NumPy练习

100 道NumPy练习题

翻译：YingJoy
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)
print (Z)

19. 创建一个8x8的棋盘矩阵（填充为棋盘样式） (★☆☆)

(提示: array[::2])

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

20. 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的元素进行取反 (★☆☆)

(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**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)                           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 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)?** (★★☆)

(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)

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 (★★☆)

\(C_{ij}=\frac{1}{x_i-y_j}\)

(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)).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.spatial

Z = 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, 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: 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 Weckesser

X = 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 Weckesser

Z = 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 Olsen

Z = 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 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 Horesh

w,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 Río

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)

# 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 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 Weckesser

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[[]])

# Author: Eelco Hoogendoorn

A = 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 Río

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)

# 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 Rigtorp
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 - 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 Rougier

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)

# 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 Walt

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 Barker

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 Walt

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 Rougier

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:]])

# 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 Walt

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 Kern

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)
# 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 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 Río

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)

# 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 Swinckels

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. 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. Hamrick

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)