How#

numpy is a large library with incredible functionality all of which will not be listed here. Instead some specific tools will be described so as to give a sufficient understanding of the capabilities of the library.

How to create an array#

To create a numpy array we use the numpy.array tool which takes any iterable.

Tip

numpy.array(iterable)

For example:

import numpy as np

array = np.array((0, 12, 3, 1))
array

array([ 0, 12,  3,  1])

How to create a given number of values between two bounds#

numpy has a popular tool to create a linear space: numpy.linspace which take a lower bound, an upper bounds and a number. It returns the given number of points uniformly spaced between the bounds.

Tip

numpy.linspace(lower_bound, upper_bound, number)

For example:

import numpy as np

np.linspace(10, 400, 4)

array([ 10., 140., 270., 400.])

How to create an array of zeros#

To create an array of zeros we can use the numpy.zeros tool. It takes an argument for the dimension of the array. This can either be a single number in which case a single dimensional array is created or a tuple with multiple dimensions.

Tip

numpy.zeros(size)

For example:

import numpy as np

np.zeros(4)

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

Or:

np.zeros((3, 5))

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

How to generate random arrays#

numpy has a powerful random number generator. It can be accessed from numpy.random and has multiple tools. The simplest of which is numpy.random.random. This takes an optional argument that is the dimension of the array.

Tip

numpy.random.random(size)

For example:

import numpy as np

np.random.random()

0.9751254262035829

Or:

import numpy as np

np.random.random((3, 5))

array([[0.09341972, 0.37613151, 0.83028029, 0.02190668, 0.02515066],
       [0.77539691, 0.71381096, 0.15948014, 0.52059435, 0.0562347 ],
       [0.95199511, 0.24924032, 0.10597235, 0.38800237, 0.28974885]])

How to index arrays#

Multiple dimensional arrays can be indexed in a natural mathematical way using array[position].

Tip

array[position]

For example:

import numpy as np

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

np.int64(6)

How to do arithmetic on arrays#

It is possible to directly do arithmetic on arrays in a mathematical way.

Tip

array1 + array2

For example to do element wise multiplication:

array1 = np.array((1, 2, 3, 4))
array2 = np.array((2, 0, -1, 0.5))
array1 * array2

array([ 2.,  0., -3.,  2.])

How to invert a matrix#

numpy can invert a matrix using np.linalg.inv. There are numerous other linear algebraic tools available in np.linalg.

Tip

np.linalg.inv(array)

For example:

import numpy as np

matrix = np.array(((1, 2), (3, 1)))
matrix_inverse = np.linalg.inv(matrix)
matrix_inverse

array([[-0.2,  0.4],
       [ 0.6, -0.2]])

We can confirm the expected result:

matrix @ matrix_inverse

array([[1., 0.],
       [0., 1.]])

How to raise a matrix to a power#

Using the usual operator for exponentiation ** with a numpy array carries out element wise exponentiation. To raise a matrix to a power we use np.linalg.matrix_power. This takes an array and the exponent.

Tip

np.linalg.ing(array, exponent)

For example:

import numpy as np

matrix = np.array(((1, 2), (3, 1)))
np.linalg.matrix_power(matrix, 3)

array([[19, 18],
       [27, 19]])

How to fit a line of best fit#

numpy can be used to fit polynomials to a points. This is done with the numpy.polyfit tool. This takes an array of x values, an array of y values and a degree. It returns the coefficients of a polynomial of given degree that best approximates \(f(x)=y\).

Tip

np.polyfit(x, y, degree)

For example, the code below creates y using a quadratic and recovers the coefficients of the quadratic:

x = np.array((1, 2, 3, 4))
y = 2 * x ** 2 + 3 * x + 1
a, b, c = np.polyfit(x, y, 2)
a, b, c

(np.float64(2.0000000000000004),
 np.float64(3.0000000000000013),
 np.float64(1.0000000000000036))