numpy实战小练习集锦附代码

Abstract：Numpy是Python做数据分析所必须要掌握的基础库之一。这篇练习通过89道题目带你快速玩转Numpy。

介绍

Numpy是Python做数据分析所必须要掌握的基础库之一。这篇练习通过89道题目带你快速玩转Numpy。

练习

  # coding:utf-8
  import numpy as np 
  import pandas as pd 
  ​
  # 1.Print the numpy version and the configuration
  print (np.__version__)
  print np.show_config()
  ​
  # 2. Create a null vector of size 10
  Z = np.zeros(10)
  print Z 
  ​
  # 3.Create a null vector of size 10 but the fifth value which is 1
  A = np.zeros(10)
  A[4] = 1
  print A 
  ​
  # 4.Create a vector with values ranging from 10 to 49 
  A = np.arange(50)
  print A 
  ​
  # 5.Reverse a vector (first element becomes last)
  A = np.arange(50)
  A = A[::-1]
  print A  
  ​
  # 6.Create a 3x3 matrix with values ranging from 0 to 8
  Z = np.arange(9).reshape(3,3)
  print Z 
  ​
  # 7.Find indices of non-zero elements from [1,2,0,0,4,0]
  nz = np.nonzero([1,2,0,0,4,0])
  print (nz)
  ​
  # 8.Create a 3x3 identity matrix
  A = np.eye(3)
  print A 
  ​
  # 9.create a 3*3*3 array with random values
  A = np.random.random((3,3,3))
  print (Z)
  ​
  # 10.Create a 10x10 array with random values and find the minimum and maximum values
  Z = np.random.random((10,10))
  Zmin,Zmax = Z.min(), Z.max()
  print (Zmin,Zmax)
  ​
  # 11.Create a random vector of size 30 and find the mean value
  A = np.random.random(30)
  m = A.mean()
  print (m)
  ​
  # 12.Create a 2d array with 1 on the border and 0 inside
  Z = np.ones((10,10))
  Z[1:-1,1:-1] = 0
  print(Z)
  ​
  # 13.How to add a border (filled with 0's) around an existing array?
  A = np.ones((5,5))  # ones(): 返回给定形状和类型的新数组，用数字填充
  A = np.pad(A,pad_width=1, mode='constant', constant_values=0)   # pad():filling the array
  print A 
  ​
  # 14.What is the result of the following expression?
  print (0 * np.nan)
  print (np.nan == np.nan)
  print (np.nan - np.nan)
  print (0.3 == 3 * 0.1)
  ​
  # 15.Create a 5x5 matrix with values 1,2,3,4 just below the diagonal
  A = np.diag(1+np.arange(4),k=-1)
  print A 
  ​
  # 16.Create a 8x8 matrix and fill it with a checkerboard pattern
  A = np.zeros((8,8),dtype=int)
  A[1::2,::2] = 1
  A[::2,1::2] = 1
  print A 
  ​
  # 17.Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element
  print (np.unravel_index(100,(6,7,8)))   # unravel_index(): 将平面索引的平面索引或数组转换为坐标数组的元组
  ​
  # 18.Create a checkerboard 8x8 matrix using the tile function
  Z = np.tile( np.array([[0,1],[1,0]]), (4,4))
  print(Z)
  ​
  # 19.Normalize a 5x5 random matrix
  Z = np.random.random((5,5))
  Zmax, Zmin = Z.max(), Z.min()
  Z = (Z - Zmin)/(Zmax - Zmin)
  print(Z)
  ​
  # 20. Create a custom dtype that describes a color as four unsigned bytes (RGBA)
  color = np.dtype([("r", np.ubyte, 1),
                    ("g", np.ubyte, 1),
                    ("b", np.ubyte, 1),
                    ("a", np.ubyte, 1)])
  ​
  # 21.Multiply a 5x3 matrix by a 3x2 matrix (real matrix product)
  A = np.dot(np.ones((5,3)),np.ones((3,2)))
  print A 
  ​
  B = np.dot(np.ones((1,2)),np.ones((2,2)))
  print B 
  ​
  # 22.Given a 1D array, negate all elements which are between 3 and 8, in place.
  A = np.arange(11)
  A[(3 < A) & (A <= 8)] *= -1
  print A 
  ​
  # 23.What is the output of the following script?
  print (sum(range(5),-1))
  ​
  # 24.What are the result of the following expressions?
  print(np.array(0) / np.array(0))
  print(np.array(0) // np.array(0))
  print(np.array([np.nan]).astype(int).astype(float))
  ​
  # 25.How to round away from zero a float array ?
  Z = np.random.uniform(-10,+10,10)
  print (np.copysign(np.ceil(np.abs(Z)), Z))
  ​
  # 26.How to find common values between two arrays?
  A1 = np.random.randint(0,10,10)
  A2 = np.random.randint(0,10,10)
  print A1,A2
  print (np.intersect1d(A1,A2))
  ​
  # 27.How to ignore all numpy warnings (not recommended)?
  defaults = np.seterr(all="ignore")
  Z = np.ones(1) / 0
  _ = np.seterr(**defaults)
  ​
  with np.errstate(divide='ignore'):
      Z = np.ones(1) / 0
  ​
  # 28. Is the following expressions true? 
  # numpy.sqrt():按元素方式返回数组的正平方根
  print np.sqrt(-1) == np.emath.sqrt(-1)
  ​
  ​
  # 29. How to get the dates of yesterday, today and tomorrow?
  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,today,tomorrow
  ​
  # 30.How to get all the dates corresponding to the month of July 2016? 
  A = np.arange('2018-01','2018-02',dtype='datetime64[D]')
  print A 
  A = np.arange('2019-03','2019-05',dtype='datetime64[D]')
  print A 
  ​
  # 31.How to compute ((A+B)*(-A/2)) in place (without copy)?
  A = np.ones(3)*1
  B = np.ones(3)*2
  C = np.ones(3)*3
  print np.add(A,B,out=B)
  print np.divide(A,2,out=A)
  print np.negative(A,out=A)
  print np.multiply(A,B,out=A)
  ​
  # 32.Extract the integer part of a random array using 5 different methods
  # uniform():从均匀分布绘制样本
  # floor():逐元素地返回输入的底
  # ceil():元素方式返回输入的上限
  # astype():数组的复制，强制转换为指定的类型
  # trunc():按元素方式返回输入的截断值
  Z = np.random.uniform(0,10,10)
  print Z 
  print (Z - Z%1)
  print (np.floor(Z))
  print (np.ceil(Z) - 1)
  print (Z.astype(int))
  print (np.trunc(Z))
  ​
  # 33.Create a 5x5 matrix with row values ranging from 0 to 4
  A = np.zeros((5,5))
  A += np.arange(5)
  print A 
  ​
  # 34.onsider a generator function that generates 10 integers and use it to build an array
  # zeros():返回给定形状和类型的新数组，用零填充
  # numpy.fromiter():从可迭代对象创建新的1维数组
  def generate():
      for x in range(10):
          yield x
  Z = np.fromiter(generate(),dtype=float,count=-1)
  print Z 
  ​
  # 35.Create a vector of size 10 with values ranging from 0 to 1, both excluded
  # linsapce():在指定的间隔内返回均匀间隔的数字
  Z = np.linspace(0,1,11,endpoint=False)[1:]
  print(Z) 
  ​
  # 36.Create a random vector of size 10 and sort it
  Z = np.random.random(10)
  Z.sort()
  print Z 
  ​
  # 37.How to sum a small array faster than np.sum? 
  # add():按元素添加参数
  Z = np.arange(10)
  print np.add.reduce(Z)
  ​
  # 38.Consider two random array A and B, check if they are equal
  # allclose():如果两个数组在元素级别在容差内相等，则返回True
  # array_equal():如果两个数组具有相同的形状和元素，则为True，否则为False
  A = np.random.randint(0,2,5)
  B = np.random.randint(0,2,5)
  equal = np.allclose(A,B)
  print (equal)
  equal = np.array_equal(A,B)
  print (equal)
  ​
  C = np.random.randint(0,10,10)
  D = np.random.randint(0,10,10)
  print C,D 
  print np.allclose(C,D)
  print np.array_equal(C,D)
  ​
  # 39.Make an array immutable (read-only)
  # writeable:确保返回的数组可以写入
  Z = np.zeros(10)
  Z.flags.writeable = False
  ​
  # 40.Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates 
  A = np.random.random((10,2))
  X,Y = A[:,0],A[:,1]
  R = np.sqrt(X**2+Y**2)
  T = np.arctan2(Y,X)
  print (R)
  print (T)
  ​
  # 41.Create random vector of size 10 and replace the maximum value by 0
  # argmax():返回沿轴的最大值的索引
  Z = np.random.random(10)
  Z[Z.argmax()] = 0
  print (Z)
  ​
  # 42.Create a structured array with x and y coordinates covering the [0,1]x[0,1] area
  # meshgrid():从坐标向量返回坐标矩阵
  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)
  ​
  # 43.Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj))
  # outer():计算两个向量的外积
  # numpy.linalg.det():计算数组的行列式
  X = np.arange(8)
  Y = X + 0.5
  C = 1.0 / np.subtract.outer(X,Y)
  print (np.linalg.det(C))
  ​
  # 44.Print the minimum and maximum representable value for each numpy scalar type
  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)
  ​
  # 45.Print the minimum and maximum representable value for each numpy scalar type
  np.set_printoptions(threshold=np.nan)
  Z = np.zeros((8,8))
  print Z 
  ​
  # 46.How to find the closest value (to a given scalar) in a vector? 
  A = np.arange(100)
  v = np.random.uniform(0,100)
  index = (np.abs(A - v)).argmin()
  print (A[index])
  ​
  # 47.创建一个表示位置(x,y)和颜色(r,g,b)的结构化数组
  Z = np.zeros(10, [ ('position', [ ('x', float, 1),
                                    ('y', float, 1)]),
                      ('color',    [ ('r', float, 1),
                                   ('g', float, 1),
                                    ('b', float, 1)])])
  print (Z)
  ​
  # 48.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
  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)
  ​
  # 49.如何将32位的浮点数(float)转换为对应的整数(integer)?
  A = np.arange(10,dtype=np.int32)
  A = A.astype(np.float32, copy=False)
  print A
  ​
  # 50.对于numpy数组，enumerate的等价操作是什么？
  # enumerate:多维索引迭代器;返回迭代器产生数组坐标和值的对
  Z = np.arange(9).reshape(3,3)
  print Z
  for index,value in np.ndenumerate(Z):
      print (index, value)
  for index in np.ndindex(Z.shape):
      print (index, Z[index])
  ​
  # 51.生成一个通用的二维Gaussian-like数组
  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)
  ​
  # 52.对一个二维数组，如何在其内部随机放置p个元素?
  # numpy.random.choice():从给定的1-D数组生成随机样本
  # numpy.put():用给定值替换数组的指定元素
  n = 10
  p = 4
  A = np.zeros((n,n))
  np.put(A, np.random.choice(range(n*n), p, replace=False), 1)
  print A 
  ​
  # 53.减去一个矩阵中的每一行的平均值
  X = np.random.rand(5,10)
  Y = X - X.mean(axis=1,keepdims=True)
  print Y 
  ​
  Y = X - X.mean(axis=1).reshape(-1,1)
  print Y
  ​
  # 54.如何通过第n列对一个数组进行排序?
  Z = np.random.randint(0,10,(3,3))
  print Z 
  print (Z[Z[:,1].argsort()])
  ​
  # 55.如何检查一个二维数组是否有空列？
  Z = np.random.randint(0,3,(3,10))
  print ((~Z.any(axis=0).any()))
  ​
  # 56.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?
  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])
  ​
  # 57.创建一个具有name属性的数组类
  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)
  ​
  # 58.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)?
  Z = np.ones(10)
  I = np.random.randint(0,len(Z),20)
  Z += np.bincount(I, minlength=len(Z))
  print(Z)
  ​
  # 59.根据索引列表(I)，如何将向量(X)的元素累加到数组(F)?
  # numpy.bincount():计算非负整数数组中每个值的出现次数
  X = [1,2,3,4,5,6]
  I = [1,3,5,7,9,4]
  F = np.bincount(I,X)
  print F 
  ​
  # 60.考虑一个(dtype=ubyte) 的 (w,h,3)图像，计算其唯一颜色的数量
  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 n
  ​
  # 61.考虑一个四维数组，如何一次性计算出最后两个轴(axis)的和？
  # randint():将随机整数从低（包括）返回到高（不包含）.
  A = np.random.randint(0,10,(3,4,3,4))
  print A 
  sum = A.sum(axis=(-2,-1))
  print sum
  ​
  # 62.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？
  D = np.random.uniform(0,1,100)
  S = np.random.randint(0,10,100)
  D_sums = np.bincount(S)
  D_counts = np.bincount(S)
  D_means = D_sums / D_counts
  print (D_means)
  ​
  print (pd.Series(D).groupby(S).mean())
  ​
  # 63.如何获得点积 dot prodcut的对角线?
  # np.sum
  A = np.random.uniform(0,1,(5,5))
  B = np.random.uniform(0,1,(5,5))
  print np.sum(A*B.T, axis=1)
  # np.diag
  print np.diag(np.dot(A,B))
  # np.einsum()
  print np.einsum("ij,ji->i", A, B)
  ​
  # 64.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？
  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
  ​
  # 65.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？
  A = np.arange(25).reshape(5,5)
  A[0,1] = A[1,0]
  print A 
  ​
  # 66.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
  faces = np.random.randint(0,100,(10,3))
  F = np.roll(faces.repeat(2,axis=1),-1,axis=1)
  F = np.sort(F,axis=1)
  G = F.view( dtype=[('p0',F.dtype),('p1',F.dtype)] )
  G = np.unique(G)
  print G 
  ​
  # 67.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
  # np.repeat
  C = np.bincount([1,1,2,3,4,4,6])
  A = np.repeat(np.arange(len(C)), C)
  print A 
  ​
  # 68.如何通过滑动窗口计算一个数组的平均数?
  # 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))
  ​
  # 69.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]) 
  # from.numpy.lib
  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 
  ​
  # 70.如何对布尔值取反，或者原位(in-place)改变浮点数的符号(sign)？
  # np.logical_not, np.negative
  Z = np.random.randint(0,2,100)
  print np.logical_not(Z,out=Z)
  Z = np.random.uniform(-1.0,1.0,100)
  print np.negative(Z, out=Z)
  ​
  ​
  # 71.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))
  ​
  # 72.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？
  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]))
  ​
  # 73.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]]?
  # stride_tricks.as_strided
  Z = np.arange(1,15,dtype=np.uint32)
  R = stride_tricks.as_strided(Z,(11,4),(4,4))
  print R
  ​
  # 74.计算一个矩阵的秩
  # np.linalg.svd
  Z = np.random.uniform(0,1,(10,10))
  U, S, V = np.linalg.svd(Z)
  rank = np.sum(S > 1e-10)
  print rank 
  ​
  # 75.如何找到一个数组中出现频率最高的值？
  # np.bincount, argmax
  Z = np.random.randint(0,10,50)
  print (np.bincount(Z).argmax())
  ​
  # 76.从一个10x10的矩阵中提取出连续的3x3区块
  # 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 
  ​
  # 77.创建一个满足 Z[i,j] == Z[j,i]的子类
  # class 
  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)
  ​
  # 78.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)？
  # 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 
  ​
  # 79.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)?
  # 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)
  ​
  # 80.如何利用numpy数组实现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)
  ​
  # 81.如何找到一个数组的第n个最大值?
  # np.argsort
  # numpy.random.shuffle():通过随机播放其内容来修改序列
  Z = np.arange(10000)
  np.random.shuffle(Z)
  n = 5
  print (Z[np.argsort(Z)[-n:]])
  ​
  # 82.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)(
  # 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])))
  ​
  # 82.如何从一个正常数组创建记录数组(record array)?
  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)
  ​
  # 83.考虑一个大向量Z, 用三种不同的方法计算它的立方
  # np.power:第一个数组元素从第二个数组提升到权力，逐元素
  x = np.random.rand()
  print np.power(x,3)
  ​
  # 84. 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 
  E = np.all(Z[:,1:] == Z[:,:-1], axis=1)
  U = Z[~E]
  print (U)
  ​
  U = Z[Z.max(axis=1) != Z.min(axis=1),:]
  print (U)
  ​
  # 85.将一个整数向量转换为matrix binary的表现形式
  print (np.unpackbits(I[:, np.newaxis], axis=1))
  ​
  # 86.给定一个二维数组，如何提取出唯一的(unique)行?
  # 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)
  ​
  # 87.考虑两个向量A和B，写出用einsum等式对应的inner, outer, sum, mul函数
  # 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)
  ​
  # 88. 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
  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)
  ​
  # 89.对于一个一维数组X，计算它boostrapped之后的95%置信区间的平均
  # 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)

REFERENCE

这100道练习，带你玩转Numpy

100 numpy exercises

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