2 Creating NumPy Arrays

In Python, vectors are typically represented by lists and matrices by nested lists. For example, the vector

\[ (1, 2, 3, 4, 5, 6) \]

and the matrix

\[ \begin{pmatrix} 1 & 2 & 3\\ 4 & 5 & 6 \end{pmatrix} \]

can be natively created in Python like this:

lst = [1, 2, 3, 4, 5, 6]

matrix = [[1, 2, 3], [4, 5, 6]]

print(lst)
print(matrix)

[1, 2, 3, 4, 5, 6]
[[1, 2, 3], [4, 5, 6]]

If you want to use NumPy arrays, you can use the np.array() command:

lst = np.array([1, 2, 3, 4, 5, 6])

matrix = np.array([[1, 2, 3], [4, 5, 6]])

print(lst)
print(matrix)

[1 2 3 4 5 6]
[[1 2 3]
 [4 5 6]]

If you look at the output from the print() commands, two things stand out. First, the commas are gone, and second, the matrix is printed in a clean, readable format.

It is also possible to create higher-dimensional arrays. This requires another level of nesting. In the following example, a three-dimensional matrix is created:

matrix_3d = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])

It is considered good practice to always initialize arrays. NumPy offers three functions to create pre-initialized arrays. Alternatively, arrays can be initialized with fixed values. You can use np.zeros() to set all values to 0 or np.ones() to initialize all values with 1. These functions take the shape in the form [rows, columns]. If you want to initialize all elements with a specific value, use the np.full() function.

np.zeros([2,3])

array([[0., 0., 0.],
       [0., 0., 0.]])

np.ones([2,3])

array([[1., 1., 1.],
       [1., 1., 1.]])

np.full([2,3],7)

array([[7, 7, 7],
       [7, 7, 7]])

How could you create arrays filled with a specific value x?

The trick is to initialize an array with np.ones() and then multiply the array by the number x. In the following example, x = 5:

np.ones([2,3]) * 5

array([[5., 5., 5.],
       [5., 5., 5.]])

If you want to create a vector with evenly spaced values, e.g., for an axis in a plot, NumPy offers two options. Use np.linspace(start, stop, #values) or np.arange(start, stop, step) to generate such arrays.

np.linspace(0,1,11)

array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])

np.arange(0,10,2)

array([0, 2, 4, 6, 8])

Practice Exercise: Array Creation

Create one NumPy array for each of the following tasks:

with the values 1, 7, 42, 99
ten times the number 5
with numbers from 35 up to and including 50
with all even numbers from 20 up to and including 40
a matrix with 5 columns and 4 rows filled with the value 4
with 10 values evenly spaced from 22 up to and including 40

Solution

# 1. 
print(np.array([1, 7, 42, 99]))

[ 1  7 42 99]

# 2. 
print(np.full(10,5))

[5 5 5 5 5 5 5 5 5 5]

# 3. 
print(np.arange(35, 51))

[35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50]

# 4. 
print(np.arange(20, 41, 2))

[20 22 24 26 28 30 32 34 36 38 40]

# 5. 
print(np.full([4,5],4))

[[4 4 4 4 4]
 [4 4 4 4 4]
 [4 4 4 4 4]
 [4 4 4 4 4]]

# 6. 
print(np.linspace(22, 40, 10))

[22. 24. 26. 28. 30. 32. 34. 36. 38. 40.]