Book Image

Scientific Computing with Python - Second Edition

By : Claus Führer, Jan Erik Solem, Olivier Verdier
Book Image

Scientific Computing with Python - Second Edition

By: Claus Führer, Jan Erik Solem, Olivier Verdier

Overview of this book

Python has tremendous potential within the scientific computing domain. This updated edition of Scientific Computing with Python features new chapters on graphical user interfaces, efficient data processing, and parallel computing to help you perform mathematical and scientific computing efficiently using Python. This book will help you to explore new Python syntax features and create different models using scientific computing principles. The book presents Python alongside mathematical applications and demonstrates how to apply Python concepts in computing with the help of examples involving Python 3.8. You'll use pandas for basic data analysis to understand the modern needs of scientific computing, and cover data module improvements and built-in features. You'll also explore numerical computation modules such as NumPy and SciPy, which enable fast access to highly efficient numerical algorithms. By learning to use the plotting module Matplotlib, you will be able to represent your computational results in talks and publications. A special chapter is devoted to SymPy, a tool for bridging symbolic and numerical computations. By the end of this Python book, you'll have gained a solid understanding of task automation and how to implement and test mathematical algorithms within the realm of scientific computing.
Table of Contents (23 chapters)
20
About Packt
22
References

16.3.2 Examples for linear algebra methods in SymPy

The basic task in linear algebra is to solve linear equation systems:

Let's do this symbolically for a  matrix:

A = Matrix(3,3,symbols('A1:4(1:4)'))
b = Matrix(3,1,symbols('b1:4'))
x = A.LUsolve(b)

The output of this relatively small problem is already merely readable, which can be seen in the following graphical expression:

               

Again, the use of simplify command helps us to detect canceling terms and to collect common factors:

simplify(x)

Which will result in the following output, which looks much better:

             

Symbolic computations become very slow when increasing matrix dimensions. For dimensions bigger than 15, memory problems might even occur.

The next figure (Figure 16.3) illustrates the differences in CPU time between symbolically and numerically solving a linear system...