[转]numpy 100道练习题 - Python

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100 numpy exercise

翻译：YingJoy
网址： https://www.yingjoy.cn/
来源：https://github.com/rougier/numpy-100

Numpy是Python做数据分析必须掌握的基础库之一，非常适合刚学习完Numpy基础的同学，完成以下习题可以帮助你更好的掌握这个基础库。

Python版本：Python 3.6.2

Numpy版本：Numpy 1.13.1

1. 导入numpy库并取别名为np (★☆☆)

(提示: import … as …)

import numpy as np

2. 打印输出numpy的版本和配置信息 (★☆☆)

(提示: np.__verison__, np.show_config)

print (np.__version__) np.show_config()

3. 创建长度为10的零向量 (★☆☆)

(提示: np.zeros)

Z = np.zeros(10) print (Z)

4. 获取数组所占内存大小 (★☆☆)

(提示: size, itemsize)

Z = np.zeros((10, 10)) print (Z.size * Z.itemsize)

5. 怎么用命令行获取numpy add函数的文档说明？ (★☆☆)

(提示: np.info)

np.info(np.add)

6. 创建一个长度为10的零向量，并把第五个值赋值为1 (★☆☆)

(提示: array[4])

Z = np.zeros(10) Z[4] = 1 print (Z)

7. 创建一个值域为10到49的向量 (★☆☆)

(提示: np.arange)

Z = np.arange(10, 50) print (Z)

8**. 将一个向量进行反转（第一个元素变为最后一个元素） (★☆☆)

(提示: array[::-1])

Z = np.arange(50) Z = Z[::-1] print (Z)

9. 创建一个3x3的矩阵，值域为0到8**(★☆☆)

(提示: reshape)

Z = np.arange(9).reshape(3, 3) print (Z)

10. 从数组[1, 2, 0, 0, 4, 0]中找出非0元素的位置索引 (★☆☆)

(提示: np.nonzero)

nz = np.nonzero([1, 2, 0, 0, 4, 0]) print (NZ)

11. 创建一个3x3的单位矩阵 (★☆☆)

(提示: np.eye)

Z = np.eye(3) print (Z)

12. 创建一个3x3x3的随机数组**(★☆☆)

(提示: np.random.random)

Z = np.random.random((3, 3, 3)) print (Z)

13. 创建一个10x10的随机数组，并找出该数组中的最大值与最小值**(★☆☆)

(提示: max, min)

Z = np.random.random((10, 10)) Zmax, Zmin = Z.max(), Z.min() print (Z.max, Z.min)

14. 创建一个长度为30的随机向量，并求它的平均值 (★☆☆)

(提示: mean)

Z = np.random.random(30) mean = Z.mean() print (mean)

15. 创建一个2维数组，该数组边界值为1，内部的值为0 (★☆☆)

(提示: array[1:-1, 1:-1])

Z = np.ones((10, 10)) Z[1:-1, 1:-1] = 0 print (Z)

16. 如何用0来填充一个数组的边界？ (★☆☆)

(提示: np.pad)

Z = np.ones((10, 10)) Z = np.pad(Z, pad_width=1, mode='constant', constant_values=0) print (Z)

17. 下面表达式运行的结果是什么？**(★☆☆)

(提示: NaN = not a number, inf = infinity)

(提示：NaN : 不是一个数，inf : 无穷)

# 表达式# 结果 0 * np.nan nan np.nan == np.nan False np.inf > np.nan False np.nan - np.nan nan 0.3 == 3 * 0.1 False

18. 创建一个5x5的矩阵，且设置值1, 2, 3, 4在其对角线下面一行**(★☆☆)

(提示: np.diag)

Z = np.diag([1, 2, 3, 4], k=-1) #k=-1保证了偏移 print (Z)

输出为：

array([[0, 0, 0, 0, 0], [1, 0, 0, 0, 0], [0, 2, 0, 0, 0], [0, 0, 3, 0, 0], [0, 0, 0, 4, 0]])

19. 创建一个8x8的国际象棋棋盘矩阵（黑块为0，白块为1） (★☆☆)

(提示: array[::2])

Z = np.zeros((8, 8), dtype=int) Z[1::2, ::2] = 1 Z[::2, 1::2] = 1 print (Z)

20. 思考一下形状为(6, 7, 8)的数组的形状，且第100个元素的索引(x, y, z)分别是什么？**(★☆☆)

(提示: np.unravel_index)

print (np.unravel_index(100, (6, 7, 8)))

21. 用tile函数创建一个8x8的棋盘矩阵**(★☆☆)

(提示: np.tile)

Z = np.tile(np.array([[1, 0], [0, 1]]), (4, 4)) print (Z)

22. 对5x5的随机矩阵进行归一化 (★☆☆)

(提示: (x - min) / (max - min))

Z = np.random.random((5, 5)) Zmax, Zmin = Z.max(), Z.min() Z = (Z-Zmin)/(Zmax-Zmin) print (Z)

23. 创建一个dtype来表示颜色(RGBA) (★☆☆)

(提示: np.dtype)

color = np.dtype([("r", np.ubyte, 1), ("g", np.ubyte, 1), ("b", np.ubyte, 1), ("a", np.ubyte, 1)]) c = np.array((255, 255, 255, 1), dtype=color) print (c)Out[80]: array((255, 255, 255, 1), dtype=[('r', 'u1'), ('g', 'u1'), ('b', 'u1'), ('a', 'u1')])

24. 一个5x3的矩阵和一个3x2的矩阵相乘，结果是什么？**(★☆☆)

(提示: np.dot | @)

Z = np.dot(np.zeros((5, 3)), np.zeros((3, 2))) # 或者 Z = np.zeros((5, 3))@ np.zeros((3, 2)) print (Z)

25. 给定一个一维数组把它索引从3到8的元素求相反数 (★☆☆)

(提示: >, <=)

Z = np.arange(11) Z[(3 <= Z) & (Z < 8)] *= -1 print (Z)

26. 下面的脚本的结果是什么？ (★☆☆)

(提示: np.sum)

# Author: Jake VanderPlas# 结果print(sum(range(5),-1))9 from numpy import * print(sum(range(5),-1))10 #numpy.sum(a, axis=None)

27. 关于整形的向量Z下面哪些表达式正确？ (★☆☆)

Z**ZTrue 2 << Z >> 2False Z <- ZTrue 1j*ZTrue #复数 Z/1/1True Z<Z>ZFalse

28. 下面表达式的结果分别是什么？ (★☆☆)

np.array(0) / np.array(0)nan np.array(0) // np.array(0)0 np.array([np.nan]).astype(int).astype(float)-2.14748365e+09

29. 如何从零位开始舍入浮点数组？ (★☆☆)

(提示: np.uniform, np.copysign, np.ceil, np.abs)

# Author: Charles R HarrisZ = np.random.uniform(-10,+10,10) print (np.copysign(np.ceil(np.abs(Z)), Z))

30. 如何找出两个数组公共的元素? (★☆☆)

(提示: np.intersect1d)

Z1 = np.random.randint(0, 10, 10) Z2 = np.random.randint(0, 10, 10) print (np.intersect1d(Z1, Z2))

numpy集合合并np.unique(np.concat(a,b))

31. 如何忽略numpy的警告信息（不推荐）? (★☆☆)

(提示: np.seterr, np.errstate)

# Suicide mode on defaults = np.seterr(all="ignore") Z = np.ones(1) / 0# Back to sanity _ = np.seterr(**defaults)# 另一个等价的方式，使用上下文管理器（context manager） with np.errstate(divide='ignore'): Z = np.ones(1) / 0

32. 下面的表达式是否为真? (★☆☆)

(提示: 虚数)

np.sqrt(-1) == np.emath.sqrt(-1) False

33. 如何获得昨天，今天和明天的日期? (★☆☆)

(提示: np.datetime64, np.timedelta64)

yesterday = np.datetime64('today', 'D') - np.timedelta64(1, 'D') today = np.datetime64('today', 'D') tomorrow = np.datetime64('today', 'D') + np.timedelta64(1, 'D')

34. 怎么获得所有与2016年7月的所有日期? (★★☆)

(提示: np.arange(dtype=datetime64['D']))

Z = np.arange('2016-07', '2016-08', dtype='datetime64[D]') print (Z)

35. 如何计算 ((A+B)*(-A/2)) (不使用中间变量)? (★★☆)

合理使用out可以提升时空效率。

(提示: np.add(out=), np.negative(out=), np.multiply(out=), np.divide(out=))

A = np.ones(3) * 1 B = np.ones(3) * 1 C = np.ones(3) * 1 np.add(A, B, out=B) np.divide(A, 2, out=A) np.negative(A, out=A) np.multiply(A, B, out=A)

36. 用5种不同的方法提取随机数组中的整数部分 (★★☆)

(提示: %, np.floor, np.ceil, astype, np.trunc)

Z = np.random.uniform(0, 10, 10) print (Z - Z % 1) print (np.floor(Z)) print (np.cell(Z)-1) print (Z.astype(int)) print (np.trunc(Z))

37. 创建一个5x5的矩阵且每一行的值范围为从0到4 (★★☆)

(提示: np.arange)

Z = np.zeros((5, 5)) Z += np.arange(5) print (Z)

38. 如何用一个生成10个整数的函数来构建数组 (★☆☆)

(提示: np.fromiter)

def generate(): for x in range(10): yield x Z = np.fromiter(generate(), dtype=float, count=-1) print (Z)

39. 创建一个大小为10的向量，值域为0到1，不包括0和1 (★★☆)

(提示: np.linspace)

Z = np.linspace(0, 1, 12, endpoint=True)[1: -1] print (Z)

40. 创建一个大小为10的随机向量，并把它排序 (★★☆)

(提示: sort)

Z = np.random.random(10) Z.sort() print (Z)

另一种复杂写法：按照下标进行排序。Z=Z[np.argsort(Z)]

41. 对一个小数组进行求和有没有办法比np.sum更快? (★★☆)

(提示: np.add.reduce)

# Author: Evgeni BurovskiZ = np.arange(10) np.add.reduce(Z)# np.add.reduce 是numpy.add模块中的一个ufunc(universal function)函数,C语言实现

等价于np.cumsum(Z)

42. 如何判断两随机数组相等 (★★☆)

(提示: np.allclose, np.array_equal)

A = np.random.randint(0, 2, 5) B = np.random.randint(0, 2, 5)# 假设array的形状(shape)相同和一个误差容限（tolerance） equal = np.allclose(A,B) print(equal)# 检查形状和元素值，没有误差容限（值必须完全相等） equal = np.array_equal(A,B) print(equal)

43. 把数组变为只读 (★★☆)

(提示: flags.writeable)

Z = np.zeros(5) Z.flags.writeable = False Z[0] = 1

44. 将一个10x2的笛卡尔坐标矩阵转换为极坐标 (★★☆)

(提示: np.sqrt, np.arctan2)

Z = np.random.random((10, 2)) X, Y = Z[:, 0], Z[:, 1] R = np.sqrt(X**2 + Y**2) T = np.arctan2(Y, X) print (R) print (T)

45. 创建一个大小为10的随机向量并且将该向量中最大的值替换为0**(★★☆)

(提示: argmax)

Z = np.random.random(10) Z[Z.argmax()] = 0 print (Z)

46. 创建一个结构化数组，其中`x`和`y`坐标覆盖`[0, 1]x[1, 0]`区域 (★★☆)

(提示: np.meshgrid)

Z = np.zeros((5, 5), [('x', float), ('y', float)]) Z['x'], Z['y'] = np.meshgrid(np.linspace(0, 1, 5), np.linspace(0, 1, 5)) print (Z)

4**7. 给定两个数组`X`和`Y`，构造柯西(Cauchy)矩阵C ($C_{ij}=\frac{1}{x_i-y_j}$) (★★☆)

(提示: np.subtract.outer)

# Author: Evgeni BurovskiX = np.arange(8) Y = X + 0.5 C = 1.0 / np.subtract.outer(X, Y) print (C) print(np.linalg.det(C)) # 计算行列式

48. 打印每个numpy 类型的最小和最大可表示值 (★★☆)

(提示: np.iinfo, np.finfo, eps)

for dtype in [np.int8, np.int32, np.int64]: print(np.iinfo(dtype).min) print(np.iinfo(dtype).max) for dtype in [np.float32, np.float64]: print(np.finfo(dtype).min) print(np.finfo(dtype).max) print(np.finfo(dtype).eps)

49. 如何打印数组中所有的值？**(★★☆)

(提示: np.set_printoptions)

np.set_printoptions(threshold=np.nan) Z = np.zeros((16,16)) print(Z)

50. 如何在数组中找到与给定标量接近的值? (★★☆)

(提示: argmin)

Z = np.arange(100) v = np.random.uniform(0, 100) index = (np.abs(Z-v)).argmin() print(Z[index])

51. 创建表示位置(x, y)和颜色(r, g, b, a)的结构化数组 (★★☆)

(提示: dtype)

Z = np.zeros(10, [('position', [('x', float, 1), ('y', float, 1)]), ('color', [('r', float, 1), ('g', float, 1), ('b', float, 1)])]) print (Z)

52. 思考形状为(100, 2)的随机向量，求出点与点之间的距离 (★★☆)

(提示: np.atleast_2d, T, np.sqrt)

Z = np.random.random((100, 2)) X, Y = np.atleast_2d(Z[:, 0], Z[:, 1]) D = np.sqrt((X-X.T)**2 + (Y-Y.T)**2) print (D)# 使用scipy库可以更快 import scipy.spatialZ = np.random.random((100,2)) D = scipy.spatial.distance.cdist(Z,Z) print(D)

53. 如何将类型为float(32位)的数组类型转换为integer(32位)? (★★☆)

(提示: astype(copy=False))

Z = np.arange(10, dtype=np.int32) Z = Z.astype(np.float32, copy=False) print(Z)

54. 如何读取下面的文件? (★★☆)

(提示: np.genfromtxt)

1, 2, 3, 4, 5 6, , , 7, 8 , , 9,10,11# 先把上面保存到文件example.txt中 # 这里不使用StringIO，因为Python2 和Python3 在这个地方有兼容性问题 Z = np.genfromtxt("example.txt", delimiter=",") print(Z)

55. numpy数组枚举(enumerate)的等价操作? (★★☆)

(提示: np.ndenumerate, np.ndindex)

Z = np.arange(9).reshape(3,3) for index, value in np.ndenumerate(Z): print(index, value) for index in np.ndindex(Z.shape): print(index, Z[index])

56. 构造一个二维高斯矩阵**(★★☆)

(提示: np.meshgrid, np.exp)

X, Y = np.meshgrid(np.linspace(-1, 1, 10), np.linspace(-1, 1, 10)) D = np.sqrt(X**2 + Y**2) sigma, mu = 1.0, 0.0 G = np.exp(-( (D-mu)**2 / (2.0*sigma**2) )) print (G)

57. 如何在二维数组的随机位置放置p个元素? (★★☆)

(提示: np.put, np.random.choice)

# Author: Divakarn = 10 p = 3 Z = np.zeros((n,n)) np.put(Z, np.random.choice(range(n*n), p, replace=False),1) print(Z)

58. 减去矩阵每一行的平均值 (★★☆)

(提示: mean(axis=,keepdims=))

# Author: Warren WeckesserX = np.random.rand(5, 10)# 新 Y = X - X.mean(axis=1, keepdims=True)# 旧 Y = X - X.mean(axis=1).reshape(-1, 1)print(Y)

59. 如何对数组通过第n列进行排序? (★★☆)

(提示: argsort)

# Author: Steve TjoaZ = np.random.randint(0,10,(3,3)) print(Z) print(Z[ Z[:,1].argsort() ])

60. 如何判断一个给定的二维数组存在空列? (★★☆)

(提示: any, ~)

# Author: Warren WeckesserZ = np.random.randint(0,3,(3,10)) print((~Z.any(axis=0)).any())

61. 从数组中找出与给定值最接近的值 (★★☆)

(提示: np.abs, argmin, flat)

Z = np.random.uniform(0,1,10) z = 0.5 m = Z.flat[np.abs(Z - z).argmin()] print(m)

62. 思考形状为(1, 3)和(3, 1)的两个数组形状，如何使用迭代器计算它们的和? (★★☆)

(提示: np.nditer)

A = np.arange(3).reshape(3, 1) B = np.arange(3).reshape(1, 3) it = np.nditer([A, B, None]) for x, y, z in it: z[...] = x + y print (it.operands[2])

63. 创建一个具有name属性的数组类 (★★☆)

(提示: class method)

class NameArray(np.ndarray): def __new__(cls, array, name="no name"): obj = np.asarray(array).view(cls) obj.name = name return obj def __array_finalize__(self, obj): if obj is None: return self.info = getattr(obj, 'name', "no name")Z = NamedArray(np.arange(10), "range_10") print (Z.name)

64. 给定一个向量，如何让在第二个向量索引的每个元素加1(注意重复索引)? (★★★)

(提示: np.bincount | np.add.at)

# Author: Brett OlsenZ = np.ones(10) I = np.random.randint(0,len(Z),20) Z += np.bincount(I, minlength=len(Z)) print(Z)# Another solution # Author: Bartosz Telenczuk np.add.at(Z, I, 1) print(Z)

65. 如何根据索引列表`I`将向量`X`的元素累加到数组`F`? (★★★)

(提示: np.bincount)

# Author: Alan G IsaacX = [1,2,3,4,5,6] I = [1,3,9,3,4,1] F = np.bincount(I,X) print(F)

66. 思考(dtype = ubyte)的(w, h, 3)图像，计算唯一颜色的值**(★★★)

(提示: np.unique)

# Author: Nadav Horeshw,h = 16,16 I = np.random.randint(0,2,(h,w,3)).astype(np.ubyte) F = I[...,0]*256*256 + I[...,1]*256 +I[...,2] n = len(np.unique(F)) print(np.unique(I))

67. 思考如何求一个四维数组最后两个轴的数据和**(★★★)

(提示: sum(axis=(-2,-1)))

A = np.random.randint(0,10,(3,4,3,4)) # 传递一个元组(numpy 1.7.0) sum = A.sum(axis=(-2,-1)) print(sum)# 将最后两个维度压缩为一个 # (适用于不接受轴元组参数的函数) sum = A.reshape(A.shape[:-2] + (-1,)).sum(axis=-1) print(sum)

68. 考虑一维向量D，如何使用相同大小的向量S来计算D的子集的均值，其描述子集索引？ (★★★)

(提示: np.bincount)

# Author: Jaime Fernández del RíoD = np.random.uniform(0,1,100) S = np.random.randint(0,10,100) D_sums = np.bincount(S, weights=D) D_counts = np.bincount(S) D_means = D_sums / D_counts print(D_means)# Pandas solution as a reference due to more intuitive code import pandas as pd print(pd.Series(D).groupby(S).mean())

69. **如何获得点积的对角线？ (★★★)

(提示: np.diag)

# Author: Mathieu BlondelA = np.random.uniform(0,1,(5,5)) B = np.random.uniform(0,1,(5,5))# Slow version np.diag(np.dot(A, B))# Fast version np.sum(A * B.T, axis=1)# Faster version np.einsum("ij,ji->i", A, B)

70.考虑向量[1,2,3,4,5]，如何建立一个新的向量，在每个值之间交错有3个连续的零？ (★★★)

(提示: array[::4])

# Author: Warren WeckesserZ = np.array([1,2,3,4,5]) nz = 3 Z0 = np.zeros(len(Z) + (len(Z)-1)*(nz)) Z0[::nz+1] = Z print(Z0)

71. 考虑一个维度(5,5,3)的数组，如何将其与一个(5,5)的数组相乘？ (★★★)

(提示: array[:, :, None])

A = np.ones((5,5,3)) B = 2*np.ones((5,5)) print(A * B[:,:,None])

72. 如何对一个数组中任意两行做交换? (★★★)

(提示: array[[]] = array[[]])

# Author: Eelco HoogendoornA = np.arange(25).reshape(5,5) A[[0,1]] = A[[1,0]] print(A)

73. 思考描述10个三角形（共享顶点）的一组10个三元组，找到组成所有三角形的唯一线段集 (★★★)

(提示: repeat, np.roll, np.sort, view, np.unique)

# Author: Nicolas P. Rougierfaces = np.random.randint(0,100,(10,3)) F = np.roll(faces.repeat(2,axis=1),-1,axis=1) F = F.reshape(len(F)*3,2) F = np.sort(F,axis=1) G = F.view( dtype=[('p0',F.dtype),('p1',F.dtype)] ) G = np.unique(G) print(G)

74. 给定一个二进制的数组`C`，如何生成一个数组`A`满足`np.bincount(A)==C`? (★★★)

(提示: np.repeat)

# Author: Jaime Fernández del RíoC = np.bincount([1,1,2,3,4,4,6]) A = np.repeat(np.arange(len(C)), C) print(A)

75. 如何通过滑动窗口计算一个数组的平均数? (★★★)

(提示: np.cumsum)

# Author: Jaime Fernández del Ríodef moving_average(a, n=3) : ret = np.cumsum(a, dtype=float) ret[n:] = ret[n:] - ret[:-n] return ret[n - 1:] / n Z = np.arange(20) print(moving_average(Z, n=3))

76. 思考以为数组Z，构建一个二维数组，其第一行是(Z[0],Z[1],Z[2])，然后每一行移动一位，最后一行为 (Z[-3],Z[-2],Z[-1]) (★★★)

(提示: from numpy.lib import stride_tricks)

# Author: Joe Kington / Erik Rigtorp from numpy.lib import stride_tricksdef rolling(a, window): shape = (a.size - window + 1, window) strides = (a.itemsize, a.itemsize) return stride_tricks.as_strided(a, shape=shape, strides=strides) Z = rolling(np.arange(10), 3) print(Z)

77. 如何对布尔值取反，或改变浮点数的符号(`sign`)? (★★★)

(提示: np.logical_not, np.negative)

# Author: Nathaniel J. SmithZ = np.random.randint(0,2,100) np.logical_not(Z, out=Z)Z = np.random.uniform(-1.0,1.0,100) np.negative(Z, out=Z)

78. 思考两组点集`P0`和`P1`去描述一组线(二维)和一个点`p`,如何计算点`p`到每一条线 i `(P0[i],P1[i])`的距离？ (★★★)

def distance(P0, P1, p): T = P1 - P0 L = (T**2).sum(axis=1) U = -((P0[:,0]-p[...,0])*T[:,0] + (P0[:,1]-p[...,1])*T[:,1]) / L U = U.reshape(len(U),1) D = P0 + U*T - p return np.sqrt((D**2).sum(axis=1))P0 = np.random.uniform(-10,10,(10,2)) P1 = np.random.uniform(-10,10,(10,2)) p = np.random.uniform(-10,10,( 1,2)) print(distance(P0, P1, p))

79. 考虑两组点集`P0`和`P1`去描述一组线(二维)和一组点集`P`，如何计算每一个点 `j(P[j])` 到每一条线 i `(P0[i],P1[i])`的距离? (★★★)

# Author: Italmassov Kuanysh# based on distance function from previous question P0 = np.random.uniform(-10, 10, (10,2)) P1 = np.random.uniform(-10,10,(10,2)) p = np.random.uniform(-10, 10, (10,2)) print(np.array([distance(P0,P1,p_i) for p_i in p]))

80. 思考一个任意的数组，编写一个函数，该函数提取一个具有固定形状的子部分，并以一个给定的元素为中心(在该部分填充值) (★★★)

(提示: minimum, maximum)

# Author: Nicolas RougierZ = np.random.randint(0,10,(10,10)) shape = (5,5) fill = 0 position = (1,1)R = np.ones(shape, dtype=Z.dtype)*fill P = np.array(list(position)).astype(int) Rs = np.array(list(R.shape)).astype(int) Zs = np.array(list(Z.shape)).astype(int)R_start = np.zeros((len(shape),)).astype(int) R_stop = np.array(list(shape)).astype(int) Z_start = (P-Rs//2) Z_stop = (P+Rs//2)+Rs%2R_start = (R_start - np.minimum(Z_start,0)).tolist() Z_start = (np.maximum(Z_start,0)).tolist() R_stop = np.maximum(R_start, (R_stop - np.maximum(Z_stop-Zs,0))).tolist() Z_stop = (np.minimum(Z_stop,Zs)).tolist()r = [slice(start,stop) for start,stop in zip(R_start,R_stop)] z = [slice(start,stop) for start,stop in zip(Z_start,Z_stop)] R[r] = Z[z] print(Z) print(R)

81. 考虑一个数组`Z = [1,2,3,4,5,6,7,8,9,10,11,12,13,14]`,如何生成一个数组`R = [[1,2,3,4], [2,3,4,5], [3,4,5,6], ...,[11,12,13,14]]`? (★★★)

(提示: stride_tricks.as_strided)

# Author: Stefan van der WaltZ = np.arange(1,15,dtype=np.uint32) R = stride_tricks.as_strided(Z,(11,4),(4,4)) print(R)

82. 计算矩阵的秩 (★★★)

(提示: np.linalg.svd)

# Author: Stefan van der WaltZ = np.random.uniform(0,1,(10,10)) U, S, V = np.linalg.svd(Z) # Singular Value Decomposition rank = np.sum(S > 1e-10) print(rank)

83. 如何找出数组中出现频率最高的值?**(★★★)

(提示: np.bincount, argmax)

Z = np.random.randint(0,10,50) print(np.bincount(Z).argmax())

84. 从一个`10x10`的矩阵中提取出连续的`3x3`区块**(★★★)

(提示: stride_tricks.as_strided)

# Author: Chris BarkerZ = np.random.randint(0,5,(10,10)) n = 3 i = 1 + (Z.shape[0]-3) j = 1 + (Z.shape[1]-3) C = stride_tricks.as_strided(Z, shape=(i, j, n, n), strides=Z.strides + Z.strides) print(C)

85.创建一个满足 `Z[i,j] == Z[j,i]`的二维数组子类 (★★★)

(提示: class method)

# Author: Eric O. Lebigot # Note: only works for 2d array and value setting using indicesclass Symetric(np.ndarray): def __setitem__(self, index, value): i,j = index super(Symetric, self).__setitem__((i,j), value) super(Symetric, self).__setitem__((j,i), value)def symetric(Z): return np.asarray(Z + Z.T - np.diag(Z.diagonal())).view(Symetric)S = symetric(np.random.randint(0,10,(5,5))) S[2,3] = 42 print(S)

86. 考虑p个 `nxn` 矩阵和一组形状为`(n,1)`的向量，如何直接计算p个矩阵的乘积`(n,1)`? (★★★)

(提示: np.tensordot)

# Author: Stefan van der Waltp, n = 10, 20 M = np.ones((p,n,n)) V = np.ones((p,n,1)) S = np.tensordot(M, V, axes=[[0, 2], [0, 1]]) print(S)# It works, because: # M is (p,n,n) # V is (p,n,1) # Thus, summing over the paired axes 0 and 0 (of M and V independently), # and 2 and 1, to remain with a (n,1) vector.

87. 对于一个`16x16`的数组，如何得到一个区域的和(区域大小为`4x4`)? (★★★)

(提示: np.add.reduceat)

# Author: Robert KernZ = np.ones((16,16)) k = 4 S = np.add.reduceat(np.add.reduceat(Z, np.arange(0, Z.shape[0], k), axis=0), np.arange(0, Z.shape[1], k), axis=1) print(S)

88. 如何利用`numpy`数组实现Game of Life? (★★★)

(提示: Game of Life , Game of Life有哪些图形？)

# Author: Nicolas Rougierdef iterate(Z): # Count neighbours N = (Z[0:-2,0:-2] + Z[0:-2,1:-1] + Z[0:-2,2:] + Z[1:-1,0:-2] + Z[1:-1,2:] + Z[2: ,0:-2] + Z[2: ,1:-1] + Z[2: ,2:]) # Apply rules birth = (N==3) & (Z[1:-1,1:-1]==0) survive = ((N==2) | (N==3)) & (Z[1:-1,1:-1]==1) Z[...] = 0 Z[1:-1,1:-1][birth | survive] = 1 return ZZ = np.random.randint(0,2,(50,50)) for i in range(100): Z = iterate(Z) print(Z)

89. 如何找到一个数组的第n个最大值?** (★★★)

(提示: np.argsort | np.argpartition)

Z = np.arange(10000) np.random.shuffle(Z) n = 5# Slow print (Z[np.argsort(Z)[-n:]])# Fast print (Z[np.argpartition(-Z,n)[:n]])

90. 给定任意个数向量，创建笛卡尔积(每一个元素的每一种组合) (★★★)

(提示: np.indices)

# Author: Stefan Van der Waltdef cartesian(arrays): arrays = [np.asarray(a) for a in arrays] shape = (len(x) for x in arrays) ix = np.indices(shape, dtype=int) ix = ix.reshape(len(arrays), -1).T for n, arr in enumerate(arrays): ix[:, n] = arrays[n][ix[:, n]] return ixprint (cartesian(([1, 2, 3], [4, 5], [6, 7])))

91. 如何从一个常规数组中创建记录数组(`record array`)? (★★★)

(提示: np.core.records.fromarrays)

Z = np.array([("Hello", 2.5, 3), ("World", 3.6, 2)]) R = np.core.records.fromarrays(Z.T, names='col1, col2, col3', formats = 'S8, f8, i8') print(R)

92. 思考一个大向量`Z`, 用三种不同的方法计算它的立方 (★★★)

(提示: np.power, *, np.einsum)

# Author: Ryan G.x = np.random.rand(5e7)%timeit np.power(x,3) %timeit x*x*x %timeit np.einsum('i,i,i->i',x,x,x)

93. 考虑两个形状分别为`(8,3)` 和`(2,2)`的数组`A`和`B`. 如何在数组`A`中找到满足包含`B`中元素的行？(不考虑`B`中每行元素顺序)？ (★★★)

(提示: np.where)

# Author: Gabe SchwartzA = np.random.randint(0,5,(8,3)) B = np.random.randint(0,5,(2,2))C = (A[..., np.newaxis, np.newaxis] == B) rows = np.where(C.any((3,1)).all(1))[0] print(rows)

94. 思考一个`10x3`的矩阵，如何分解出有不全相同值的行 (如 `[2,2,3]`)** (★★★)

# Author: Robert KernZ = np.random.randint(0,5,(10,3)) print(Z) # solution for arrays of all dtypes (including string arrays and record arrays) E = np.all(Z[:,1:] == Z[:,:-1], axis=1) U = Z[~E] print(U) # soluiton for numerical arrays only, will work for any number of columns in Z U = Z[Z.max(axis=1) != Z.min(axis=1),:] print(U)

95. 将一个整数向量转换为二进制矩阵 (★★★)

(提示: np.unpackbits)

# Author: Warren WeckesserI = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128]) B = ((I.reshape(-1,1) & (2**np.arange(8))) != 0).astype(int) print(B[:,::-1])# Author: Daniel T. McDonaldI = np.array([0, 1, 2, 3, 15, 16, 32, 64, 128], dtype=np.uint8) print(np.unpackbits(I[:, np.newaxis], axis=1))

96. 给定一个二维数组，如何提取出唯一的行?**(★★★)

(提示: np.ascontiguousarray)

# Author: Jaime Fernández del RíoZ = np.random.randint(0,2,(6,3)) T = np.ascontiguousarray(Z).view(np.dtype((np.void, Z.dtype.itemsize * Z.shape[1]))) _, idx = np.unique(T, return_index=True) uZ = Z[idx] print(uZ)

97. 考虑两个向量`A`和`B`，写出用`einsum`等式对应的`inner, outer, sum, mul`函数 (★★★)

(提示: np.einsum)

# Author: Alex Riley # Make sure to read: http://ajcr.net/Basic-guide-to-einsum/A = np.random.uniform(0,1,10) B = np.random.uniform(0,1,10)np.einsum('i->', A) # np.sum(A) np.einsum('i,i->i', A, B) # A * B np.einsum('i,i', A, B) # np.inner(A, B) np.einsum('i,j->ij', A, B) # np.outer(A, B)

98. 考虑一个由两个向量描述的路径`(X,Y)`，如何用等距样例(`equidistant samples`)对其进行采样(`sample`)**(★★★)?

(提示: np.cumsum, np.interp)

# Author: Bas Swinckelsphi = np.arange(0, 10*np.pi, 0.1) a = 1 x = a*phi*np.cos(phi) y = a*phi*np.sin(phi)dr = (np.diff(x)**2 + np.diff(y)**2)**.5 # segment lengths r = np.zeros_like(x) r[1:] = np.cumsum(dr) # integrate path r_int = np.linspace(0, r.max(), 200) # regular spaced path x_int = np.interp(r_int, r, x) # integrate path y_int = np.interp(r_int, r, y)

99. 给定一个整数n 和一个二维数组X，从X中选择可以被解释为从多n度的多项分布式的行，即这些行只包含整数对n的和. (★★★)

(提示: np.logical_and.reduce, np.mod)

# Author: Evgeni BurovskiX = np.asarray([[1.0, 0.0, 3.0, 8.0], [2.0, 0.0, 1.0, 1.0], [1.5, 2.5, 1.0, 0.0]]) n = 4 M = np.logical_and.reduce(np.mod(X, 1) == 0, axis=-1) M &= (X.sum(axis=-1) == n) print(X[M])

100. 对于一个一维数组`X`，计算它boostrapped之后的95%置信区间的平均值. (★★★)

(提示: np.percentile)

# Author: Jessica B. HamrickX = np.random.randn(100) # random 1D array N = 1000 # number of bootstrap samples idx = np.random.randint(0, X.size, (N, X.size)) means = X[idx].mean(axis=1) confint = np.percentile(means, [2.5, 97.5]) print(confint)