深度学习|numpy 练习题（附难度、答案、解析）深度学习|Python

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
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 BurovskiZ = np.arange(11) Z[(3 < Z) & (Z <= 8)] *= -1 print(Z)

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

# Author: Jake VanderPlasprint(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 ZZ

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)

【深度学习|numpy 练习题（附难度、答案、解析）】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 BurovskiX = 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.spatialZ = 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: Divakarn = 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 WeckesserX = 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 TjoaZ = 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 WeckesserZ = 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 OlsenZ = np.ones(10) I = np.random.randint(0,len(Z),20) Z += np.bincount(I, minlength=len(Z)) print(Z)# Another solution # Author: Bartosz 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 IsaacX = [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 Horeshw,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 RíoD = np.random.uniform(0,1,100) S = np.random.randint(0,10,100) D_sums = np.bincount(S, weights=D) D_counts = np.bincount(S) D_means = D_sums / D_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 BlondelA = 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 WeckesserZ = 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 HoogendoornA = 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. Rougierfaces = 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 RíoC = 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 Ríodef 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_tricksdef rolling(a, window): shape = (a.size - window + 1, window) strides = (a.itemsize, a.itemsize) return stride_tricks.as_strided(a, shape=shape, strides=strides) Z = rolling(np.arange(10), 3) print(Z)

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

# Author: Nathaniel J. SmithZ = 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 RougierZ = 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%2R_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 WaltZ = 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 WaltZ = 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 BarkerZ = 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 indicesclass 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 Waltp, 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 KernZ = 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 Rougierdef 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 ZZ = 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 Waltdef cartesian(arrays): arrays = [np.asarray(a) for a in arrays] shape = (len(x) for x in arrays)ix = np.indices(shape, dtype=int) ix = ix.reshape(len(arrays), -1).Tfor n, arr in enumerate(arrays): ix[:, n] = arrays[n][ix[:, n]]return ixprint (cartesian(([1, 2, 3], [4, 5], [6, 7])))

91. 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 SchwartzA = 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 KernZ = np.random.randint(0,5,(10,3)) print(Z) # solution for arrays of all dtypes (including string arrays and record arrays) E = np.all(Z[:,1:] == Z[:,:-1], axis=1) U = Z[~E] print(U) # soluiton for numerical arrays only, will work for any number of columns in 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 WeckesserI = 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. McDonaldI = 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 RíoZ = np.random.randint(0,2,(6,3)) T = np.ascontiguousarray(Z).view(np.dtype((np.void, Z.dtype.itemsize * Z.shape[1]))) _, idx = np.unique(T, return_index=True) uZ = Z[idx] print(uZ)# 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 Swinckelsphi = 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 BurovskiX = 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. HamrickX = 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)

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