "cell_type": "markdown",
  2813. "metadata": {},
  2814. "source": [
  2815. "#### 行列式"
  2816. ]
  2817. },
  2818. {
  2819. "cell_type": "code",
  2820. "execution_count": 147,
  2821. "metadata": {},
  2822. "outputs": [
  2823. {
  2824. "data": {
  2825. "text/plain": [
  2826. "(2.0000000000000004+0j)"
  2827. ]
  2828. },
  2829. "execution_count": 147,
  2830. "metadata": {},
  2831. "output_type": "execute_result"
  2832. }
  2833. ],
  2834. "source": [
  2835. "np.linalg.det(C)"
  2836. ]
  2837. },
  2838. {
  2839. "cell_type": "code",
  2840. "execution_count": 148,
  2841. "metadata": {},
  2842. "outputs": [
  2843. {
  2844. "data": {
  2845. "text/plain": [
  2846. "(0.49999999999999967+0j)"
  2847. ]
  2848. },
  2849. "execution_count": 148,
  2850. "metadata": {},
  2851. "output_type": "execute_result"
  2852. }
  2853. ],
  2854. "source": [
  2855. "np.linalg.det(C.I)"
  2856. ]
  2857. },
  2858. {
  2859. "cell_type": "markdown",
  2860. "metadata": {},
  2861. "source": [
  2862. "### 7.7 数据处理"
  2863. ]
  2864. },
  2865. {
  2866. "cell_type": "markdown",
  2867. "metadata": {},
  2868. "source": [
  2869. "通常将数据集存储在Numpy数组中是非常有用的。Numpy提供了许多函数用于计算数组中数据集的统计。\n",
  2870. "\n",
  2871. "例如,让我们从上面使用的斯德哥尔摩温度数据集计算一些属性。"
  2872. ]
  2873. },
  2874. {
  2875. "cell_type": "code",
  2876. "execution_count": 149,
  2877. "metadata": {},
  2878. "outputs": [
  2879. {
  2880. "data": {
  2881. "text/plain": [
  2882. "(77431, 7)"
  2883. ]
  2884. },
  2885. "execution_count": 149,
  2886. "metadata": {},
  2887. "output_type": "execute_result"
  2888. }
  2889. ],
  2890. "source": [
  2891. "import numpy as np\n",
  2892. "data = np.genfromtxt('stockholm_td_adj.dat')\n",
  2893. "\n",
  2894. "# 提醒一下,温度数据集存储在数据变量中:\n",
  2895. "np.shape(data)"
  2896. ]
  2897. },
  2898. {
  2899. "cell_type": "markdown",
  2900. "metadata": {},
  2901. "source": [
  2902. "#### mean"
  2903. ]
  2904. },
  2905. {
  2906. "cell_type": "code",
  2907. "execution_count": 150,
  2908. "metadata": {},
  2909. "outputs": [
  2910. {
  2911. "name": "stdout",
  2912. "output_type": "stream",
  2913. "text": [
  2914. "(77431, 7)\n"
  2915. ]
  2916. },
  2917. {
  2918. "data": {
  2919. "text/plain": [
  2920. "6.197109684751585"
  2921. ]
  2922. },
  2923. "execution_count": 150,
  2924. "metadata": {},
  2925. "output_type": "execute_result"
  2926. }
  2927. ],
  2928. "source": [
  2929. "# 温度数据在第三列中\n",
  2930. "print(data.shape)\n",
  2931. "np.mean(data[:,3])"
  2932. ]
  2933. },
  2934. {
  2935. "cell_type": "code",
  2936. "execution_count": 151,
  2937. "metadata": {},
  2938. "outputs": [
  2939. {
  2940. "data": {
  2941. "text/plain": [
  2942. "0.49494514118786737"
  2943. ]
  2944. },
  2945. "execution_count": 151,
  2946. "metadata": {},
  2947. "output_type": "execute_result"
  2948. }
  2949. ],
  2950. "source": [
  2951. "A = np.random.rand(4, 3)\n",
  2952. "np.mean(A)"
  2953. ]
  2954. },
  2955. {
  2956. "cell_type": "markdown",
  2957. "metadata": {},
  2958. "source": [
  2959. "在过去的200年里,斯德哥尔摩每天的平均气温大约是6.2 C。"
  2960. ]
  2961. },
  2962. {
  2963. "cell_type": "markdown",
  2964. "metadata": {},
  2965. "source": [
  2966. "#### 标准差和方差"
  2967. ]
  2968. },
  2969. {
  2970. "cell_type": "code",
  2971. "execution_count": 152,
  2972. "metadata": {},
  2973. "outputs": [
  2974. {
  2975. "data": {
  2976. "text/plain": [
  2977. "(8.282271621340573, 68.59602320966341)"
  2978. ]
  2979. },
  2980. "execution_count": 152,
  2981. "metadata": {},
  2982. "output_type": "execute_result"
  2983. }
  2984. ],
  2985. "source": [
  2986. "np.std(data[:,3]), np.var(data[:,3])"
  2987. ]
  2988. },
  2989. {
  2990. "cell_type": "markdown",
  2991. "metadata": {},
  2992. "source": [
  2993. "#### 最小值和最大值"
  2994. ]
  2995. },
  2996. {
  2997. "cell_type": "code",
  2998. "execution_count": 153,
  2999. "metadata": {},
  3000. "outputs": [
  3001. {
  3002. "data": {
  3003. "text/plain": [
  3004. "-25.8"
  3005. ]
  3006. },
  3007. "execution_count": 153,
  3008. "metadata": {},
  3009. "output_type": "execute_result"
  3010. }
  3011. ],
  3012. "source": [
  3013. "# 最低日平均温度\n",
  3014. "data[:,3].min()"
  3015. ]
  3016. },
  3017. {
  3018. "cell_type": "code",
  3019. "execution_count": 154,
  3020. "metadata": {},
  3021. "outputs": [
  3022. {
  3023. "data": {
  3024. "text/plain": [
  3025. "28.3"
  3026. ]
  3027. },
  3028. "execution_count": 154,
  3029. "metadata": {},
  3030. "output_type": "execute_result"
  3031. }
  3032. ],
  3033. "source": [
  3034. "# 最高日平均温度\n",
  3035. "data[:,3].max()"
  3036. ]
  3037. },
  3038. {
  3039. "cell_type": "markdown",
  3040. "metadata": {},
  3041. "source": [
  3042. "#### sum, prod, and trace"
  3043. ]
  3044. },
  3045. {
  3046. "cell_type": "code",
  3047. "execution_count": 156,
  3048. "metadata": {},
  3049. "outputs": [
  3050. {
  3051. "data": {
  3052. "text/plain": [
  3053. "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
  3054. ]
  3055. },
  3056. "execution_count": 156,
  3057. "metadata": {},
  3058. "output_type": "execute_result"
  3059. }
  3060. ],
  3061. "source": [
  3062. "d = np.arange(0, 10)\n",
  3063. "d"
  3064. ]
  3065. },
  3066. {
  3067. "cell_type": "code",
  3068. "execution_count": 157,
  3069. "metadata": {},
  3070. "outputs": [
  3071. {
  3072. "data": {
  3073. "text/plain": [
  3074. "45"
  3075. ]
  3076. },
  3077. "execution_count": 157,
  3078. "metadata": {},
  3079. "output_type": "execute_result"
  3080. }
  3081. ],
  3082. "source": [
  3083. "# 将所有的元素相加\n",
  3084. "np.sum(d)"
  3085. ]
  3086. },
  3087. {
  3088. "cell_type": "code",
  3089. "execution_count": 158,
  3090. "metadata": {},
  3091. "outputs": [
  3092. {
  3093. "data": {
  3094. "text/plain": [
  3095. "3628800"
  3096. ]
  3097. },
  3098. "execution_count": 158,
  3099. "metadata": {},
  3100. "output_type": "execute_result"
  3101. }
  3102. ],
  3103. "source": [
  3104. "# 全元素积分\n",
  3105. "np.prod(d+1)"
  3106. ]
  3107. },
  3108. {
  3109. "cell_type": "code",
  3110. "execution_count": 159,
  3111. "metadata": {},
  3112. "outputs": [
  3113. {
  3114. "data": {
  3115. "text/plain": [
  3116. "array([ 0, 1, 3, 6, 10, 15, 21, 28, 36, 45])"
  3117. ]
  3118. },
  3119. "execution_count": 159,
  3120. "metadata": {},
  3121. "output_type": "execute_result"
  3122. }
  3123. ],
  3124. "source": [
  3125. "# 累计求和\n",
  3126. "np.cumsum(d)"
  3127. ]
  3128. },
  3129. {
  3130. "cell_type": "code",
  3131. "execution_count": 160,
  3132. "metadata": {},
  3133. "outputs": [
  3134. {
  3135. "data": {
  3136. "text/plain": [
  3137. "array([ 1, 2, 6, 24, 120, 720, 5040,\n",
  3138. " 40320, 362880, 3628800])"
  3139. ]
  3140. },
  3141. "execution_count": 160,
  3142. "metadata": {},
  3143. "output_type": "execute_result"
  3144. }
  3145. ],
  3146. "source": [
  3147. "# 累计乘积\n",
  3148. "np.cumprod(d+1)"
  3149. ]
  3150. },
  3151. {
  3152. "cell_type": "code",
  3153. "execution_count": 161,
  3154. "metadata": {},
  3155. "outputs": [
  3156. {
  3157. "data": {
  3158. "text/plain": [
  3159. "1.2869808487677687"
  3160. ]
  3161. },
  3162. "execution_count": 161,
  3163. "metadata": {},
  3164. "output_type": "execute_result"
  3165. }
  3166. ],
  3167. "source": [
  3168. "# 计算对角线元素的和,和diag(A).sum()一样\n",
  3169. "np.trace(A)"
  3170. ]
  3171. },
  3172. {
  3173. "cell_type": "markdown",
  3174. "metadata": {},
  3175. "source": [
  3176. "### 7.8 数组子集的计算"
  3177. ]
  3178. },
  3179. {
  3180. "cell_type": "markdown",
  3181. "metadata": {},
  3182. "source": [
  3183. "我们可以使用索引、花式索引和从数组中提取数据的其他方法(如上所述)来计算数组中的数据子集。\n",
  3184. "\n",
  3185. "例如,让我们回到温度数据集:"
  3186. ]
  3187. },
  3188. {
  3189. "cell_type": "code",
  3190. "execution_count": 162,
  3191. "metadata": {},
  3192. "outputs": [
  3193. {
  3194. "name": "stdout",
  3195. "output_type": "stream",
  3196. "text": [
  3197. "1800 1 1 -6.1 -6.1 -6.1 1\r\n",
  3198. "1800 1 2 -15.4 -15.4 -15.4 1\r\n",
  3199. "1800 1 3 -15.0 -15.0 -15.0 1\r\n"
  3200. ]
  3201. }
  3202. ],
  3203. "source": [
  3204. "!head -n 3 stockholm_td_adj.dat"
  3205. ]
  3206. },
  3207. {
  3208. "cell_type": "markdown",
  3209. "metadata": {},
  3210. "source": [
  3211. "数据集的格式是:年,月,日,日平均气温,低,高,位置。\n",
  3212. "\n",
  3213. "如果我们对某个特定月份的平均温度感兴趣,比如二月,然后我们可以创建一个索引掩码,使用它来选择当月的数据:"
  3214. ]
  3215. },
  3216. {
  3217. "cell_type": "code",
  3218. "execution_count": 163,
  3219. "metadata": {},
  3220. "outputs": [
  3221. {
  3222. "data": {
  3223. "text/plain": [
  3224. "array([ 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.])"
  3225. ]
  3226. },
  3227. "execution_count": 163,
  3228. "metadata": {},
  3229. "output_type": "execute_result"
  3230. }
  3231. ],
  3232. "source": [
  3233. "np.unique(data[:,1]) # 列的值从1到12"
  3234. ]
  3235. },
  3236. {
  3237. "cell_type": "code",
  3238. "execution_count": 164,
  3239. "metadata": {},
  3240. "outputs": [
  3241. {
  3242. "name": "stdout",
  3243. "output_type": "stream",
  3244. "text": [
  3245. "[False False False ... False False False]\n"
  3246. ]
  3247. }
  3248. ],
  3249. "source": [
  3250. "mask_feb = data[:,1] == 2\n",
  3251. "print(mask_feb)"
  3252. ]
  3253. },
  3254. {
  3255. "cell_type": "code",
  3256. "execution_count": 165,
  3257. "metadata": {},
  3258. "outputs": [
  3259. {
  3260. "name": "stdout",
  3261. "output_type": "stream",
  3262. "text": [
  3263. "-3.212109570736596\n",
  3264. "5.090390768766271\n"
  3265. ]
  3266. }
  3267. ],
  3268. "source": [
  3269. "# 温度数据实在第三行\n",
  3270. "print(np.mean(data[mask_feb,3]))\n",
  3271. "print(np.std(data[mask_feb,3]))"
  3272. ]
  3273. },
  3274. {
  3275. "cell_type": "markdown",
  3276. "metadata": {},
  3277. "source": [
  3278. "有了这些工具,我们就有了非常强大的数据处理能力。例如,提取每年每个月的平均气温只需要几行代码:"
  3279. ]
  3280. },
  3281. {
  3282. "cell_type": "code",
  3283. "execution_count": 166,
  3284. "metadata": {},
  3285. "outputs": [
  3286. {
  3287. "data": {
  3288. "image/png": "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\n",
  3289. "text/plain": [
  3290. "<Figure size 432x288 with 1 Axes>"
  3291. ]
  3292. },
  3293. "metadata": {
  3294. "needs_background": "light"
  3295. },
  3296. "output_type": "display_data"
  3297. }
  3298. ],
  3299. "source": [
  3300. "%matplotlib inline\n",
  3301. "import matplotlib.pyplot as plt\n",
  3302. "\n",
  3303. "months = np.arange(1,13)\n",
  3304. "monthly_mean = [np.mean(data[data[:,1] == month, 3]) for month in months]\n",
  3305. "\n",
  3306. "fig, ax = plt.subplots()\n",
  3307. "ax.bar(months, monthly_mean)\n",
  3308. "ax.set_xlabel(\"Month\")\n",
  3309. "ax.set_ylabel(\"Monthly avg. temp.\");"
  3310. ]
  3311. },
  3312. {
  3313. "cell_type": "markdown",
  3314. "metadata": {},
  3315. "source": [
  3316. "### 7.9 高维数据的计算"
  3317. ]
  3318. },
  3319. {
  3320. "cell_type": "markdown",
  3321. "metadata": {},
  3322. "source": [
  3323. "当例如`min`, `max`等函数应用在高维数组上时,有时将计算应用于整个数组是有用的,而且很多时候有时只基于行或列。用`axis`参数我们可以决定这个函数应该怎样表现:"
  3324. ]
  3325. },
  3326. {
  3327. "cell_type": "code",
  3328. "execution_count": 167,
  3329. "metadata": {},
  3330. "outputs": [
  3331. {
  3332. "data": {
  3333. "text/plain": [
  3334. "array([[0.28760836, 0.74204101, 0.39567837],\n",
  3335. " [0.74805878, 0.405101 , 0.13400733],\n",
  3336. " [0.55124625, 0.98346507, 0.88726029],\n",
  3337. " [0.92808432, 0.75063001, 0.5832612 ]])"
  3338. ]
  3339. },
  3340. "execution_count": 167,
  3341. "metadata": {},
  3342. "output_type": "execute_result"
  3343. }
  3344. ],
  3345. "source": [
  3346. "import numpy as np\n",
  3347. "\n",
  3348. "m = np.random.rand(4,3)\n",
  3349. "m"
  3350. ]
  3351. },
  3352. {
  3353. "cell_type": "code",
  3354. "execution_count": 168,
  3355. "metadata": {},
  3356. "outputs": [
  3357. {
  3358. "data": {
  3359. "text/plain": [
  3360. "0.9834650747647675"
  3361. ]
  3362. },
  3363. "execution_count": 168,
  3364. "metadata": {},
  3365. "output_type": "execute_result"
  3366. }
  3367. ],
  3368. "source": [
  3369. "# global max\n",
  3370. "m.max()"
  3371. ]
  3372. },
  3373. {
  3374. "cell_type": "code",
  3375. "execution_count": 169,
  3376. "metadata": {},
  3377. "outputs": [
  3378. {
  3379. "data": {
  3380. "text/plain": [
  3381. "array([0.92808432, 0.98346507, 0.88726029])"
  3382. ]
  3383. },
  3384. "execution_count": 169,
  3385. "metadata": {},
  3386. "output_type": "execute_result"
  3387. }
  3388. ],
  3389. "source": [
  3390. "# max in each column\n",
  3391. "m.max(axis=0)"
  3392. ]
  3393. },
  3394. {
  3395. "cell_type": "code",
  3396. "execution_count": 170,
  3397. "metadata": {},
  3398. "outputs": [
  3399. {
  3400. "data": {
  3401. "text/plain": [
  3402. "array([0.74204101, 0.74805878, 0.98346507, 0.92808432])"
  3403. ]
  3404. },
  3405. "execution_count": 170,
  3406. "metadata": {},
  3407. "output_type": "execute_result"
  3408. }
  3409. ],
  3410. "source": [
  3411. "# max in each row\n",
  3412. "m.max(axis=1)"
  3413. ]
  3414. },
  3415. {
  3416. "cell_type": "markdown",
  3417. "metadata": {},
  3418. "source": [
  3419. "许多其他的在`array` 和`matrix`类中的函数和方法接受同样(可选的)的关键字参数`axis`"
  3420. ]
  3421. },
  3422. {
  3423. "cell_type": "markdown",
  3424. "metadata": {},
  3425. "source": [
  3426. "## 8. 阵列的重塑、调整大小和堆叠"
  3427. ]
  3428. },
  3429. {
  3430. "cell_type": "markdown",
  3431. "metadata": {},
  3432. "source": [
  3433. "Numpy数组的形状可以被确定而无需复制底层数据,这使得即使对于大型数组也能有较快的操作。"
  3434. ]
  3435. },
  3436. {
  3437. "cell_type": "code",
  3438. "execution_count": 171,
  3439. "metadata": {},
  3440. "outputs": [
  3441. {
  3442. "name": "stdout",
  3443. "output_type": "stream",
  3444. "text": [
  3445. "[[0.98346378 0.63646196 0.08381973]\n",
  3446. " [0.21685601 0.27589121 0.0874428 ]\n",
  3447. " [0.96690659 0.95725769 0.52492868]\n",
  3448. " [0.98482663 0.90069241 0.42153789]]\n"
  3449. ]
  3450. }
  3451. ],
  3452. "source": [
  3453. "import numpy as np\n",
  3454. "\n",
  3455. "A = np.random.rand(4, 3)\n",
  3456. "print(A)"
  3457. ]
  3458. },
  3459. {
  3460. "cell_type": "code",
  3461. "execution_count": 172,
  3462. "metadata": {},
  3463. "outputs": [
  3464. {
  3465. "name": "stdout",
  3466. "output_type": "stream",
  3467. "text": [
  3468. "4 3\n"
  3469. ]
  3470. }
  3471. ],
  3472. "source": [
  3473. "n, m = A.shape\n",
  3474. "print(n, m)"
  3475. ]
  3476. },
  3477. {
  3478. "cell_type": "code",
  3479. "execution_count": 173,
  3480. "metadata": {},
  3481. "outputs": [
  3482. {
  3483. "data": {
  3484. "text/plain": [
  3485. "array([[0.98346378, 0.63646196, 0.08381973, 0.21685601, 0.27589121,\n",
  3486. " 0.0874428 , 0.96690659, 0.95725769, 0.52492868, 0.98482663,\n",
  3487. " 0.90069241, 0.42153789]])"
  3488. ]
  3489. },
  3490. "execution_count": 173,
  3491. "metadata": {},
  3492. "output_type": "execute_result"
  3493. }
  3494. ],
  3495. "source": [
  3496. "B = A.reshape((1,n*m))\n",
  3497. "B"
  3498. ]
  3499. },
  3500. {
  3501. "cell_type": "code",
  3502. "execution_count": 174,
  3503. "metadata": {},
  3504. "outputs": [
  3505. {
  3506. "name": "stdout",
  3507. "output_type": "stream",
  3508. "text": [
  3509. "[[0.98346378]\n",
  3510. " [0.63646196]\n",
  3511. " [0.08381973]\n",
  3512. " [0.21685601]\n",
  3513. " [0.27589121]\n",
  3514. " [0.0874428 ]\n",
  3515. " [0.96690659]\n",
  3516. " [0.95725769]\n",
  3517. " [0.52492868]\n",
  3518. " [0.98482663]\n",
  3519. " [0.90069241]\n",
  3520. " [0.42153789]]\n",
  3521. "(12, 1)\n"
  3522. ]
  3523. }
  3524. ],
  3525. "source": [
  3526. "B2 = A.reshape((n*m, 1))\n",
  3527. "print(B2)\n",
  3528. "print(B2.shape)"
  3529. ]
  3530. },
  3531. {
  3532. "cell_type": "code",
  3533. "execution_count": 176,
  3534. "metadata": {},
  3535. "outputs": [
  3536. {
  3537. "data": {
  3538. "text/plain": [
  3539. "array([[5. , 5. , 5. , 5. , 5. ,\n",
  3540. " 0.0874428 , 0.96690659, 0.95725769, 0.52492868, 0.98482663,\n",
  3541. " 0.90069241, 0.42153789]])"
  3542. ]
  3543. },
  3544. "execution_count": 176,
  3545. "metadata": {},
  3546. "output_type": "execute_result"
  3547. }
  3548. ],
  3549. "source": [
  3550. "B[0,0:5] = 5 # modify the array\n",
  3551. "\n",
  3552. "B"
  3553. ]
  3554. },
  3555. {
  3556. "cell_type": "code",
  3557. "execution_count": 177,
  3558. "metadata": {},
  3559. "outputs": [
  3560. {
  3561. "data": {
  3562. "text/plain": [
  3563. "array([[5. , 5. , 5. ],\n",
  3564. " [5. , 5. , 0.0874428 ],\n",
  3565. " [0.96690659, 0.95725769, 0.52492868],\n",
  3566. " [0.98482663, 0.90069241, 0.42153789]])"
  3567. ]
  3568. },
  3569. "execution_count": 177,
  3570. "metadata": {},
  3571. "output_type": "execute_result"
  3572. }
  3573. ],
  3574. "source": [
  3575. "A # and the original variable is also changed. B is only a different view of the same data"
  3576. ]
  3577. },
  3578. {
  3579. "cell_type": "markdown",
  3580. "metadata": {},
  3581. "source": [
  3582. "We can also use the function `flatten` to make a higher-dimensional array into a vector. But this function create a copy of the data."
  3583. ]
  3584. },
  3585. {
  3586. "cell_type": "code",
  3587. "execution_count": 178,
  3588. "metadata": {},
  3589. "outputs": [
  3590. {
  3591. "data": {
  3592. "text/plain": [
  3593. "array([5. , 5. , 5. , 5. , 5. ,\n",
  3594. " 0.0874428 , 0.96690659, 0.95725769, 0.52492868, 0.98482663,\n",
  3595. " 0.90069241, 0.42153789])"
  3596. ]
  3597. },
  3598. "execution_count": 178,
  3599. "metadata": {},
  3600. "output_type": "execute_result"
  3601. }
  3602. ],
  3603. "source": [
  3604. "B = A.flatten()\n",
  3605. "\n",
  3606. "B"
  3607. ]
  3608. },
  3609. {
  3610. "cell_type": "code",
  3611. "execution_count": 179,
  3612. "metadata": {},
  3613. "outputs": [
  3614. {
  3615. "name": "stdout",
  3616. "output_type": "stream",
  3617. "text": [
  3618. "(12,)\n"
  3619. ]
  3620. }
  3621. ],
  3622. "source": [
  3623. "print(B.shape)"
  3624. ]
  3625. },
  3626. {
  3627. "cell_type": "code",
  3628. "execution_count": 180,
  3629. "metadata": {},
  3630. "outputs": [
  3631. {
  3632. "name": "stdout",
  3633. "output_type": "stream",
  3634. "text": [
  3635. "[0.4076777 0.0032036 0.8637935 0.63928257 0.92394319 0.94463281\n",
  3636. " 0.75838245 0.77815663 0.59448528 0.05197006 0.4252758 0.51943058\n",
  3637. " 0.25521222 0.21153197 0.13903764 0.70652387 0.47792749 0.76336588\n",
  3638. " 0.35224639 0.85792682 0.37824866 0.08396315 0.6820255 0.48759341\n",
  3639. " 0.06410559 0.04382042 0.58880606 0.49957256 0.30892822 0.86214811\n",
  3640. " 0.29476108 0.58164927 0.18771192 0.62448138 0.27972963 0.64589686\n",
  3641. " 0.7414693 0.87782264 0.92350925 0.82749223 0.72188647 0.64283206\n",
  3642. " 0.57347573 0.53142496 0.92027185 0.39492156 0.3399361 0.05608057\n",
  3643. " 0.18456121 0.21670162 0.93057584 0.22099788 0.16258077 0.90794268\n",
  3644. " 0.5725359 0.67821311 0.59549661 0.7304167 0.93257325 0.95671415]\n"
  3645. ]
  3646. }
  3647. ],
  3648. "source": [
  3649. "T = np.random.rand(3, 4, 5)\n",
  3650. "T2 = T.flatten()\n",
  3651. "print(T2)"
  3652. ]
  3653. },
  3654. {
  3655. "cell_type": "code",
  3656. "execution_count": 181,
  3657. "metadata": {},
  3658. "outputs": [
  3659. {
  3660. "data": {
  3661. "text/plain": [
  3662. "array([10. , 10. , 10. , 10. , 10. ,\n",
  3663. " 0.0874428 , 0.96690659, 0.95725769, 0.52492868, 0.98482663,\n",
  3664. " 0.90069241, 0.42153789])"
  3665. ]
  3666. },
  3667. "execution_count": 181,
  3668. "metadata": {},
  3669. "output_type": "execute_result"
  3670. }
  3671. ],
  3672. "source": [
  3673. "B[0:5] = 10\n",
  3674. "\n",
  3675. "B"
  3676. ]
  3677. },
  3678. {
  3679. "cell_type": "code",
  3680. "execution_count": 182,
  3681. "metadata": {},
  3682. "outputs": [
  3683. {
  3684. "data": {
  3685. "text/plain": [
  3686. "array([[5. , 5. , 5. ],\n",
  3687. " [5. , 5. , 0.0874428 ],\n",
  3688. " [0.96690659, 0.95725769, 0.52492868],\n",
  3689. " [0.98482663, 0.90069241, 0.42153789]])"
  3690. ]
  3691. },
  3692. "execution_count": 182,
  3693. "metadata": {},
  3694. "output_type": "execute_result"
  3695. }
  3696. ],
  3697. "source": [
  3698. "A # 现在A并没有改变,因为B的数值是A的复制,并不指向同样的值。"
  3699. ]
  3700. },
  3701. {
  3702. "cell_type": "markdown",
  3703. "metadata": {},
  3704. "source": [
  3705. "## 9. 添加、删除维度:newaxis、squeeze"
  3706. ]
  3707. },
  3708. {
  3709. "cell_type": "markdown",
  3710. "metadata": {},
  3711. "source": [
  3712. "当矩阵乘法的时候,需要两个矩阵的对应的纬度保持一致才可以正确执行,有了`newaxis`,我们可以在数组中插入新的维度,例如将一个向量转换为列或行矩阵:"
  3713. ]
  3714. },
  3715. {
  3716. "cell_type": "code",
  3717. "execution_count": 183,
  3718. "metadata": {},
  3719. "outputs": [],
  3720. "source": [
  3721. "v = np.array([1,2,3])"
  3722. ]
  3723. },
  3724. {
  3725. "cell_type": "code",
  3726. "execution_count": 184,
  3727. "metadata": {},
  3728. "outputs": [
  3729. {
  3730. "name": "stdout",
  3731. "output_type": "stream",
  3732. "text": [
  3733. "(3,)\n",
  3734. "[1 2 3]\n"
  3735. ]
  3736. }
  3737. ],
  3738. "source": [
  3739. "print(np.shape(v))\n",
  3740. "print(v)"
  3741. ]
  3742. },
  3743. {
  3744. "cell_type": "code",
  3745. "execution_count": 186,
  3746. "metadata": {},
  3747. "outputs": [
  3748. {
  3749. "name": "stdout",
  3750. "output_type": "stream",
  3751. "text": [
  3752. "(3, 1)\n",
  3753. "[[1]\n",
  3754. " [2]\n",
  3755. " [3]]\n"
  3756. ]
  3757. }
  3758. ],
  3759. "source": [
  3760. "v2 = v.reshape(3, 1)\n",
  3761. "print(v2.shape)\n",
  3762. "print(v2)"
  3763. ]
  3764. },
  3765. {
  3766. "cell_type": "code",
  3767. "execution_count": 188,
  3768. "metadata": {},
  3769. "outputs": [
  3770. {
  3771. "name": "stdout",
  3772. "output_type": "stream",
  3773. "text": [
  3774. "(3,)\n",
  3775. "(3, 1)\n"
  3776. ]
  3777. }
  3778. ],
  3779. "source": [
  3780. "# 做一个向量v的列矩阵\n",
  3781. "v2 = v[:, np.newaxis]\n",
  3782. "print(v.shape)\n",
  3783. "print(v2.shape)\n"
  3784. ]
  3785. },
  3786. {
  3787. "cell_type": "code",
  3788. "execution_count": 189,
  3789. "metadata": {},
  3790. "outputs": [
  3791. {
  3792. "data": {
  3793. "text/plain": [
  3794. "(3, 1)"
  3795. ]
  3796. },
  3797. "execution_count": 189,
  3798. "metadata": {},
  3799. "output_type": "execute_result"
  3800. }
  3801. ],
  3802. "source": [
  3803. "# 列矩阵\n",
  3804. "v[:,np.newaxis].shape"
  3805. ]
  3806. },
  3807. {
  3808. "cell_type": "code",
  3809. "execution_count": 190,
  3810. "metadata": {},
  3811. "outputs": [
  3812. {
  3813. "data": {
  3814. "text/plain": [
  3815. "(1, 3)"
  3816. ]
  3817. },
  3818. "execution_count": 190,
  3819. "metadata": {},
  3820. "output_type": "execute_result"
  3821. }
  3822. ],
  3823. "source": [
  3824. "# 行矩阵\n",
  3825. "v[np.newaxis,:].shape"
  3826. ]
  3827. },
  3828. {
  3829. "cell_type": "markdown",
  3830. "metadata": {},
  3831. "source": [
  3832. "也可以通过`np.expand_dims`来实现类似的操作"
  3833. ]
  3834. },
  3835. {
  3836. "cell_type": "code",
  3837. "execution_count": 191,
  3838. "metadata": {},
  3839. "outputs": [
  3840. {
  3841. "name": "stdout",
  3842. "output_type": "stream",
  3843. "text": [
  3844. "(3, 1)\n",
  3845. "[[1]\n",
  3846. " [2]\n",
  3847. " [3]]\n"
  3848. ]
  3849. }
  3850. ],
  3851. "source": [
  3852. "v = np.array([1,2,3])\n",
  3853. "v3 = np.expand_dims(v, 1)\n",
  3854. "print(v3.shape)\n",
  3855. "print(v3)"
  3856. ]
  3857. },
  3858. {
  3859. "cell_type": "markdown",
  3860. "metadata": {},
  3861. "source": [
  3862. "在某些情况,需要将纬度为1的那个纬度删除掉,可以使用`np.squeeze`实现"
  3863. ]
  3864. },
  3865. {
  3866. "cell_type": "code",
  3867. "execution_count": 192,
  3868. "metadata": {},
  3869. "outputs": [
  3870. {
  3871. "name": "stdout",
  3872. "output_type": "stream",
  3873. "text": [
  3874. "(1, 2, 3)\n",
  3875. "[[[1 2 3]\n",
  3876. " [2 3 4]]]\n"
  3877. ]
  3878. }
  3879. ],
  3880. "source": [
  3881. "arr = np.array([[[1, 2, 3], [2, 3, 4]]])\n",
  3882. "print(arr.shape)\n",
  3883. "print(arr)"
  3884. ]
  3885. },
  3886. {
  3887. "cell_type": "code",
  3888. "execution_count": 193,
  3889. "metadata": {},
  3890. "outputs": [
  3891. {
  3892. "name": "stdout",
  3893. "output_type": "stream",
  3894. "text": [
  3895. "(2, 3)\n",
  3896. "[[1 2 3]\n",
  3897. " [2 3 4]]\n"
  3898. ]
  3899. }
  3900. ],
  3901. "source": [
  3902. "# 实际上第一个纬度为`1`,我们不需要\n",
  3903. "arr2 = np.squeeze(arr, 0)\n",
  3904. "print(arr2.shape)\n",
  3905. "print(arr2)"
  3906. ]
  3907. },
  3908. {
  3909. "cell_type": "markdown",
  3910. "metadata": {},
  3911. "source": [
  3912. "需要注意:只有数组长度在该纬度上为1,那么该纬度才可以被删除;否则会报错。"
  3913. ]
  3914. },
  3915. {
  3916. "cell_type": "markdown",
  3917. "metadata": {},
  3918. "source": [
  3919. "## 10. 叠加和重复数组"
  3920. ]
  3921. },
  3922. {
  3923. "cell_type": "markdown",
  3924. "metadata": {},
  3925. "source": [
  3926. "利用函数`repeat`, `tile`, `vstack`, `hstack`, 和`concatenate` 我们可以用较小的向量和矩阵来创建更大的向量和矩阵:"
  3927. ]
  3928. },
  3929. {
  3930. "cell_type": "markdown",
  3931. "metadata": {},
  3932. "source": [
  3933. "### 10.1 tile and repeat"
  3934. ]
  3935. },
  3936. {
  3937. "cell_type": "code",
  3938. "execution_count": 194,
  3939. "metadata": {},
  3940. "outputs": [
  3941. {
  3942. "name": "stdout",
  3943. "output_type": "stream",
  3944. "text": [
  3945. "[[1 2]\n",
  3946. " [3 4]]\n"
  3947. ]
  3948. }
  3949. ],
  3950. "source": [
  3951. "a = np.array([[1, 2], [3, 4]])\n",
  3952. "print(a)"
  3953. ]
  3954. },
  3955. {
  3956. "cell_type": "code",
  3957. "execution_count": 195,
  3958. "metadata": {},
  3959. "outputs": [
  3960. {
  3961. "data": {
  3962. "text/plain": [
  3963. "array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4])"
  3964. ]
  3965. },
  3966. "execution_count": 195,
  3967. "metadata": {},
  3968. "output_type": "execute_result"
  3969. }
  3970. ],
  3971. "source": [
  3972. "# 重复每一个元素三次\n",
  3973. "np.repeat(a, 3)"
  3974. ]
  3975. },
  3976. {
  3977. "cell_type": "code",
  3978. "execution_count": 196,
  3979. "metadata": {},
  3980. "outputs": [
  3981. {
  3982. "data": {
  3983. "text/plain": [
  3984. "array([[1, 2, 1, 2, 1, 2],\n",
  3985. " [3, 4, 3, 4, 3, 4]])"
  3986. ]
  3987. },
  3988. "execution_count": 196,
  3989. "metadata": {},
  3990. "output_type": "execute_result"
  3991. }
  3992. ],
  3993. "source": [
  3994. "# tile the matrix 3 times \n",
  3995. "np.tile(a, 3)"
  3996. ]
  3997. },
  3998. {
  3999. "cell_type": "code",
  4000. "execution_count": 197,
  4001. "metadata": {},
  4002. "outputs": [
  4003. {
  4004. "data": {
  4005. "text/plain": [
  4006. "array([[1, 2, 1, 2, 1, 2],\n",
  4007. " [3, 4, 3, 4, 3, 4]])"
  4008. ]
  4009. },
  4010. "execution_count": 197,
  4011. "metadata": {},
  4012. "output_type": "execute_result"
  4013. }
  4014. ],
  4015. "source": [
  4016. "# 更好的方案\n",
  4017. "np.tile(a, (1, 3))"
  4018. ]
  4019. },
  4020. {
  4021. "cell_type": "code",
  4022. "execution_count": 198,
  4023. "metadata": {},
  4024. "outputs": [
  4025. {
  4026. "data": {
  4027. "text/plain": [
  4028. "array([[1, 2],\n",
  4029. " [3, 4],\n",
  4030. " [1, 2],\n",
  4031. " [3, 4],\n",
  4032. " [1, 2],\n",
  4033. " [3, 4]])"
  4034. ]
  4035. },
  4036. "execution_count": 198,
  4037. "metadata": {},
  4038. "output_type": "execute_result"
  4039. }
  4040. ],
  4041. "source": [
  4042. "np.tile(a, (3, 1))"
  4043. ]
  4044. },
  4045. {
  4046. "cell_type": "markdown",
  4047. "metadata": {},
  4048. "source": [
  4049. "### 10.2 concatenate"
  4050. ]
  4051. },
  4052. {
  4053. "cell_type": "code",
  4054. "execution_count": 205,
  4055. "metadata": {},
  4056. "outputs": [],
  4057. "source": [
  4058. "b = np.array([[5, 6]])"
  4059. ]
  4060. },
  4061. {
  4062. "cell_type": "code",
  4063. "execution_count": 206,
  4064. "metadata": {},
  4065. "outputs": [
  4066. {
  4067. "data": {
  4068. "text/plain": [
  4069. "array([[1, 2],\n",
  4070. " [3, 4],\n",
  4071. " [5, 6]])"
  4072. ]
  4073. },
  4074. "execution_count": 206,
  4075. "metadata": {},
  4076. "output_type": "execute_result"
  4077. }
  4078. ],
  4079. "source": [
  4080. "np.concatenate((a, b), axis=0)"
  4081. ]
  4082. },
  4083. {
  4084. "cell_type": "code",
  4085. "execution_count": 207,
  4086. "metadata": {},
  4087. "outputs": [
  4088. {
  4089. "data": {
  4090. "text/plain": [
  4091. "array([[1, 2, 5],\n",
  4092. " [3, 4, 6]])"
  4093. ]
  4094. },
  4095. "execution_count": 207,
  4096. "metadata": {},
  4097. "output_type": "execute_result"
  4098. }
  4099. ],
  4100. "source": [
  4101. "np.concatenate((a, b.T), axis=1)"
  4102. ]
  4103. },
  4104. {
  4105. "cell_type": "markdown",
  4106. "metadata": {},
  4107. "source": [
  4108. "### 10.3 hstack and vstack"
  4109. ]
  4110. },
  4111. {
  4112. "cell_type": "code",
  4113. "execution_count": 208,
  4114. "metadata": {},
  4115. "outputs": [
  4116. {
  4117. "data": {
  4118. "text/plain": [
  4119. "array([[1, 2],\n",
  4120. " [3, 4],\n",
  4121. " [5, 6]])"
  4122. ]
  4123. },
  4124. "execution_count": 208,
  4125. "metadata": {},
  4126. "output_type": "execute_result"
  4127. }
  4128. ],
  4129. "source": [
  4130. "np.vstack((a,b))"
  4131. ]
  4132. },
  4133. {
  4134. "cell_type": "code",
  4135. "execution_count": 209,
  4136. "metadata": {},
  4137. "outputs": [
  4138. {
  4139. "data": {
  4140. "text/plain": [
  4141. "array([[1, 2, 5],\n",
  4142. " [3, 4, 6]])"
  4143. ]
  4144. },
  4145. "execution_count": 209,
  4146. "metadata": {},
  4147. "output_type": "execute_result"
  4148. }
  4149. ],
  4150. "source": [
  4151. "np.hstack((a,b.T))"
  4152. ]
  4153. },
  4154. {
  4155. "cell_type": "markdown",
  4156. "metadata": {},
  4157. "source": [
  4158. "## 11. 复制和“深度复制”"
  4159. ]
  4160. },
  4161. {
  4162. "cell_type": "markdown",
  4163. "metadata": {},
  4164. "source": [
  4165. "为了获得高性能,Python中的赋值通常不复制底层对象。例如,在函数之间传递对象时,这一点非常重要,以避免不必要时大量的内存复制(技术术语:通过引用传递)。"
  4166. ]
  4167. },
  4168. {
  4169. "cell_type": "code",
  4170. "execution_count": 210,
  4171. "metadata": {},
  4172. "outputs": [
  4173. {
  4174. "data": {
  4175. "text/plain": [
  4176. "array([[1, 2],\n",
  4177. " [3, 4]])"
  4178. ]
  4179. },
  4180. "execution_count": 210,
  4181. "metadata": {},
  4182. "output_type": "execute_result"
  4183. }
  4184. ],
  4185. "source": [
  4186. "A = np.array([[1, 2], [3, 4]])\n",
  4187. "\n",
  4188. "A"
  4189. ]
  4190. },
  4191. {
  4192. "cell_type": "code",
  4193. "execution_count": 211,
  4194. "metadata": {},
  4195. "outputs": [],
  4196. "source": [
  4197. "# 现在B和A指的是同一个数组数据\n",
  4198. "B = A "
  4199. ]
  4200. },
  4201. {
  4202. "cell_type": "code",
  4203. "execution_count": 212,
  4204. "metadata": {},
  4205. "outputs": [
  4206. {
  4207. "data": {
  4208. "text/plain": [
  4209. "array([[10, 2],\n",
  4210. " [ 3, 4]])"
  4211. ]
  4212. },
  4213. "execution_count": 212,
  4214. "metadata": {},
  4215. "output_type": "execute_result"
  4216. }
  4217. ],
  4218. "source": [
  4219. "# 改变B影响A\n",
  4220. "B[0,0] = 10\n",
  4221. "\n",
  4222. "B"
  4223. ]
  4224. },
  4225. {
  4226. "cell_type": "code",
  4227. "execution_count": 213,
  4228. "metadata": {},
  4229. "outputs": [
  4230. {
  4231. "data": {
  4232. "text/plain": [
  4233. "array([[10, 2],\n",
  4234. " [ 3, 4]])"
  4235. ]
  4236. },
  4237. "execution_count": 213,
  4238. "metadata": {},
  4239. "output_type": "execute_result"
  4240. }
  4241. ],
  4242. "source": [
  4243. "A"
  4244. ]
  4245. },
  4246. {
  4247. "cell_type": "markdown",
  4248. "metadata": {},
  4249. "source": [
  4250. "如果我们想避免这种行为,那么当我们从`A`中复制一个新的完全独立的对象`B`时,我们需要使用函数`copy`来做一个所谓的“深度复制”:"
  4251. ]
  4252. },
  4253. {
  4254. "cell_type": "code",
  4255. "execution_count": 214,
  4256. "metadata": {},
  4257. "outputs": [],
  4258. "source": [
  4259. "B = np.copy(A)"
  4260. ]
  4261. },
  4262. {
  4263. "cell_type": "code",
  4264. "execution_count": 215,
  4265. "metadata": {},
  4266. "outputs": [
  4267. {
  4268. "data": {
  4269. "text/plain": [
  4270. "array([[-5, 2],\n",
  4271. " [ 3, 4]])"
  4272. ]
  4273. },
  4274. "execution_count": 215,
  4275. "metadata": {},
  4276. "output_type": "execute_result"
  4277. }
  4278. ],
  4279. "source": [
  4280. "# 现在如果我们改变B,A不受影响\n",
  4281. "B[0,0] = -5\n",
  4282. "\n",
  4283. "B"
  4284. ]
  4285. },
  4286. {
  4287. "cell_type": "code",
  4288. "execution_count": 216,
  4289. "metadata": {},
  4290. "outputs": [
  4291. {
  4292. "data": {
  4293. "text/plain": [
  4294. "array([[10, 2],\n",
  4295. " [ 3, 4]])"
  4296. ]
  4297. },
  4298. "execution_count": 216,
  4299. "metadata": {},
  4300. "output_type": "execute_result"
  4301. }
  4302. ],
  4303. "source": [
  4304. "A"
  4305. ]
  4306. },
  4307. {
  4308. "cell_type": "markdown",
  4309. "metadata": {},
  4310. "source": [
  4311. "## 12. 遍历数组元素"
  4312. ]
  4313. },
  4314. {
  4315. "cell_type": "markdown",
  4316. "metadata": {},
  4317. "source": [
  4318. "通常,我们希望尽可能避免遍历数组元素(不惜一切代价)。原因是在像Python(或MATLAB)这样的解释语言中,迭代与向量化操作相比真的很慢。\n",
  4319. "\n",
  4320. "然而,有时迭代是不可避免的。对于这种情况,Python的For循环是最方便的遍历数组的方法:"
  4321. ]
  4322. },
  4323. {
  4324. "cell_type": "code",
  4325. "execution_count": 217,
  4326. "metadata": {},
  4327. "outputs": [
  4328. {
  4329. "name": "stdout",
  4330. "output_type": "stream",
  4331. "text": [
  4332. "1\n",
  4333. "2\n",
  4334. "3\n",
  4335. "4\n"
  4336. ]
  4337. }
  4338. ],
  4339. "source": [
  4340. "v = np.array([1,2,3,4])\n",
  4341. "\n",
  4342. "for element in v:\n",
  4343. " print(element)"
  4344. ]
  4345. },
  4346. {
  4347. "cell_type": "code",
  4348. "execution_count": 218,
  4349. "metadata": {},
  4350. "outputs": [
  4351. {
  4352. "name": "stdout",
  4353. "output_type": "stream",
  4354. "text": [
  4355. "row [1 2]\n",
  4356. "1\n",
  4357. "2\n",
  4358. "row [3 4]\n",
  4359. "3\n",
  4360. "4\n"
  4361. ]
  4362. }
  4363. ],
  4364. "source": [
  4365. "M = np.array([[1,2], [3,4]])\n",
  4366. "\n",
  4367. "for row in M:\n",
  4368. " print(\"row\", row)\n",
  4369. " \n",
  4370. " for element in row:\n",
  4371. " print(element)"
  4372. ]
  4373. },
  4374. {
  4375. "cell_type": "markdown",
  4376. "metadata": {},
  4377. "source": [
  4378. "当我们需要去\n",
  4379. "当我们需要遍历一个数组的每个元素并修改它的元素时,使用`enumerate`函数可以方便地在`for`循环中获得元素及其索引:"
  4380. ]
  4381. },
  4382. {
  4383. "cell_type": "code",
  4384. "execution_count": 219,
  4385. "metadata": {},
  4386. "outputs": [
  4387. {
  4388. "name": "stdout",
  4389. "output_type": "stream",
  4390. "text": [
  4391. "row_idx 0 row [1 2]\n",
  4392. "col_idx 0 element 1\n",
  4393. "col_idx 1 element 2\n",
  4394. "row_idx 1 row [3 4]\n",
  4395. "col_idx 0 element 3\n",
  4396. "col_idx 1 element 4\n"
  4397. ]
  4398. }
  4399. ],
  4400. "source": [
  4401. "for row_idx, row in enumerate(M):\n",
  4402. " print(\"row_idx\", row_idx, \"row\", row)\n",
  4403. " \n",
  4404. " for col_idx, element in enumerate(row):\n",
  4405. " print(\"col_idx\", col_idx, \"element\", element)\n",
  4406. " \n",
  4407. " # 更新矩阵:对每个元素求平方\n",
  4408. " M[row_idx, col_idx] = element ** 2"
  4409. ]
  4410. },
  4411. {
  4412. "cell_type": "code",
  4413. "execution_count": 109,
  4414. "metadata": {},
  4415. "outputs": [
  4416. {
  4417. "data": {
  4418. "text/plain": [
  4419. "array([[ 1, 4],\n",
  4420. " [ 9, 16]])"
  4421. ]
  4422. },
  4423. "execution_count": 109,
  4424. "metadata": {},
  4425. "output_type": "execute_result"
  4426. }
  4427. ],
  4428. "source": [
  4429. "# 现在矩阵里的每一个元素都已经求得平方\n",
  4430. "M"
  4431. ]
  4432. },
  4433. {
  4434. "cell_type": "markdown",
  4435. "metadata": {},
  4436. "source": [
  4437. "## 13. 向量化功能"
  4438. ]
  4439. },
  4440. {
  4441. "cell_type": "markdown",
  4442. "metadata": {},
  4443. "source": [
  4444. "正如前面多次提到的,为了获得良好的性能,我们应该尽量避免对向量和矩阵中的元素进行循环,而应该使用向量化算法。将标量算法转换为向量化算法的第一步是确保我们编写的函数使用向量输入。"
  4445. ]
  4446. },
  4447. {
  4448. "cell_type": "code",
  4449. "execution_count": 220,
  4450. "metadata": {},
  4451. "outputs": [],
  4452. "source": [
  4453. "def Theta(x):\n",
  4454. " \"\"\"\n",
  4455. " Heaviside阶跃函数的标量实现\n",
  4456. " \"\"\"\n",
  4457. " if x >= 0:\n",
  4458. " return 1\n",
  4459. " else:\n",
  4460. " return 0"
  4461. ]
  4462. },
  4463. {
  4464. "cell_type": "code",
  4465. "execution_count": 221,
  4466. "metadata": {},
  4467. "outputs": [
  4468. {
  4469. "ename": "ValueError",
  4470. "evalue": "The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()",
  4471. "output_type": "error",
  4472. "traceback": [
  4473. "\u001b[0;31m-----------------------------------------------------------\u001b[0m",
  4474. "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
  4475. "\u001b[0;32m<ipython-input-221-b49266106206>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mTheta\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
  4476. "\u001b[0;32m<ipython-input-220-5990c144f91d>\u001b[0m in \u001b[0;36mTheta\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mHeaviside阶跃函数的标量实现\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \"\"\"\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
  4477. "\u001b[0;31mValueError\u001b[0m: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()"
  4478. ]
  4479. }
  4480. ],
  4481. "source": [
  4482. "Theta(np.array([-3,-2,-1,0,1,2,3]))"
  4483. ]
  4484. },
  4485. {
  4486. "cell_type": "markdown",
  4487. "metadata": {},
  4488. "source": [
  4489. "这个操作并不可行因为我们没有写`Theta`函数去解决一个向量输入\n",
  4490. "\n",
  4491. "为了得到向量化的版本,我们可以使用Numpy函数`vectorize`。在许多情况下,它可以自动向量化一个函数:"
  4492. ]
  4493. },
  4494. {
  4495. "cell_type": "code",
  4496. "execution_count": 222,
  4497. "metadata": {},
  4498. "outputs": [],
  4499. "source": [
  4500. "Theta_vec = np.vectorize(Theta)"
  4501. ]
  4502. },
  4503. {
  4504. "cell_type": "code",
  4505. "execution_count": 223,
  4506. "metadata": {},
  4507. "outputs": [
  4508. {
  4509. "data": {
  4510. "text/plain": [
  4511. "array([0, 0, 0, 1, 1, 1, 1])"
  4512. ]
  4513. },
  4514. "execution_count": 223,
  4515. "metadata": {},
  4516. "output_type": "execute_result"
  4517. }
  4518. ],
  4519. "source": [
  4520. "Theta_vec(np.array([-3,-2,-1,0,1,2,3]))"
  4521. ]
  4522. },
  4523. {
  4524. "cell_type": "markdown",
  4525. "metadata": {},
  4526. "source": [
  4527. "我们也可以实现从一开始就接受矢量输入的函数(需要更多的计算,但可能会有更好的性能):"
  4528. ]
  4529. },
  4530. {
  4531. "cell_type": "code",
  4532. "execution_count": 225,
  4533. "metadata": {},
  4534. "outputs": [],
  4535. "source": [
  4536. "def Theta(x):\n",
  4537. " \"\"\"\n",
  4538. " Heaviside阶跃函数的矢量感知实现。\n",
  4539. " \"\"\"\n",
  4540. " return 1 * (x >= 0)"
  4541. ]
  4542. },
  4543. {
  4544. "cell_type": "code",
  4545. "execution_count": 226,
  4546. "metadata": {},
  4547. "outputs": [
  4548. {
  4549. "data": {
  4550. "text/plain": [
  4551. "array([0, 0, 0, 1, 1, 1, 1])"
  4552. ]
  4553. },
  4554. "execution_count": 226,
  4555. "metadata": {},
  4556. "output_type": "execute_result"
  4557. }
  4558. ],
  4559. "source": [
  4560. "Theta(np.array([-3,-2,-1,0,1,2,3]))"
  4561. ]
  4562. },
  4563. {
  4564. "cell_type": "code",
  4565. "execution_count": 227,
  4566. "metadata": {},
  4567. "outputs": [
  4568. {
  4569. "name": "stdout",
  4570. "output_type": "stream",
  4571. "text": [
  4572. "[False False False True True True True]\n"
  4573. ]
  4574. },
  4575. {
  4576. "data": {
  4577. "text/plain": [
  4578. "array([0, 0, 0, 1, 1, 1, 1])"
  4579. ]
  4580. },
  4581. "execution_count": 227,
  4582. "metadata": {},
  4583. "output_type": "execute_result"
  4584. }
  4585. ],
  4586. "source": [
  4587. "a = np.array([-3,-2,-1,0,1,2,3])\n",
  4588. "b = a>=0\n",
  4589. "print(b)\n",
  4590. "b*1"
  4591. ]
  4592. },
  4593. {
  4594. "cell_type": "code",
  4595. "execution_count": 128,
  4596. "metadata": {},
  4597. "outputs": [
  4598. {
  4599. "data": {
  4600. "text/plain": [
  4601. "(0, 1)"
  4602. ]
  4603. },
  4604. "execution_count": 128,
  4605. "metadata": {},
  4606. "output_type": "execute_result"
  4607. }
  4608. ],
  4609. "source": [
  4610. "# 同样适用于标量\n",
  4611. "Theta(-1.2), Theta(2.6)"
  4612. ]
  4613. },
  4614. {
  4615. "cell_type": "markdown",
  4616. "metadata": {},
  4617. "source": [
  4618. "## 14. 在条件中使用数组"
  4619. ]
  4620. },
  4621. {
  4622. "cell_type": "markdown",
  4623. "metadata": {},
  4624. "source": [
  4625. "当在条件中使用数组时,例如`if`语句和其他布尔表达,一个需要用`any`或者`all`,这让数组任何或者所有元素都等于`True`。"
  4626. ]
  4627. },
  4628. {
  4629. "cell_type": "code",
  4630. "execution_count": 228,
  4631. "metadata": {},
  4632. "outputs": [
  4633. {
  4634. "data": {
  4635. "text/plain": [
  4636. "array([[1, 2],\n",
  4637. " [3, 4]])"
  4638. ]
  4639. },
  4640. "execution_count": 228,
  4641. "metadata": {},
  4642. "output_type": "execute_result"
  4643. }
  4644. ],
  4645. "source": [
  4646. "M = np.array([[1, 2], [3, 4]])\n",
  4647. "M"
  4648. ]
  4649. },
  4650. {
  4651. "cell_type": "code",
  4652. "execution_count": 229,
  4653. "metadata": {},
  4654. "outputs": [
  4655. {
  4656. "data": {
  4657. "text/plain": [
  4658. "True"
  4659. ]
  4660. },
  4661. "execution_count": 229,
  4662. "metadata": {},
  4663. "output_type": "execute_result"
  4664. }
  4665. ],
  4666. "source": [
  4667. "(M > 2).any()"
  4668. ]
  4669. },
  4670. {
  4671. "cell_type": "code",
  4672. "execution_count": 230,
  4673. "metadata": {},
  4674. "outputs": [
  4675. {
  4676. "name": "stdout",
  4677. "output_type": "stream",
  4678. "text": [
  4679. "at least one element in M is larger than 2\n"
  4680. ]
  4681. }
  4682. ],
  4683. "source": [
  4684. "if (M > 2).any():\n",
  4685. " print(\"at least one element in M is larger than 2\")\n",
  4686. "else:\n",
  4687. " print(\"no element in M is larger than 2\")"
  4688. ]
  4689. },
  4690. {
  4691. "cell_type": "code",
  4692. "execution_count": 231,
  4693. "metadata": {},
  4694. "outputs": [
  4695. {
  4696. "name": "stdout",
  4697. "output_type": "stream",
  4698. "text": [
  4699. "all elements in M are not larger than 5\n"
  4700. ]
  4701. }
  4702. ],
  4703. "source": [
  4704. "if (M > 5).all():\n",
  4705. " print(\"all elements in M are larger than 5\")\n",
  4706. "else:\n",
  4707. " print(\"all elements in M are not larger than 5\")"
  4708. ]
  4709. },
  4710. {
  4711. "cell_type": "markdown",
  4712. "metadata": {},
  4713. "source": [
  4714. "## 15. 类型转换"
  4715. ]
  4716. },
  4717. {
  4718. "cell_type": "markdown",
  4719. "metadata": {},
  4720. "source": [
  4721. "因为Numpy数组是*静态类型*,数组的类型一旦创建就不会改变。但是我们可以用`astype`函数(参见类似的“asarray”函数)显式地转换一个数组的类型到其他的类型,这总是创建一个新类型的新数组。"
  4722. ]
  4723. },
  4724. {
  4725. "cell_type": "code",
  4726. "execution_count": 232,
  4727. "metadata": {},
  4728. "outputs": [
  4729. {
  4730. "data": {
  4731. "text/plain": [
  4732. "dtype('int64')"
  4733. ]
  4734. },
  4735. "execution_count": 232,
  4736. "metadata": {},
  4737. "output_type": "execute_result"
  4738. }
  4739. ],
  4740. "source": [
  4741. "M.dtype\n"
  4742. ]
  4743. },
  4744. {
  4745. "cell_type": "code",
  4746. "execution_count": 233,
  4747. "metadata": {},
  4748. "outputs": [
  4749. {
  4750. "data": {
  4751. "text/plain": [
  4752. "array([[1., 2.],\n",
  4753. " [3., 4.]])"
  4754. ]
  4755. },
  4756. "execution_count": 233,
  4757. "metadata": {},
  4758. "output_type": "execute_result"
  4759. }
  4760. ],
  4761. "source": [
  4762. "M2 = M.astype(float)\n",
  4763. "\n",
  4764. "M2"
  4765. ]
  4766. },
  4767. {
  4768. "cell_type": "code",
  4769. "execution_count": 234,
  4770. "metadata": {},
  4771. "outputs": [
  4772. {
  4773. "data": {
  4774. "text/plain": [
  4775. "dtype('float64')"
  4776. ]
  4777. },
  4778. "execution_count": 234,
  4779. "metadata": {},
  4780. "output_type": "execute_result"
  4781. }
  4782. ],
  4783. "source": [
  4784. "M2.dtype"
  4785. ]
  4786. },
  4787. {
  4788. "cell_type": "code",
  4789. "execution_count": 235,
  4790. "metadata": {},
  4791. "outputs": [
  4792. {
  4793. "data": {
  4794. "text/plain": [
  4795. "array([[ True, True],\n",
  4796. " [ True, True]])"
  4797. ]
  4798. },
  4799. "execution_count": 235,
  4800. "metadata": {},
  4801. "output_type": "execute_result"
  4802. }
  4803. ],
  4804. "source": [
  4805. "M3 = M.astype(bool)\n",
  4806. "\n",
  4807. "M3"
  4808. ]
  4809. },
  4810. {
  4811. "cell_type": "markdown",
  4812. "metadata": {},
  4813. "source": [
  4814. "## 进一步的阅读"
  4815. ]
  4816. },
  4817. {
  4818. "cell_type": "markdown",
  4819. "metadata": {},
  4820. "source": [
  4821. "* [NumPy 简易教程](https://www.runoob.com/numpy/numpy-tutorial.html)\n",
  4822. "* [NumPy 官方用户指南](https://www.numpy.org.cn/user/)\n",
  4823. "* [NumPy 官方参考手册](https://www.numpy.org.cn/reference/)\n",
  4824. "* [NumPy Tutorial](http://scipy.org/Tentative_NumPy_Tutorial)\n",
  4825. "* [一个针对MATLAB使用者的Numpy教程](http://scipy.org/NumPy_for_Matlab_Users)"
  4826. ]
  4827. }
  4828. ],
  4829. "metadata": {
  4830. "kernelspec": {
  4831. "display_name": "Python 3",
  4832. "language": "python",
  4833. "name": "python3"
  4834. },
  4835. "language_info": {
  4836. "codemirror_mode": {
  4837. "name": "ipython",
  4838. "version": 3
  4839. },
  4840. "file_extension": ".py",
  4841. "mimetype": "text/x-python",
  4842. "name": "python",
  4843. "nbconvert_exporter": "python",
  4844. "pygments_lexer": "ipython3",
  4845. "version": "3.7.9"
  4846. }
  4847. },
  4848. "nbformat": 4,
  4849. "nbformat_minor": 1
  4850. }

机器学习越来越多应用到飞行器、机器人等领域,其目的是利用计算机实现类似人类的智能,从而实现装备的智能化与无人化。本课程旨在引导学生掌握机器学习的基本知识、典型方法与技术,通过具体的应用案例激发学生对该学科的兴趣,鼓励学生能够从人工智能的角度来分析、解决飞行器、机器人所面临的问题和挑战。本课程主要内容包括Python编程基础,机器学习模型,无监督学习、监督学习、深度学习基础知识与实现,并学习如何利用机器学习解决实际问题,从而全面提升自我的《综合能力》。