Book Image

Scientific Computing with Python 3

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

Scientific Computing with Python 3

By: Claus Führer, Jan Erik Solem, Olivier Verdier

Overview of this book

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.

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Scientific Computing with Python 3
Claus Führer | Jan Erik Solem | Olivier Verdier
Dec, 2016 | 332 pages
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Table of Contents (23 chapters)
Scientific Computing with Python 3
Scientific Computing with Python 3
Credits
Credits
About the Authors
About the Authors
About the Reviewer
About the Reviewer
www.PacktPub.com
www.PacktPub.com
Acknowledgement
Acknowledgement
Preface
Preface
Free Chapter
1
Getting Started
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
Variables and Basic Types
Variables
Numeric types
Booleans
Strings
Summary
Exercises
3
Container Types
Container Types
Lists
Arrays
Tuples
Dictionaries
Sets
Container conversions
Type checking
Summary
Exercises
4
Linear Algebra – Arrays
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
Advanced Array Concepts
Array views and copies
Comparing arrays
Boolean operations on arrays
Array indexing
Performance and Vectorization
Broadcasting
Sparse matrices
Summary
6
Plotting
Plotting
Basic plotting
Formatting
Meshgrid and contours
Images and contours
Matplotlib objects
Making 3D plots
Making movies from plots
Summary
Exercises
7
Functions
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
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
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
Error Handling
What are exceptions?
Finding Errors: Debugging
Summary
11
Namespaces, Scopes, and Modules
Namespaces, Scopes, and Modules
Namespace
Scope of a variable
Modules
Summary
12
Input and Output
Input and Output
File handling
NumPy methods
Pickling
Shelves
Reading and writing Matlab data files
Reading and writing images
Summary
13
Testing
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
Comprehensive Examples
Polynomials
The polynomial class
Newton polynomial
Spectral clustering
Solving initial value problems
Summary
Exercises
15
Symbolic Computations - SymPy
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
References

Assertion tools

In this section, we collect the most important tools for raising an AssertionError. We saw the assert command and two tools from unittest, namely assertAlmostEqual. The following table (Table 13.1) summarizes the most important assertion tools and the related modules:

Assertion tool and application example

Module

assert 5==5

–

assertEqual(5.27, 5.27)

unittest.TestCase

assertAlmostEqual(5.24, 5.2,places = 1)

 unittest.TestCase

assertTrue(5 > 2)

unittest.TestCase

assertFalse(2 < 5)

unittest.TestCase

assertRaises(ZeroDivisionError,lambda x: 1/x,0.)

unittest.TestCase

assertIn(3,{3,4})

unittest.TestCase

assert_array_equal(A,B)

numpy.testing

assert_array_almost_equal(A, B, decimal=5)

numpy.testing

assert_allclose(A, B, rtol=1.e-3,atol=1.e-5)

numpy.testing

Table 13.1: Assertion tools in Python, unittest and NumPy

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