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Home > Data > Data Analysis > Scientific Computing with Python 3
Scientific Computing with Python 3
Scientific Computing with Python 3

Scientific Computing with Python 3: An example-rich, comprehensive guide for all of your Python computational needs

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Scientific Computing with Python 3

Chapter 2. Variables and Basic Types

In this chapter, we will present the most important and basic types in Python. What is a type? It is a set consisting of data content, its representation, and all possible operations. Later in this book, we will make this definition much more precise, when we introduce the concepts of a class in Chapter 8, Classes.

Variables

Variables are references to Python objects. They are created by assignments, for example:

a = 1 
diameter = 3.
height = 5.
cylinder = [diameter, height] # reference to a list

Variables take names that consist of any combination of capital and small letters, the underscore _ , and digits. A variable name must not start with a digit. Note that variable names are case sensitive. A good naming of variables is an essential part of documenting your work, so we recommend that you use descriptive variable names.

Python has some reserved keywords, which cannot be used as variable names (refer to following table, Table 2.1). An attempt to use such a keyword as variable name would raise a syntax error.

Variables

Table 2.1: Reserved Python keywords.

As opposed to other programming languages, variables require no type declaration. You can create several variables with a multiple assignment statement:

a = b = c = 1   # a, b and c get the same value 1

Variables can also be altered after their definition:

a...

Numeric types

At some point, you will have to work with numbers, so we start by considering different forms of numeric types in Python. In mathematics, we distinguish between natural numbers (ℕ), integers (ℤ), rational numbers (ℚ), real numbers (ℝ) and complex numbers (ℂ). These are infinite sets of numbers. Operations differ between these sets and may even not be defined. For example, the usual division of two numbers in ℤ might not result in an integer — it is not defined on ℤ.

In Python, like many other computer languages, we have numeric types:

  • The numeric type int, which is at least theoretically the entire ℤ
  • The numeric type float, which is a finite subset of ℝ and
  • The numeric type complex, which is a finite subset of ℂ

Finite sets have a smallest and a largest number and there is a minimum spacing between two numbers; refer to the section on Floating Point Representation for further details.

Integers

The...

Booleans

Boolean is a datatype named after George Boole (1815-1864). A Boolean variable can take only two values, True or False. The main use of this type is in logical expressions. Here are some examples:

a = True 
b = 30 > 45   # b gets the value False

Boolean expressions are often used in conjunction with the if statement:

if x > 0:
   print("positive")
else:
   print("nonpositive)

Boolean operators

Boolean operations are performed using the and, or, and not keywords in Python:

True and False # False
False or True # True
(30 > 45) or (27 < 30) # True
not True # False
not (3 > 4) # True

The operators follow some precedence rules (refer to section Executing scripts in Chapter 1, Getting started) which would make the parentheses in the third line and in the last obsolete (it is a good practice to use them anyway to increase the readability of your code). Note that the and operator is implicitly chained in the following Boolean expressions...

Strings

The type string is a type used for text:

name = 'Johan Carlsson'
child = "Åsa is Johan Carlsson's daughter"
book = """Aunt Julia 
       and the Scriptwriter"""

A string is enclosed either by single or double quotes. If a string contains several lines, it has to be enclosed by three double quotes """ or three single quotes '''.

Strings can be indexed with simple indexes or slices (refer to Chapter 3, Container Types, for a comprehensive explanation on slices):

book[-1] # returns 'r' 
book[-12:] # returns 'Scriptwriter'

Strings are immutable; that is, items cannot be altered. They share this property with tuples. The command book[1] = 'a' returns:

TypeError: 'str' object does not support item assignment

The string '\n' is used to insert a line break  and 't' inserts a horizontal tabulator (TAB) into the string to align several lines...

Variables

Variables are references to Python objects. They are created by assignments, for example:

a = 1 
diameter = 3.
height = 5.
cylinder = [diameter, height] # reference to a list

Variables take names that consist of any combination of capital and small letters, the underscore _ , and digits. A variable name must not start with a digit. Note that variable names are case sensitive. A good naming of variables is an essential part of documenting your work, so we recommend that you use descriptive variable names.

Python has some reserved keywords, which cannot be used as variable names (refer to following table, Table 2.1). An attempt to use such a keyword as variable name would raise a syntax error.

Table 2.1: Reserved Python keywords.

As opposed to other programming languages, variables require no type declaration. You can create several variables with a multiple assignment statement:

a = b = c = 1   # a, b and c get the same value 1

Variables can also be altered after their...

Numeric types

At some point, you will have to work with numbers, so we start by considering different forms of numeric types in Python. In mathematics, we distinguish between natural numbers (ℕ), integers (ℤ), rational numbers (ℚ), real numbers (ℝ) and complex numbers (ℂ). These are infinite sets of numbers. Operations differ between these sets and may even not be defined. For example, the usual division of two numbers in ℤ might not result in an integer — it is not defined on ℤ.

In Python, like many other computer languages, we have numeric types:

  • The numeric type int, which is at least theoretically the entire ℤ
  • The numeric type float, which is a finite subset of ℝ and
  • The numeric type complex, which is a finite subset of ℂ

Finite sets have a smallest and a largest number and there is a minimum spacing between two numbers; refer to the section on Floating Point Representation for further details.

Integers

The simplest numerical type is the integer type.

Plain integers

The statement k = 3 assigns...

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Key benefits

  • Your ultimate resource for getting up and running with Python numerical computations
  • Explore numerical computing and mathematical libraries using Python 3.x code with SciPy and NumPy modules
  • A hands-on guide to implementing mathematics with Python, with complete coverage of all the key concepts

Description

Python can be used for more than just general-purpose programming. It is a free, open source language and environment that has tremendous potential for use within the domain of scientific computing. This book presents Python in tight connection with mathematical applications and demonstrates how to use various concepts in Python for computing purposes, including examples with the latest version of Python 3. Python is an effective tool to use when coupling scientific computing and mathematics and this book will teach you how to use it for linear algebra, arrays, plotting, iterating, functions, polynomials, and much more.

Who is this book for?

This book is for anyone who wants to perform numerical and mathematical computations in Python. It is especially useful for developers, students, and anyone who wants to use Python for computation. Readers are expected to possess basic a knowledge of scientific computing and mathematics, but no prior experience with Python is needed.

What you will learn

  • The principal syntactical elements of Python
  • The most important and basic types in Python
  • The essential building blocks of computational mathematics, linear algebra, and related Python objects
  • Plot in Python using matplotlib to create high quality figures and graphics to draw and visualize your results
  • Define and use functions and learn to treat them as objects
  • How and when to correctly apply object-oriented programming for scientific computing in Python
  • Handle exceptions, which are an important part of writing reliable and usable code
  • Two aspects of testing for scientific programming: Manual and Automatic

Product Details

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Publication date, Length, Edition, Language, ISBN-13
Publication date : Dec 23, 2016
Length: 332 pages
Edition : 1st
Language : English
ISBN-13 : 9781786463647
Category :
Data
Languages :
Python
Concepts :
Data Analysis
Tools :
SciPy

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Publication date : Dec 23, 2016
Length: 332 pages
Edition : 1st
Language : English
ISBN-13 : 9781786463647
Category :
Data
Languages :
Python
Concepts :
Data Analysis
Tools :
SciPy

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Table of Contents

16 Chapters
1. Getting Started Chevron down icon Chevron up icon
1. Getting Started
Installation and configuration instructions
Program and program flow
Basic types
Repeating statements with loops
Conditional statements
Encapsulating code with functions
Scripts and modules
Interpreter
Summary
2. Variables and Basic Types Chevron down icon Chevron up icon
2. Variables and Basic Types
Variables
Numeric types
Booleans
Strings
Summary
Exercises
3. Container Types Chevron down icon Chevron up icon
3. Container Types
Lists
Arrays
Tuples
Dictionaries
Sets
Container conversions
Type checking
Summary
Exercises
4. Linear Algebra – Arrays Chevron down icon Chevron up icon
4. Linear Algebra – Arrays
Overview of the array type
Mathematical preliminaries
The array type
Accessing array entries
Functions to construct arrays
Accessing and changing the shape
Stacking
Functions acting on arrays
Linear algebra methods in SciPy
Summary
Exercises
5. Advanced Array Concepts Chevron down icon Chevron up icon
5. Advanced Array Concepts
Array views and copies
Comparing arrays
Boolean operations on arrays
Array indexing
Performance and Vectorization
Broadcasting
Sparse matrices
Summary
6. Plotting Chevron down icon Chevron up icon
6. Plotting
Basic plotting
Formatting
Meshgrid and contours
Images and contours
Matplotlib objects
Making 3D plots
Making movies from plots
Summary
Exercises
7. Functions Chevron down icon Chevron up icon
7. Functions
Basics
Parameters and arguments
Variable number of arguments
Return values
Recursive functions
Function documentation
Functions are objects
Anonymous functions - the  lambda keyword
Functions as decorators
Summary
Exercises
8. Classes Chevron down icon Chevron up icon
8. Classes
Introduction to classes
Attributes and methods
Attributes that depend on each other
Bound and unbound methods
Class attributes
Class methods
Subclassing and inheritance
Encapsulation
Classes as decorators
Summary
Exercises
9. Iterating Chevron down icon Chevron up icon
9. Iterating
The for statement
Controlling the flow inside the loop
Iterators
Convergence acceleration
List filling patterns
When iterators behave as lists
Iterator objects
Infinite iterations
Summary
Exercises
10. Error Handling Chevron down icon Chevron up icon
10. Error Handling
What are exceptions?
Finding Errors: Debugging
Summary
11. Namespaces, Scopes, and Modules Chevron down icon Chevron up icon
11. Namespaces, Scopes, and Modules
Namespace
Scope of a variable
Modules
Summary
12. Input and Output Chevron down icon Chevron up icon
12. Input and Output
File handling
NumPy methods
Pickling
Shelves
Reading and writing Matlab data files
Reading and writing images
Summary
13. Testing Chevron down icon Chevron up icon
13. Testing
Manual testing
Automatic testing
Using unittest package
Parameterizing tests
Assertion tools
Float comparisons
Unit and functional tests
Debugging
Test discovery
Measuring execution time
Summary
Exercises
14. Comprehensive Examples Chevron down icon Chevron up icon
14. Comprehensive Examples
Polynomials
The polynomial class
Newton polynomial
Spectral clustering
Solving initial value problems
Summary
Exercises
15. Symbolic Computations - SymPy Chevron down icon Chevron up icon
15. Symbolic Computations - SymPy
What are symbolic computations?
Basic elements of SymPy
Elementary Functions
Symbolic Linear Algebra
Examples for Linear Algebra Methods in SymPy
Substitutions
Evaluating symbolic expressions
Converting a symbolic expression into a numeric function
Summary
References Chevron down icon Chevron up icon
References

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Customer reviews

Rating distribution
Full star icon Full star icon Full star icon Full star icon Empty star icon 4
(2 Ratings)
5 star 0%
4 star 100%
3 star 0%
2 star 0%
1 star 0%
D. A. Robinson Jul 08, 2018
Full star icon Full star icon Full star icon Full star icon Empty star icon 4
I have been using Python 2.7 on all my projects so far but decided to upgrade to Python 3 for all subsequent projects, and needed a text book to get to know where the important differences are. So far this seems an adequate tome for this task
Amazon Verified review Amazon
Tim Y Oct 14, 2021
Full star icon Full star icon Full star icon Full star icon Empty star icon 4
This book can help you get started rapidly with using Python in scientific computation. It has detailed exposition on the basic syntax and data structures of Python. It also consists of advanced contents such as error handling, symbolic calculations and parallel computations. However, I wish it would focus more on numerical algorithms such as equation solving, matrix diagonalization, optimization, interpolation etc. Overall, it's a great book for those who are beginners in scientific computation with Python.
Amazon Verified review Amazon

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About the 4 authors

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Profile icon Führer
Führer
Claus Führer is a professor of scientific computations at Lund University, Sweden. He has an extensive teaching record that includes intensive programming courses in numerical analysis and engineering mathematics across various levels in many different countries and teaching environments. Claus also develops numerical software in research collaboration with industry and received Lund University's Faculty of Engineering Best Teacher Award in 2016.
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Profile icon Claus Fuhrer
Claus Fuhrer
Claus Führer is a professor of scientific computations at Lund University, Sweden. He has an extensive teaching record that includes intensive programming courses in numerical analysis and engineering mathematics across various levels in many different countries and teaching environments. Claus also develops numerical software in research collaboration with industry and received Lund University's Faculty of Engineering Best Teacher Award in 2016.
Read more
See other products by Claus Fuhrer
Profile icon Solem
Solem
Jan Erik Solem is a Python enthusiast, former associate professor, and computer vision entrepreneur. He co-founded several computer vision startups, most recently Mapillary, a street imagery computer vision company, and has worked in the tech industry for two decades. Jan Erik is a World Economic Forum technology pioneer and won the Best Nordic Thesis Award 2005-2006 for his dissertation on image analysis and pattern recognition. He is also the author of "Programming Computer Vision with Python" (O'Reilly 2012).
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Profile icon Verdier
Verdier
Olivier Verdier began using Python for scientific computing back in 2007 and received a PhD in mathematics from Lund University in 2009. He has held post-doctoral positions in Cologne, Trondheim, Bergen, and Ume and is now an associate professor of mathematics at Bergen University College, Norway.
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