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

Solving a linear system

If  is a matrix and is a vector, you can solve the linear equation system

by using the function solve from the linear algebra submodule numpy.linalg:

from numpy.linalg import solve
x = solve(A, b)

For example, to solve

the following Python statements are executed:

from numpy.linalg import solve
A = array([[1., 2.], [3., 4.]])
b = array([1., 4.])
x = solve(A, b)
allclose(dot(A, x), b) # True
allclose(A @ x, b) # alternative formulation

The command allclose is used here to compare two vectors. If they are close enough to each other, this command returns True. Optionally a tolerance value can be set. For more methods related to linear equation systems, see Section 4.9: Linear algebra methods in SciPy.

Now, you have seen the first and essential way of how to use arrays in Python. In the following sections, we'll show you more details and the underlying principles.