# 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

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

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