Simple function classes
Challenge: functions with parameters
Representing a function as a class
The self variable
Another function class example
Alternative function class implementations
Making classes without the class construct
Closures
More examples on classes
Bank accounts
Phone book
A circle
Special methods
The call special method
Example: Automagic differentiation
Example: Automagic integration
Turning an instance into a string
Example: Phone book with special methods
Adding objects
Example: Class for polynomials
Arithmetic operations and other special methods
Special methods for string conversion
Example: Class for vectors in the plane
Some mathematical operations on vectors
Implementation
Usage
Example: Class for complex numbers
Implementation
Illegal operations
Mixing complex and real numbers
Dynamic, static, strong, weak, and duck typing
Special methods for "right" operands
Inspecting instances
Static methods and attributes
Summary
Chapter topics
Example: interval arithmetic
Exercises
Exercise 1: Make a function class
Exercise 2: Add a data attribute to a class
Exercise 3: Add functionality to a class
Exercise 4: Make classes for a rectangle and a triangle
Exercise 5: Make a class for quadratic functions
Exercise 6: Make a class for straight lines
Exercise 7: Flexible handling of function arguments
Exercise 8: Wrap functions in a class
Exercise 9: Flexible handling of function arguments
Exercise 10: Deduce a class implementation
Exercise 11: Implement special methods in a class
Exercise 12: Make a class for summation of series
Exercise 13: Apply a numerical differentiation class
Exercise 14: Implement an addition operator
Exercise 15: Implement in-place += and -= operators
Exercise 16: Implement a class for numerical differentiation
Exercise 17: Examine a program
Exercise 18: Modify a class for numerical differentiation
Exercise 19: Make a class for the Heaviside function
Exercise 20: Make a class for the indicator function
Exercise 21: Make a class for piecewise constant functions
Exercise 22: Speed up repeated integral calculations
Exercise 23: Apply a class for polynomials
Exercise 24: Find a bug in a class for polynomials
Exercise 25: Implement subtraction of polynomials
Exercise 26: Test the functionality of pretty print of polynomials
Exercise 27: Vectorize a class for polynomials
Exercise 28: Use a dict to hold polynomial coefficients
Exercise 29: Extend class Vec2D to work with lists/tuples
Exercise 30: Extend class Vec2D to 3D vectors
Exercise 31: Use NumPy arrays in class Vec2D
Exercise 32: Impreciseness of interval arithmetics
Exercise 33: Make classes for students and courses
Exercise 34: Find local and global extrema of a function
Exercise 35: Find the optimal production for a company
References
A class packs a set of data (variables) together with a set of functions operating on the data. The goal is to achieve more modular code by grouping data and functions into manageable (often small) units. Most of the mathematical computations in this document can easily be coded without using classes, but in many problems, classes enable either more elegant solutions or code that is easier to extend at a later stage. In the non-mathematical world, where there are no mathematical concepts and associated algorithms to help structure the problem solving, software development can be very challenging. Classes may then improve the understanding of the problem and contribute to simplify the modeling of data and actions in programs. As a consequence, almost all large software systems being developed in the world today are heavily based on classes.
Programming with classes is offered by most modern programming languages, also Python. In fact, Python employs classes to a very large extent, but one can use the language for lots of purposes without knowing what a class is. However, one will frequently encounter the class concept when searching books or the World Wide Web for Python programming information. And more important, classes often provide better solutions to programming problems. This document therefore gives an introduction to the class concept with emphasis on applications to numerical computing. More advanced use of classes, including inheritance and object orientation, is treated in the document Object-oriented programming [1].
The folder src/class contains all the program examples from the present document.