DS Utilities: Numpy

TD; DR

Numpy

In this Chapter, take the following 25 exercises to learn how to use the basic APIs of numpy.


Exercise on Numpy

1. Import the numpy package under the name np

import numpy as np

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

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

4. Create a vector with values ranging from 10 to 49

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

5. Reverse a vector (first element becomes last)

Z = np.arange(10)
Z = Z[::-1]
print(Z)

Also tries:

Z = np.arange(10)
Z = Z[::-2]
print(Z)
Z = np.arange(10)
Z = Z[::3]
print(Z)

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

Identity matrix: values on positive diagnosis of matrix are 1, and others are 0

Also recognized as I_n

Z = np.eye(3)
print(Z)

9. Create a 3x3x3 array with random values

Z = 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

Z = np.random.random(30)
m = Z.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?

Z = np.arange(25).reshape(5, 5)
Z = np.pad(Z, pad_width=1, mode='constant', constant_values=0)
print(Z)

14. Create a 5x5 matrix with values 0,1,2,3,4 on the diagonal

Z = np.diag(np.arange(5))
print(Z)

15. Create a 8x8 matrix and fill it with a chess board pattern

Chess board Pattern is just like:

0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
Z = np.zeros((8,8),dtype=int)
Z[1::2,::2] = 1
Z[::2,1::2] = 1
print(Z)

# Alternative

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

16. 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)))

17. Matrix Addition and Subtraction

Add up two matries A and B, where A and B respectively be:

A = [[1 2 3]
     [4 5 6]
     [7 8 9]]
     
B = [[9 8 7]
     [6 5 4]
     [3 2 1]]
A = np.arange(1, 10).reshape(3, 3)
B = np.arange(9, 0, -1).reshape(3, 3)
print(A + B)

18. Normalize a 5x5 random matrix

Normalize a matrix(归一化矩阵) is to make every values in the matrix lies on [min, max], as an example: we have an array valued [-1, 1, 3]. After normalization, it becomes [0, 0.5, 1].

Z = np.random.random((5, 5))
Z = (Z - Z.min())/(Z.max() - Z.min())
print(Z)

19. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product)

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

20. Given a 1D array, negate all elements which are between 3 and 8, in place.

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

21. How to find common values between two arrays?

Z1 = np.random.randint(0,10,10)
Z2 = np.random.randint(0,10,10)
print(Z1, Z2)
print(np.intersect1d(Z1,Z2))

22. How to get the dates of yesterday, today and tomorrow?

yesterday = np.datetime64('today') - np.timedelta64(1)
today     = np.datetime64('today')
tomorrow  = np.datetime64('today') + np.timedelta64(1)
print(yesterday, today, tomorrow)

23. Create a vector of size 6 with values in equal spacing ranges [0, 20]

Z = np.linspace(0,20,6)
print(Z)

24. Create a random vector of size 10 and sort it

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

25. Create random vector of size 10 and replace the maximum value by 0

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

What is the relationship between Z.argmax() and Z.max()?

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

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