Numpy是Python做数据分析所必须要掌握的基础库之一。

---

1. 导入numpy库并简写为 np (★☆☆)

(提示: import … as …)

# import numpy as np

2. 打印numpy的版本和配置说明 (★☆☆)

(提示: np.__version__, np.show_config)

# print(np.__version__)
# 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)

# 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] = 1
# print(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.mean()
# print(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. 以下表达式运行的结果分别是什么? (★☆☆)

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

0 * np.nan
np.nan == np.nan
np.inf > np.nan
np.nan - np.nan
0.3 == 3 * 0.1

# print(0 * np.nan)

# print(np.nan == np.nan)

# print(np.inf > np.nan)

# print(np.nan - np.nan)

# print(0.3 == 3 * 0.1)

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.min()
# Z = (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)

print(sum(range(5),-1))
from numpy import *
print(sum(range(5),-1))

# print(sum(range(5),-1))

# from numpy import *
# print(sum(range(5),-1))

27. 考虑一个整数向量Z,下列表达合法的是哪个? (★☆☆)

Z**Z
2 << Z >> 2
Z <- Z
1j*Z
Z/1/1
Z<Z>Z

# Z = np.arange(5)
# Z ** Z  # legal

# Z = np.arange(5)
# 2 << Z >> 2  # false

# Z = np.arange(5)
# Z <- Z   # legal

# Z = np.arange(5)
# 1j*Z   # legal

# Z = np.arange(5)
# Z/1/1   # legal

# Z = np.arange(5)
# Z<Z>Z    # false

28. 下列表达式的结果分别是什么?(★☆☆)

np.array(0) / np.array(0)
np.array(0) // np.array(0)
np.array([np.nan]).astype(int).astype(float)

# print(np.array(0) / np.array(0))

# print(np.array(0) // np.array(0))

# print(np.array([np.nan]).astype(int).astype(float))

29. 如何从零位对浮点数组做舍入 ? (★☆☆)

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

# Z = np.random.uniform(-10,+10,10)
# print (np.copysign(np.ceil(np.abs(Z)), Z))

30. 如何找到两个数组中的共同元素? (★☆☆)

(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)

An equivalent way, with a context manager:

with np.errstate(divide='ignore'):
    Z = np.ones(1) / 0

32. 下面的表达式是正确的吗? (★☆☆)

(提示: imaginary number)

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

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

33. 如何得到昨天，今天，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')
# print ("Yesterday is " + str(yesterday))
# print ("Today is " + str(today))
# print ("Tomorrow is "+ str(tomorrow))

34. 如何得到所有与2016年7月对应的日期？ (★★☆)

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

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

35. 如何直接在位计算(A+B)\*(-A/2)(不建立副本)? (★★☆)

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

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

# np.divide(A,2,out=A)

# np.negative(A,out=A)

# np.multiply(A,B,out=A)

36. 用五种不同的方法去提取一个随机数组的整数部分(★★☆)

(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.ceil(Z)-1)

# print (Z.astype(int))

# print (np.trunc(Z))

37. 创建一个5x5的矩阵，其中每行的数值范围从0到4 (★★☆)

(提示: np.arange)

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

38. 通过考虑一个可生成10个整数的函数，来构建一个数组(★☆☆)

(提示: np.fromiter)

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

39. 创建一个长度为10的随机向量，其值域范围从0到1，但是不包括0和1 (★★☆)

(提示: np.linspace)

# Z = np.linspace(0,1,11,endpoint=False)[1:]
# print (Z)

40. 创建一个长度为10的随机向量，并将其排序 (★★☆)

(提示: sort)

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

41.对于一个小数组，如何用比 np.sum更快的方式对其求和？(★★☆)

(提示: np.add.reduce)

# Z = np.arange(10)
# np.add.reduce(Z)

42. 对于两个随机数组A和B，检查它们是否相等(★★☆)

(提示: np.allclose, np.array_equal)

# A = np.random.randint(0,2,5)
# B = np.random.randint(0,2,5)
# # Assuming identical shape of the arrays and a tolerance for the comparison of values
# equal = np.allclose(A,B)
# print(equal)

# # 方法2
# # Checking both the shape and the element values, no tolerance (values have to be exactly equal)
# equal = np.array_equal(A,B)
# print(equal)

43. 创建一个只读数组(read-only) (★★☆)

(提示: flags.writeable)

# 使用如下过程实现
Z = np.zeros(10)
Z.flags.writeable = False
Z[0] = 1
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-54-6fd4c6570dd1> in <module>()
      1 Z = np.zeros(10)
      2 Z.flags.writeable = False
----> 3 Z[0] = 1

ValueError: assignment destination is read-only

44. 将笛卡尔坐标下的一个10x2的矩阵转换为极坐标形式(★★☆)

(hint: 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. 创建一个长度为10的向量，并将向量中最大值替换为1 (★★☆)

(提示: argmax)

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

46. 创建一个结构化数组，并实现 x 和 y 坐标覆盖 [0,1]x[0,1] 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Cauchy矩阵C (Cij =1/(xi - yj))

(提示: np.subtract.outer)

# X = np.arange(8)
# Y = X + 0.5
# C = 1.0 / np.subtract.outer(X, Y)
# print(np.linalg.det(C))

48. 打印每个numpy标量类型的最小值和最大值？ (★★☆)

(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. 如何打印一个数组中的所有数值? (★★☆)

(提示: np.set_printoptions)

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

50. 给定标量时，如何找到数组中最接近标量的值？(★★☆)

(提示: argmin)

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

51. 创建一个表示位置(x,y)和颜色(r,g,b)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. 对一个表示坐标形状为(100,2)的随机向量，找到点与点的距离(★★☆)

(提示: np.atleast_2d, T, np.sqrt)

# Z = np.random.random((10,2))
# X,Y = np.atleast_2d(Z[:,0], Z[:,1])
# D = np.sqrt( (X-X.T)**2 + (Y-Y.T)**2)
# print (D)

# # 方法2
# # Much faster with scipy
# import scipy
# # Thanks Gavin Heverly-Coulson (#issue 1)
# import scipy.spatial
# D = scipy.spatial.distance.cdist(Z,Z)
# print (D)

53. 如何将32位的浮点数(float)转换为对应的整数(integer)?

(提示: astype(copy=False))

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

54. 如何读取以下文件? (★★☆)

(提示: np.genfromtxt)

1, 2, 3, 4, 5
6,  ,  , 7, 8
 ,  , 9,10,11

参考链接

55. 对于numpy数组，enumerate的等价操作是什么？(★★☆)

(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. 生成一个通用的二维Gaussian-like数组 (★★☆)

(提示: np.meshgrid, np.exp)

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

57. 对一个二维数组，如何在其内部随机放置p个元素? (★★☆)

(提示: np.put, np.random.choice)

# 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. 减去一个矩阵中的每一行的平均值 (★★☆)

(提示: mean(axis=,keepdims=))

# X = np.random.rand(5, 10)
# # Recent versions of numpy
# Y = X - X.mean(axis=1, keepdims=True)
# print(Y)

# # 方法2
# # Older versions of numpy
# Y = X - X.mean(axis=1).reshape(-1, 1)
# print (Y)

59. 如何通过第n列对一个数组进行排序? (★★☆)

(提示: argsort)

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

60. 如何检查一个二维数组是否有空列？(★★☆)

(提示: any, ~)

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

61. 从数组中的给定值中找出最近的值 (★★☆)

(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. 如何用迭代器(iterator)计算两个分别具有形状(1,3)和(3,1)的数组? (★★☆)

(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方法)

# class NamedArray(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. 考虑一个给定的向量，如何对由第二个向量索引的每个元素加1(小心重复的索引)? (★★★)

(提示: np.bincount | np.add.at)

# Z = np.ones(10)
# I = np.random.randint(0,len(Z),20)
# Z += np.bincount(I, minlength=len(Z))
# print(Z)

# # 方法2
# np.add.at(Z, I, 1)
# print(Z)

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

(提示: np.bincount)

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

66. 考虑一个(dtype=ubyte) 的 (w,h,3)图像，计算其唯一颜色的数量(★★★)

(提示: np.unique)

# w,h = 16,16
# I = np.random.randint(0,2,(h,w,3)).astype(np.ubyte)
# #Note that we should compute 256*256 first. 
# #Otherwise numpy will only promote F.dtype to 'uint16' and overfolw will occur
# F = I[...,0]*(256*256) + I[...,1]*256 +I[...,2]
# n = len(np.unique(F))
# print (n)

67. 考虑一个四维数组，如何一次性计算出最后两个轴(axis)的和？ (★★★)

(提示: sum(axis=(-2,-1)))

# A = np.random.randint(0,10,(3,4,3,4))
# # solution by passing a tuple of axes (introduced in numpy 1.7.0)
# sum = A.sum(axis=(-2,-1))
# print (sum)

# # 方法2
# sum = A.reshape(A.shape[:-2] + (-1,)).sum(axis=-1)
# print (sum)

68. 考虑一个一维向量D，如何使用相同大小的向量S来计算D子集的均值？(★★★)

(提示: np.bincount)

# D = 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)

# # 方法2
# import pandas as pd
# print(pd.Series(D).groupby(S).mean())

69. 如何获得点积 dot prodcut的对角线? (★★★)

(提示: np.diag)

# A = np.random.uniform(0,1,(5,5))
# B = np.random.uniform(0,1,(5,5))
# # slow version
# np.diag(np.dot(A, B))

## 方法2
# # Fast version
# np.sum(A * B.T, axis=1)

## 方法3
# # Faster version
# np.einsum("ij,ji->i", A, B)

70. 考虑一个向量[1,2,3,4,5],如何建立一个新的向量，在这个新向量中每个值之间有3个连续的零？(★★★)

(提示: array[::4])

# Z = 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[[]])

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

73. 考虑一个可以描述10个三角形的triplets，找到可以分割全部三角形的line segment

Consider a set of 10 triplets describing 10 triangles (with shared vertices), find the set of unique line segments composing all the triangles (★★★)
(提示: repeat, np.roll, np.sort, view, np.unique)

# 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，如何产生一个数组A满足np.bincount(A)==C(★★★)

(提示: np.repeat)

# C = 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)

# 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. Consider a one-dimensional array Z, build a two-dimensional array whose first row is (Z[0],Z[1],Z[2]) and each subsequent row is shifted by 1 (last row should be (Z[-3],Z[-2],Z[-1]) (★★★)

(提示: from numpy.lib import stride_tricks)

# from numpy.lib import stride_tricks

# def 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，或者原位(in-place)改变浮点数的符号(sign)？(★★★)

(提示: np.logical_not, np.negative)

# 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. 考虑两组点集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？(★★★)

# # 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.Consider an arbitrary array, write a function that extract a subpart with a fixed shape and centered on a given element (pad with a fill value when necessary) (★★★)

(hint: minimum, maximum)

# Z = 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%2

# R_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)

# Z = np.arange(1,15,dtype=np.uint32)
# R = stride_tricks.as_strided(Z,(11,4),(4,4))
# print (R)

82. 计算一个矩阵的秩(★★★)

(提示: np.linalg.svd)

# Z = 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. 如何找到一个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)

# Z = 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]的子类 (★★★)

(提示: class 方法)

# 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)

# p, 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(block-sum)的和(区域大小为4x4)? (★★★)

(提示: np.add.reduceat)

# 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)

# def 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 Z

# Z = 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:]])

# # 方法2
# # 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)

# def 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 ix

# print (cartesian(([1, 2, 3], [4, 5], [6, 7])))

91. 如何从一个正常数组创建记录数组(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. 考虑一个大向量Z, 用三种不同的方法计算它的立方(★★★)

(提示: np.power, \*, np.einsum)

# x = np.random.rand()
# np.power(x,3)

## 方法2
# x*x*x

## 方法3
# 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)

# 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. 考虑一个10x3的矩阵，分解出有不全相同值的行 (如 [2,2,3]) (★★★)

# Z = 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)

# # 方法2
# # 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matrix binary的表现形式 (★★★)

(提示: np.unpackbits)

# 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])

# # 方法2
# 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(unique)行?(★★★)

(提示: np.ascontiguousarray)

# Z = 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)

# A = np.random.uniform(0,1,10)
# B = np.random.uniform(0,1,10)
# print ('sum')
# print (np.einsum('i->', A))# np.sum(A)

# print ('A * B')
# print (np.einsum('i,i->i', A, B)) # A * B

# print ('inner')
# print (np.einsum('i,i', A, B))    # np.inner(A, B)

# print ('outer')
# print (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)? (★★★)

Considering a path described by two vectors (X,Y), how to sample it using equidistant samples
(提示: np.cumsum, np.interp)

# phi = 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. Given an integer n and a 2D array X, select from X the rows which can be interpreted as draws from a multinomial distribution with n degrees, i.e., the rows which only contain integers and which sum to n. (★★★)

(提示: np.logical_and.reduce, np.mod)

# 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。

(Compute bootstrapped 95% confidence intervals for the mean of a 1D array X，i.e. resample the elements of an array with replacement N times, compute the mean of each sample, and then compute percentiles over the means). (★★★)
(提示: np.percentile)

# X = 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)