Numpy arrays¶

Numpy array basics¶

Numpy is the standard module for doing numerical computations in Python. It provides tools for writing code which is both easier to develop and usually a lot faster than it would be without numpy.

We begin by importing numpy:

import numpy as np

The main objects provided by numpy are numpy arrays, than in their simplest form are similar to lists. A list can be converted into a numpy array using the numpy array() function:

mylist = [1, 2, 3]
print(numbers)

[1, 2, 3]

a = np.array(numbers)
print(numbers_arr)

[1 2 3]

A visible difference between lists and numpy arrays is that arrays are printed without commas separating their elements. We can also use the type() function to verify that a is a numpy array:

type(mylist)

list

type(a)

numpy.ndarray

One advantage of using numpy arrays that many computations can be performed on all array elements at once:

print(2*a)  # multiplication by a number

[2 4 6]

print(a**3) # exponentiation

[ 1 8 27]

a += 10  # incrementing elements of an array
print(a)

[11 12 13]

b = np.array([100, 200, 300])

print(a+b) # addition of arrays

[111 212 313]

print(b/a) # division of one array by another

[ 9.09090909 16.66666667 23.07692308]

The numpy module contains implementations of many mathematical functions (trigonometric, logarithmic etc.) that can be applied to whole numpy arrays:

print(np.sin(a))  # compute sine of every element of an array

[-0.99999021 -0.53657292 0.42016704]

In other respects numpy array behave the same way as lists. For example, for loops work with numpy arrays as usual:

x = np.array([1,2,3,4,5,6,8])

for t in x:
    print(t**2)

1 4 9 16 25 36 64

Indexing and slicing operations are also unchanged:

x[0] = 100
print(x)

[100 2 3 4 5 6 8]

y = x[:4]
print(y)

[100 2 3 4]

Some differences between lists and numpy arrays¶

1. Lists can contain objects of different types, but in numpy arrays all objects must be of the same type (integers, floats, strings, booleans etc).

a = np.array([100, 200, 300])  # a is an array of integers
a[0] = 'hello'                 # assigning a string as an array element results in an error

ValueError Traceback (most recent call last)

<ipython-input-67-3c04f588b76c> in <module>() 1 a = np.array([100, 200, 300]) # a is an array of integers —-> 2 a[0] = ‘hello’ # assigning a string as an array element results in an error

ValueError: invalid literal for int() with base 10: ‘hello’

2. Lists can be shortened and extended (e.g. using append). The size of a numpy array is fixed when the array is created and can’t be changed.

3. Lists slicing produces a new list, independent of the original list. For numpy arrays slicing produces a view of the original array; changing a slice changes the original array:

a = np.array([1, 2, 3, 4])
b = a[:3]
b[0] = 999
print('b = {}'.format(b))
print('a = {}'.format(a))

b = [999 2 3] a = [999 2 3 4]

We can use the copy() function to get an independent copy of an array or its slice:

a = np.array([1, 2, 3, 4])
b = np.copy(a[:3])
b[0] = 999
print('b = {}'.format(b))
print('a = {}'.format(a))

b = [999 2 3] a = [1 2 3 4]

How to create a numpy array¶

Numpy arrays can be created in several ways:

1. The np.array() function converts a list into a numpy array:

a = np.array([1,2,3])
print(a)

[1 2 3]

2. np.zeros() creates an array of zeros of a given length:

a0 = np.zeros(5)
print(a0)

[ 0. 0. 0. 0. 0.]

3. np.ones() creates an array of ones:

a1 = np.ones(7)
print(a1)

[ 1. 1. 1. 1. 1. 1. 1.]

From here we can easily get an array with any fixed value for its entries:

b = 3.14*a1
print(b)

[ 3.14 3.14 3.14 3.14 3.14 3.14 3.14]

4. np.empty() creates an array of a given length with unitialized entries (more precisely, values of the array will be equal to whatever is in the computer memory in the region allocated to the array) . This is useful if we want to set values of the array at some later point. For large arrays np.empty() works faster than np.zeros() and np.ones():

c = np.empty(4)
print(c)

[ 4.94065646e-324 9.88131292e-324 1.48219694e-323 1.97626258e-323]

Note. By default np.zeros(), np.ones(), and np.empty() create arrays of floats, but we can use the dtype argument to specify a different data type:

a = np.zeros(5, dtype=int)   # creates an array of integers
print(a)

[0 0 0 0 0]

5. np.arange() is similar to the range() function but it produces a numpy array:

numbers = np.arange(10)
print(numbers)

[0 1 2 3 4 5 6 7 8 9]

evens = np.arange(10, 20, 2) # start at 10, stop at 20, increment by 2
print(evens)

[10 12 14 16 18]

Note. Arguments of np.arange() need not be integers:

w = np.arange(0.3, 1.0, 0.2) # start at 0.3, stop at 1.0, increment by 0.2
print(w)

[ 0.3 0.5 0.7 0.9]

6. np.linspace(a, b, n) creates an array of n evenly spaced points between the numbers a and b:

x = np.linspace(0,1,5)
print(x)

[ 0. 0.25 0.5 0.75 1. ]

Numpy and matplotlib¶

matplotlib works directly with numpy arrays:

import matplotlib.pyplot as plt

x = np.linspace(-10, 10, 100)
y = x**2
plt.plot(x, y)
plt.show()

Numpy arrays¶

Numpy array basics¶

Some differences between lists and numpy arrays¶

How to create a numpy array¶

Numpy and matplotlib¶

Further reading¶