Numpy闯关100题，我闯了95关

转自：数据不追牛

链接：
https://mp.weixin.qq.com/s/iyRjPLwxM2NVrgXKOacLTQ

对于Numpy，我讲的不多，因为和Pandas相比，他距离日常的数据处理更“远”一些。

但是，Numpy仍然是Python做数据分析所必须要掌握的基础库之一，以下题是github上的开源项目，主要为了检测你的Numpy能力，同时对你的学习作为一个补充。

来源：
https://github.com/rougier/numpy-100

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.version, np.show_config)

print(np.__version__)print(np.show_config)

3. 创建一个长度为10的空向量 (★☆☆)

(提示: np.zeros)

Z = np.zeros(10)

print(Z)

4. 如何找到任何一个数组的内存大小？(★☆☆)

(提示: size, itemsize)

Z = np.zeros((10,10))print('%d bytes' % (Z.size * Z.itemsize))

5. 如何从命令行得到numpy中add函数的说明文档? (★☆☆)

(提示: np.info)

import numpy

numpy.info(numpy.add)

6. 创建一个长度为10并且除了第五个值为1的空向量 (★☆☆)

(提示: array[4])

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

7. 创建一个值域范围从10到49的向量(★☆☆)

(提示: np.arange)

Z = np.arange(10,50)

print(Z)

8. 反转一个向量(第一个元素变为最后一个) (★☆☆)

(提示: array[::-1])

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

9. 创建一个 3x3 并且值从0到8的矩阵(★☆☆)

(提示: reshape)

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

print(Z)

10. 找到数组[1,2,0,0,4,0]中非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 的随机数组并找到它的最大值和最小值 (★☆☆)

(提示: min, max)

Z = np.random.random((10,10))

Zmin, Zmax = Z.min, Z.max

print(Zmin, Zmax)

14. 创建一个长度为30的随机向量并找到它的平均值 (★☆☆)

(提示: mean)

Z = np.random.random(30)m = Z.meanprint(m)

15. 创建一个二维数组，其中边界值为1，其余值为0 (★☆☆)

(提示: array[1:-1, 1:-1])

Z = np.ones((10,10))

Z[1:-1,1:-1] = 0

print(Z)

16. 对于一个存在在数组，如何添加一个用0填充的边界? (★☆☆)

(提示: np.pad)

Z = np.ones((5,5))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，并设置值1,2,3,4落在其对角线下方位置 (★☆☆)

(提示: np.diag)

Z = np.diag(1+np.arange(4),k=-1)print(Z)

19. 创建一个8x8 的矩阵，并且设置成棋盘样式 (★☆☆)

(提示: array[::2])

Z = np.zeros((8,8),dtype=int)

Z[1::2,::2] = 1

Z[::2,1::2] = 1

print(Z)

20. 考虑一个 (6,7,8) 形状的数组，其第100个元素的索引(x,y,z)是什么?

(提示: np.unravel_index)

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

21. 用tile函数去创建一个 8x8的棋盘样式矩阵(★☆☆)

(提示: np.tile)

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

print(Z)

22. 对一个5x5的随机矩阵做归一化(★☆☆)

(提示: (x - min) / (max - min))

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

23. 创建一个将颜色描述为(RGBA)四个无符号字节的自定义dtype？(★☆☆)

(提示: np.dtype)

color = np.dtype([('r', np.ubyte, 1),

('g', np.ubyte, 1),

('b', np.ubyte, 1),

('a', np.ubyte, 1)])

color

24. 一个5x3的矩阵与一个3x2的矩阵相乘，实矩阵乘积是什么？(★☆☆)

(提示: np.dot | @)

Z = np.dot(np.ones((5,3)), np.ones((3,2)))print(Z)

25. 给定一个一维数组，对其在3到8之间的所有元素取反 (★☆☆)

(提示: >, <=)

Z = np.arange(11)

Z[(3 < Z) & (Z <= 8)] *= -1

print(Z)

26. 下面脚本运行后的结果是什么? (★☆☆)

(提示: np.sum)

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

27. 考虑一个整数向量Z,下列表达合法的是哪个? (★☆☆)

（提示：这里还有“位运算符”）

Z**Z True

2 << Z >> 2 False

Z <- Z True

1j*Z True #复数

Z/1/1 True

Z<Z>Z False

28. 下面表达式的结果分别是什么？(★☆☆)

np.array(0) / np.array(0) nannp.array(0) // np.array(0) 0np.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 Harris

Z = 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))

31. 如何忽略所有的 numpy 警告(尽管不建议这么做)? (★☆☆)

(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) Faslse

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)? (★★☆)

(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 xZ = 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.sortprint (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 Burovski

Z = 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

42. 如何判断两和随机数组相等 (★★☆)

(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)

47. 给定两个数组X和Y，构造柯西(Cauchy)矩阵C (★★☆)

(提示: np.subtract.outer)

# Author: Evgeni Burovski

X = 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)).argminprint(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)的数组类型转换位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, 56, , , 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, 0.0G = 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: Divakar

n = 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 Tjoa

Z = 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 + yprint (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 = NameArray(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 Telenczuknp.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 Isaac

X = [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 = 16,16I = 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_countsprint(D_means)# Pandas solution as a reference due to more intuitive codeimport pandas as pdprint(pd.Series(D).groupby(S).mean)

69. 如何获得点积的对角线？(★★★)

(提示: np.diag)

# Author: Mathieu Blondel

A = 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 = 3Z0 = np.zeros(len(Z) + (len(Z)-1)*(nz))Z0[::nz+1] = Zprint(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. Rougier

faces = 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 Río

def 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 Rigtorpfrom 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. Smith

Z = 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 - P0L = (T**2).sum(axis=1)U = -((P0[:,0]-p[...,0])*T[:,0] + (P0[:,1]-p[...,1])*T[:,1]) / LU = U.reshape(len(U),1)D = P0 + U*T - preturn 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 = 0position = (1,1)R = np.ones(shape, dtype=Z.dtype)*fillP = 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)).tolistZ_start = (np.maximum(Z_start,0)).tolistR_stop = np.maximum(R_start, (R_stop - np.maximum(Z_stop-Zs,0))).tolistZ_stop = (np.minimum(Z_stop,Zs)).tolistr = [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 Walt

Z = 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 Decompositionrank = 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 = 3i = 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 indices

class 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, 20M = 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 Kern

Z = 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 neighboursN = (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 rulesbirth = (N==3) & (Z[1:-1,1:-1]==0)survive = ((N==2) | (N==3)) & (Z[1:-1,1:-1]==1)Z[...] = 0Z[1:-1,1:-1][birth | survive] = 1return 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).Tfor 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 Schwartz

A = 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 ZU = 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 Weckesser

I = 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. McDonald

I = 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 = 1x = a*phi*np.cos(phi)y = a*phi*np.sin(phi)dr = (np.diff(x)**2 + np.diff(y)**2)**.5 # segment lengthsr = np.zeros_like(x)r[1:] = np.cumsum(dr) # integrate pathr_int = np.linspace(0, r.max, 200) # regular spaced pathx_int = np.interp(r_int, r, x) # integrate pathy_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 Burovski

X = 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 arrayN = 1000 # number of bootstrap samplesidx = 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)