100 Numpy Exercises for Data Science!
By: Sasidhar Sirivella
Tags: Machine Learning, Analytics, Numpy, Python, Data Science

NumPy is an extension library for Python language, supporting operations of many high-dimensional arrays and matrices. In addition, it also provides many mathematical function libraries for array operations. Machine learning involves a lot of transformations and operations on arrays, which makes NumPy one of the essential tools.

All the below 100 exercises have been collected from the numpy mailing list, on stack overflow and in the numpy documentation. The goal of these numpy exercises is to serve as a reference as well as to get you to apply numpy beyond the basics.

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]

print(Z)

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

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

print(nz)

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)

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? (★☆☆)

0 * np.nan

np.nan == np.nan

np.inf > np.nan

np.nan - np.nan

np.nan in set([np.nan])

0.3 == 3 * 0.1 print(0 * np.nan)

print(np.nan == np.nan)

print(np.inf > np.nan)

print(np.nan - np.nan)

print(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 (★☆☆)

Z = np.random.random((5,5))

Z = (Z - np.mean (Z)) / (np.std (Z))

print(Z)

23. 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)])

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

Z = np.dot(np.ones((5,3)), np.ones((3,2)))

print(Z) # Alternative solution, in Python 3.5 and above

Z = np.ones((5,3)) @ np.ones((3,2))

print(Z)

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))

from numpy import *

print(sum(range(5),-1)) # Author: Jake VanderPlas print(sum(range(5),-1))

from numpy import *

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

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 Z**Z

2 << Z >> 2

Z <- Z

1j*Z

Z/1/1

Z<Z>Z

28. What are the result of the following expressions?

np.array(0) / np.array(0)

np.array(0) // np.array(0)

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

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

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

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

# Author: Charles R Harris Z = np.random.uniform(-10,+10,10)

print (np.copysign(np.ceil(np.abs(Z)), Z))

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

Z1 = np.random.randint(0,10,10)

Z2 = np.random.randint(0,10,10)

print(np.intersect1d(Z1,Z2))

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) # Equivalently with a context manager

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

print(nz)

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

np.sqrt(-1) == np.emath.sqrt(-1) 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(0,10,10) print (Z - Z%1)

print (np.floor(Z))

print (np.ceil(Z)-1)

print (Z.astype(int))

print (np.trunc(Z))

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)

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)

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

Z = np.random.random(10)

Z.sort()

print(Z)

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

# Author: Evgeni Burovski 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) # Assuming identical shape of the arrays and a tolerance for the comparison of values

equal = np.allclose(A,B)

print(equal) # Checking both the shape and the element values, no tolerance (values have to be exactly equal)

equal = np.array_equal(A,B)

print(equal)

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

Z = np.zeros(10)

Z.flags.writeable = False

Z[0] = 1

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

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?

# Thanks Vikas (https://stackoverflow.com/a/10622758/5989906)

# & unutbu (https://stackoverflow.com/a/4396247/5989906)

Z = (np.random.rand(10)*100).astype(np.float32)

Y = Z.view(np.int32)

Y[:] = Z

print(Y)

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

1, 2, 3, 4, 5

6, , , 7, 8

, , 9,10,11 from io import StringIO # Fake file

s = StringIO('''1, 2, 3, 4, 5 6, , , 7, 8 , , 9,10,11

''')

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 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 (★★★)



# Make sure to read: # 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)

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