1.5 The NumPy Library

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In Python, a software library is a reusable collection of code. NumPy, pronounced "Num-Pie" for Numerical Python is the fundamental package for scientific computing with Python. https://numpy.org/

Unlike print which is a built-in function, we need to import numpy before using its functions such as numpy.absolute. Importing refers to allowing Python to access the script from another Python module or library. The numpy library provides access to an extensive mathematical functions.

import numpy

To access one of its functions, specify the name (or its alias) of the library and the name of the function, separated by a dot(period).

Some Python Functions (Methods) from the numpy library

Name	Method	Example	Results (rounded)
Square root	`numpy.sqrt(x)`	$the square root of 5$	`2.23606797749979`
Absolute value	`numpy.absolute(x)`	-5	`5`
Rounding	`numpy.round(x,2)`	1.3333	1.33
the number pi	`numpy.pi`	$π$	`3.141592653589793`
e	`numpy.e`	`e`	`2.718281828459045`
e raised to	`numpy.exp(x)`	$e^{2}$	`7.38905609893065`
Natural log	`numpy.log(x)`	$ln 5$	`1.6094379124341003`
Common log	`numpy.log10(x)`	$log open parenthesis 9 close parenthesis$	`0.9542425094393249`

Example: Given the formula $E = | z | \sqrt{\frac{p (1 - p)}{n}}$ , evaluate $E$ , if $z = - 2.575$ , $p equals 0.34$ , and $n equals 800$ .

Option 1: substitute all into the formula

import numpy as np
np.absolute(-2.575)*(0.34*(1-0.34)/800)**(1/2)

Show expected output

0.043126445627943884

Option 2: use some variables to break-down the steps

import numpy as np
a = 0.34*(1-.34)/800
b = a**(1/2)
np.absolute(-2.575)*b

Show expected output

0.043126445627943884

Option 3: declare z, p and n as variables and assign the given values first then use the formula to evaluate E using these variables:

import numpy as np
z = -2.575
p = 0.34
n = 800
E = np.absolute(z)*(p*(1-p)/n)**(1/2)
E

Show expected output

0.043126445627943884

Example: Round the value of $\frac{1}{3}$ to two decimal places.

import numpy as np
np.round(1/3,2)

Show expected output

0.33

Example: Round the value of $the square root of 2$ to three decimal places.

import numpy as np
np.round(2**(1/2),3)

Show expected output

1.414

Example: What is the (rounded) value of $π$ in Python?

Click + Code
Type import numpy
Type numpi.pi
Click play button to execute the code
3.141592653589793 (displayed)

import numpy
numpy.pi

Show expected output

3.141592653589793

Example: Area of a circle with radius r is given by the formula $A = π r^{2}$

Find the area of a circle with radius 5.
Round your answer to a whole number.

Type import numpy
Type numpy.pi*5**2 on the second line
Click play to execute the code

import numpy
numpy.pi*5**2

Show expected output

78.53981633974483

import numpy
Area = numpy.pi*5**2 
round(Area,0)

Show expected output

79.0

Example: what is the rounded value of $e^{3}$ ?

import numpy
numpy.exp(3)

Show expected output

20.085536923187668

Example: what is the rounded value of $the square root of 3$ ?

numpy.sqrt(3)

Show expected output

1.7320508075688772

Example: use ** to find $the square root of 3$

3**(1/2)

Show expected output

1.7320508075688772

Adapted from Python for Introductory Statistics, by Simon Aman (Truman College, City Colleges of Chicago), licensed under CC BY 4.0. Changes were made: reformatted as an accessible XYZ web edition with live in-browser code cells. License: CC-BY-4.0.