numpy 练习题（附难度、答案、解析）

谁借莪１个温暖的怀抱￠ 2021-11-04 16:31 1443阅读 0赞

**NumPy数据分析库需要掌握的知识点：**

*  **NumPy基本数据结构**
 *  **NumPy数组操作**
 *  **NumPy矩阵操作**
 *  **NumPy随机数的生成**
 *  **NumPy常用函数（数学类、统计学类等）**
 *  **NumPy数据处理**
 *  **NumPy文件操作**

# 100 numpy exercises #

> Github资源链接：[https://github.com/rougier/numpy-100][https_github.com_rougier_numpy-100]  
> 版本：Python 3.0

#### 1. Import the numpy package under the name `np` (★☆☆) ####

import numpy as np

#### 2. Print the numpy version and the configuration (★☆☆) ####

print(np.__version__)
    np.show_config()

#### 3. Create a null vector of size 10 (★☆☆) ####

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

#### 4. How to find the memory size of any array (★☆☆) ####

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

#### 5. How to get the documentation of the numpy add function from the command line? (★☆☆) ####

%run `python -c "import numpy; numpy.info(numpy.add)"`

#### 6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆) ####

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

#### 7. Create a vector with values ranging from 10 to 49 (★☆☆) ####

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

#### 8. Reverse a vector (first element becomes last) (★☆☆) ####

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

#### 9. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆) ####

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

#### 10. Find indices of non-zero elements from \[1,2,0,0,4,0\] (★☆☆) ####

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

#### 11. Create a 3x3 identity matrix (★☆☆) ####

Z = np.eye(3)  #单位矩阵
    print(Z)

#### 12. Create a 3x3x3 array with random values (★☆☆) ####

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

#### 13. 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)

#### 14. Create a random vector of size 30 and find the mean value (★☆☆) ####

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

#### 15. 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)

#### 16. How to add a border (filled with 0’s) around an existing array? (★☆☆) ####

Z = np.ones((5,5))
    Z = np.pad(Z, pad_width=1, mode='constant', constant_values=0)
    print(Z)

#### 17. What is the result of the following expression? (★☆☆) ####

print(0 * np.nan)
    print(np.nan == np.nan)
    print(np.inf > np.nan)
    print(np.nan - np.nan)
    print(np.nan in set([np.nan]))
    print(0.3 == 3 * 0.1)

#### 18. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal (★☆☆) ####

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

#### 19. Create a 8x8 matrix and fill it with a checkerboard pattern (★☆☆) ####

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

#### 20. Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element? ####

print(np.unravel_index(99,(6,7,8)))

#### 21. Create a checkerboard 8x8 matrix using the tile function (★☆☆) ####

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

#### 22. Normalize a 5x5 random matrix (★☆☆) ####

# 矩阵标准化
    Z = np.random.random((5,5))
    Z1 = (Z-np.mean(Z))/(np.std(Z)) # mean取平均值，std计算矩阵标准差
    # Z2 = (Z-Z.mean())/(Z.std()) 结果相同
    print(Z1)

#### 23. Create a custom dtype that describes a color as four unsigned bytes (RGBA) (★☆☆) ####

# 自定义数据类型
    color = np.dtype([("r", np.ubyte, 1),
                      ("g", np.ubyte, 1),
                      ("b", np.ubyte, 1),
                      ("a", np.ubyte, 1)])

#### 24. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆) ####

A = np.ones((5,3))
    B = np.ones((3,2))
    C = np.dot(A,B) 
    # 等同于 C = A @ B
    print (C)

#### 25. Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆) ####

# Author: Evgeni Burovski
    
    Z = np.arange(11)
    Z[(3 < Z) & (Z <= 8)] *= -1
    print(Z)

#### 26. What is the output of the following script? (★☆☆) ####

# Author: Jake VanderPlas
    
    print(sum(range(5),-1)) # python内置sum，求和后再加（-1）
    from numpy import *
    print(sum(range(5),-1)) # np内sum，-1是维度

#### 27. Consider an integer vector Z, which of these expressions are legal? (★☆☆) ####

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

#### 28. 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))

#### 29. How to round away from zero a float array ? (★☆☆) ####

# 远离0取整
    Z = np.random.uniform(-10,+10,10) # uniform() 随机实数
    print (np.copysign(np.ceil(np.abs(Z)), Z)) # copysign() 复制符号

#### 30. How to find common values between two arrays? (★☆☆) ####

Z1 = np.random.randint(0,10,10)
    Z2 = np.random.randint(0,10,10)
    print("Z1: " , Z1)
    print("Z2: " , Z2)
    print(np.intersect1d(Z1, Z2)) # 取交集

#### 31. How to ignore all numpy warnings (not recommended)? (★☆☆) ####

# 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. Is the following expressions true? (★☆☆) ####

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

#### 33. 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')

#### 34. How to get all the dates corresponding to the month of July 2016? (★★☆) ####

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

#### 35. 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
    np.add(A,B,out=B)
    np.divide(A,2,out=A)
    np.negative(A,out=A)
    np.multiply(A,B,out=A)

#### 36. Extract the integer part of a random array using 5 different methods (★★☆) ####

Z = np.random.uniform(0,10,5)
    print (Z)
    print (Z - Z%1) # Z%1可以取小数部分
    print (np.floor(Z))
    print (np.ceil(Z)-1)
    print (Z.astype(int))
    print (np.trunc(Z)) # trunc()去掉小数部分

#### 37. Create a 5x5 matrix with row values ranging from 0 to 4 (★★☆) ####

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

#### 38. Consider a generator function that generates 10 integers and use it to build an array (★☆☆) ####

def generate():
        for x in range(10):
            yield x
    Z = np.fromiter(generate(),dtype=float,count=-1)
    # numpy.fromiter 方法从可迭代对象中建立 ndarray 对象，返回一维数组。
    print(Z)

#### 39. Create a vector of size 10 with values ranging from 0 to 1, both excluded (★★☆) ####

Z = np.linspace(0,1,11,endpoint=False)[1:]
    print(Z)
    # numpy.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None)
    # 在指定的间隔内返回均匀间隔的数字。
    # 返回num均匀分布的样本，在[start, stop]。
    # 这个区间的端点可以任意的被排除在外。

#### 40. Create a random vector of size 10 and sort it (★★☆) ####

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

#### 41. How to sum a small array faster than np.sum? (★★☆) ####

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

#### 42. Consider two random array A and B, check if they are equal (★★☆) ####

A = np.random.randint(0,2,5)
    B = np.random.randint(0,2,5)
    
    # 比较两个array是不是每一元素都相等，默认在1e-05的误差范围内
    equal = np.allclose(A,B)
    print(equal)
    
    # shape和各元素相等
    equal = np.array_equal(A,B)
    print(equal)

#### 43. Make an array immutable (read-only) (★★☆) ####

Z = np.zeros(10)
    Z.flags.writeable = False
    Z[0] = 1 # 改为只读后，报错

#### 44. Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates (★★☆) ####

# 笛卡尔坐标转极坐标
    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. Create random vector of size 10 and replace the maximum value by 0 (★★☆) ####

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

#### 46. Create a structured array with `x` and `y` coordinates covering the \[0,1\]x\[0,1\] area (★★☆) ####

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. Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj)) ####

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

#### 48. 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)

#### 49. How to print all the values of an array? (★★☆) ####

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

#### 50. How to find the closest value (to a given scalar) in a vector? (★★☆) ####

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

#### 51. Create a structured array representing a position (x,y) and a color (r,g,b) (★★☆) ####

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

#### 52. Consider a random vector with shape (100,2) representing coordinates, find point by point distances (★★☆) ####

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)
    
    # Much faster with scipy
    import scipy
    # Thanks Gavin Heverly-Coulson (#issue 1)
    import scipy.spatial
    
    Z = np.random.random((10,2))
    D = scipy.spatial.distance.cdist(Z,Z)
    print(D)

#### 53. How to convert a float (32 bits) array into an integer (32 bits) in place? ####

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

#### 54. How to read the following file? (★★☆) ####

from io import StringIO
    
    # Fake file
    s = StringIO("""1, 2, 3, 4, 5\n
                    6,  ,  , 7, 8\n
                     ,  , 9,10,11\n""")
    Z = np.genfromtxt(s, delimiter=",", dtype=np.int)
    print(Z)

#### 55. What is the equivalent of enumerate for numpy arrays? (★★☆) ####

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. Generate a generic 2D Gaussian-like array (★★☆) ####

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. How to randomly place p elements in a 2D array? (★★☆) ####

# 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. Subtract the mean of each row of a matrix (★★☆) ####

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

#### 59. How to I sort an array by the nth column? (★★☆) ####

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

#### 60. How to tell if a given 2D array has null columns? (★★☆) ####

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

#### 61. Find the nearest value from a given value in an array (★★☆) ####

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

#### 62. Considering two arrays with shape (1,3) and (3,1), how to compute their sum using an iterator? (★★☆) ####

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. Create an array class that has a name attribute (★★☆) ####

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. Consider a given vector, how to add 1 to each element indexed by a second vector (be careful with repeated indices)? (★★★) ####

# 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. How to accumulate elements of a vector (X) to an array (F) based on an index list (I)? (★★★) ####

# 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. Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique colors (★★★) ####

# 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. Considering a four dimensions array, how to get sum over the last two axis at once? (★★★) ####

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)
    # solution by flattening the last two dimensions into one
    # (useful for functions that don't accept tuples for axis argument)
    sum = A.reshape(A.shape[:-2] + (-1,)).sum(axis=-1)
    print(sum)

#### 68. Considering a one-dimensional vector D, how to compute means of subsets of D using a vector S of same size describing subset indices? (★★★) ####

# 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. How to get the diagonal of a dot product? (★★★) ####

# 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. Consider the vector \[1, 2, 3, 4, 5\], how to build a new vector with 3 consecutive zeros interleaved between each value? (★★★) ####

# 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. Consider an array of dimension (5,5,3), how to mulitply it by an array with dimensions (5,5)? (★★★) ####

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

#### 72. How to swap two rows of an array? (★★★) ####

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

#### 73. Consider a set of 10 triplets describing 10 triangles (with shared vertices), find the set of unique line segments composing all the triangles (★★★) ####

# 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. Given an array C that is a bincount, how to produce an array A such that np.bincount(A) == C? (★★★) ####

# 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. How to compute averages using a sliding window over an array? (★★★) ####

# 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. 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\[-1\]) (★★★) ####

# 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. How to negate a boolean, or to change the sign of a float inplace? (★★★) ####

# 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. Consider 2 sets of points P0,P1 describing lines (2d) and a point p, how to compute distance from p to each line i (P0\[i\],P1\[i\])? (★★★) ####

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. Consider 2 sets of points P0,P1 describing lines (2d) and a set of points P, how to compute distance from each point j (P\[j\]) to each line i (P0\[i\],P1\[i\])? (★★★) ####

# 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. 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) (★★★) ####

# 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. Consider an array Z = \[1,2,3,4,5,6,7,8,9,10,11,12,13,14\], how to generate an array R = \[\[1,2,3,4\], \[2,3,4,5\], \[3,4,5,6\], …, \[11,12,13,14\]\]? (★★★) ####

# 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. Compute a matrix rank (★★★) ####

# 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. How to find the most frequent value in an array? ####

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

#### 84. Extract all the contiguous 3x3 blocks from a random 10x10 matrix (★★★) ####

# 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. Create a 2D array subclass such that Z\[i,j\] == Z\[j,i\] (★★★) ####

# 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. Consider a set of p matrices wich shape (n,n) and a set of p vectors with shape (n,1). How to compute the sum of of the p matrix products at once? (result has shape (n,1)) (★★★) ####

# 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. Consider a 16x16 array, how to get the block-sum (block size is 4x4)? (★★★) ####

# 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. How to implement the Game of Life using numpy arrays? (★★★) ####

# 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. How to get the n largest values of an array (★★★) ####

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. Given an arbitrary number of vectors, build the cartesian product (every combinations of every item) (★★★) ####

# 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. How to create a record array from a regular array? (★★★) ####

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. Consider a large vector Z, compute Z to the power of 3 using 3 different methods (★★★) ####

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

#### 93. Consider two arrays A and B of shape (8,3) and (2,2). How to find rows of A that contain elements of each row of B regardless of the order of the elements in B? (★★★) ####

# 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. Considering a 10x3 matrix, extract rows with unequal values (e.g. \[2,2,3\]) (★★★) ####

# 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. Convert a vector of ints into a matrix binary representation (★★★) ####

# 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. Given a two dimensional array, how to extract unique rows? (★★★) ####

# 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)
    
    # Author: Andreas Kouzelis
    # NumPy >= 1.13
    uZ = np.unique(Z, axis=0)
    print(uZ)

#### 97. Considering 2 vectors A & B, write the einsum equivalent of inner, outer, sum, and mul function (★★★) ####

# 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. Considering a path described by two vectors (X,Y), how to sample it using equidistant samples (★★★)? ####

# 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. 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. (★★★) ####

# 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. 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). (★★★) ####

# 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)

[附一篇带有中文翻译的博客][Link 1]

[https_github.com_rougier_numpy-100]: https://github.com/rougier/numpy-100
[Link 1]: https://blog.csdn.net/qq_39362996/article/details/90204737