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Mastering Python Scientific Computing

By : Hemant Kumar Mehta

4 (6)

Mastering Python Scientific Computing

4 (6)

By: Hemant Kumar Mehta

Overview of this book

In today's world, along with theoretical and experimental work, scientific computing has become an important part of scientific disciplines. Numerical calculations, simulations and computer modeling in this day and age form the vast majority of both experimental and theoretical papers. In the scientific method, replication and reproducibility are two important contributing factors. A complete and concrete scientific result should be reproducible and replicable. Python is suitable for scientific computing. A large community of users, plenty of help and documentation, a large collection of scientific libraries and environments, great performance, and good support makes Python a great choice for scientific computing. At present Python is among the top choices for developing scientific workflow and the book targets existing Python developers to master this domain using Python. The main things to learn in the book are the concept of scientific workflow, managing scientific workflow data and performing computation on this data using Python. The book discusses NumPy, SciPy, SymPy, matplotlib, Pandas and IPython with several example programs.

Preface

Preface

What this book covers

What you need for this book

Who this book is for

Conventions

Reader feedback

Customer support

Free Chapter

1. The Landscape of Scientific Computing – and Why Python?

1. The Landscape of Scientific Computing – and Why Python?

Definition of scientific computing

A simple flow of the scientific computation process

Examples from scientific/engineering domains

A strategy for solving complex problems

Approximation, errors, and associated concepts and terms

Computer arithmetic and floating-point numbers

The background of the Python programming language

Summary

2. A Deeper Dive into Scientific Workflows and the Ingredients of Scientific Computing Recipes

2. A Deeper Dive into Scientific Workflows and the Ingredients of Scientific Computing Recipes

Mathematical components of scientific computations

Python scientific computing

A brief idea of interactive programming using IPython

Symbolic computing using SymPy

Summary

3. Efficiently Fabricating and Managing Scientific Data

3. Efficiently Fabricating and Managing Scientific Data

The basic concepts of data

Data storage software and toolkits

Possible operations on data

Scientific data format

Ready-to-use standard datasets

Data generation

Synthetic data generation (fabrication)

A brief note about large-scale datasets

Summary

4. Scientific Computing APIs for Python

4. Scientific Computing APIs for Python

Numerical scientific computing in Python

Symbolic computations using SymPy

APIs and toolkits for data analysis and visualization

Summary

5. Performing Numerical Computing

5. Performing Numerical Computing

The NumPy fundamental objects

Introduction to SciPy

Summary

6. Applying Python for Symbolic Computing

6. Applying Python for Symbolic Computing

Symbols, expressions, and basic arithmetic

Equation solving

Functions for rational numbers, exponentials, and logarithms

Polynomials

Trigonometry and complex numbers

Linear algebra

Calculus

Vectors

The physics module

Pretty printing

The cryptography module

Parsing input

The logic module

The geometry module

Symbolic integrals

Polynomial manipulation

Sets

The simplify and collect operations

Summary

7. Data Analysis and Visualization

7. Data Analysis and Visualization

Matplotlib

The pandas library

I/O operations

IPython

Summary

8. Parallel and Large-scale Scientific Computing

8. Parallel and Large-scale Scientific Computing

Parallel computing using IPython

The architecture of IPython parallel computing

Example of performing parallel computing

Advanced features of IPython

A note on security of IPython

Summary

9. Revisiting Real-life Case Studies

9. Revisiting Real-life Case Studies

Scientific computing applications developed in Python

Python for developing a Blind Audio Tactile Mapping System

Scientific computing libraries developed in Python

Summary

10. Best Practices for Scientific Computing

10. Best Practices for Scientific Computing

The best practices for designing

The implementation of best practices

The best practices for data management and application deployment

The best practices to achieving high performance

The best practices for data privacy and security

Testing and maintenance best practices

General Python best practices

Summary

Index

Index

A strategy for solving complex problems

A simple strategy to find a solution for a complex computational problem is to first identify the difficult areas in the solution. Now, one by one, start replacing these small difficult parts with their solutions that will lead to the same solution or to a solution within the problem-specific permissible limit. In other words, the best idea is to reduce a large, complex problem to a set of smaller problems. Each of them may be complex or simple. Now each of the complex subproblems may be replaced with a similar and simple problem, and in this way, we ultimately get a simpler problem to solve. The basic idea is to combine the divide-and-conquer technique with the change of smaller complex problems with similar simple problems.

We should take care of two important points when adopting this idea. The first is that we need to search for a similar problem or a problem that has a solution from the same class. The second is that just after the replacement of one problem with another, we need to determine whether the ultimate solution is preserved within the tolerance limit, if not completely preserved. Some examples may be as follows:

Changing infinite-dimensional spaces in the problem to finite-dimensional spaces for simplicity
Change infinite processes with finite processes, such as replacing integrals or infinite series with finite summations or a derivative of finite differences
If feasible, then algebraic equations can be used to replace differential equations
Try replacing nonlinear problems with linear problems as linear problems are very simple to solve
If feasible, complicated functions can be changed to multiple simple functions to achieve simplicity

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Tech Concepts

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Programming languages

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