Scientific Computing with Python 3 by Fuhrer, Claus -- Read -- Imperial Library of Trantor

Index

Scientific Computing with Python 3

Scientific Computing with Python 3 Credits About the Authors About the Reviewer www.PacktPub.com

Why subscribe?

Acknowledgement Preface

What this book covers What you need for this book Who this book is for

Python vs Other Languages

Other Python literature Conventions Reader feedback Customer support

Downloading the example code Downloading the color images of this book Errata Piracy Questions

1. Getting Started

Installation and configuration instructions

Installation Anaconda Configuration Python Shell Executing scripts Getting Help Jupyter – Python notebook

Program and program flow

Comments Line joining

Basic types

Numbers Strings Variables Lists Operations on lists Boolean expressions

Repeating statements with loops

Repeating a task Break and else

Conditional statements Encapsulating code with functions Scripts and modules

Simple modules - collecting functions Using modules and namespaces

Interpreter Summary

2. Variables and Basic Types

Variables Numeric types

Integers

Plain integers

Floating point numbers

Floating point representation Infinite and not a number Underflow - Machine Epsilon Other float types in NumPy

Complex numbers

Complex Numbers in Mathematics The j notation Real and imaginary parts

Booleans

Boolean operators Boolean casting Automatic Boolean casting Return values of and and or Boolean and integer

Strings

Operations on strings and string methods

String formatting

Summary Exercises

3. Container Types

Lists

Slicing Strides Altering lists Belonging to a list List methods In–place operations Merging lists – zip List comprehension

Arrays Tuples Dictionaries

Creating and altering dictionaries Looping over dictionaries

Sets Container conversions Type checking Summary Exercises

4. Linear Algebra – Arrays

Overview of the array type

Vectors and matrices Indexing and slices Linear algebra operations

Solving a linear system

Mathematical preliminaries

Arrays as functions Operations are elementwise Shape and number of dimensions The dot operations

The array type

Array properties Creating arrays from lists

Accessing array entries

Basic array slicing Altering an array using slices

Functions to construct arrays Accessing and changing the shape

The shape function Number of dimensions Reshape

Transpose

Stacking

Stacking vectors

Functions acting on arrays

Universal functions

Built-in universal functions Create universal functions

Array functions

Linear algebra methods in SciPy

Solving several linear equation systems with LU Solving a least square problem with SVD More methods

Summary Exercises

5. Advanced Array Concepts

Array views and copies

Array views Slices as views Transpose and reshape as views Array copy

Comparing arrays

Boolean arrays

Checking for equality

Boolean operations on arrays Array indexing

Indexing with Boolean arrays Using where

Performance and Vectorization

Vectorization

Broadcasting

Mathematical view

Constant functions Functions of several variables General mechanism Conventions

Broadcasting arrays

The broadcasting problem Shape mismatch

Typical examples

Rescale rows Rescale columns Functions of two variables

Sparse matrices

Sparse matrix formats

Compressed sparse row Compressed Sparse Column Row-based linked list format

Altering and slicing matrices in LIL format

Generating sparse matrices Sparse matrix methods

Summary

6. Plotting

Basic plotting Formatting Meshgrid and contours Images and contours Matplotlib objects

The axes object Modifying line properties Annotations Filling areas between curves Ticks and ticklabels

Making 3D plots Making movies from plots Summary Exercises

7. Functions

Basics Parameters and arguments

Passing arguments - by position and by keyword Changing arguments Access to variables defined outside the local namespace Default arguments

Beware of mutable default arguments

Variable number of arguments Return values Recursive functions Function documentation Functions are objects

Partial application

Using Closures

Anonymous functions - the lambda keyword

The lambda construction is always replaceable

Functions as decorators Summary Exercises

8. Classes

Introduction to classes

Class syntax The __init__ method

Attributes and methods

Special methods

Reverse operations

Attributes that depend on each other

The property function

Bound and unbound methods Class attributes Class methods Subclassing and inheritance Encapsulation Classes as decorators Summary Exercises

9. Iterating

The for statement Controlling the flow inside the loop Iterators

Generators Iterators are disposable Iterator tools Generators of recursive sequences

Arithmetic geometric mean

Convergence acceleration List filling patterns

List filling with the append method List from iterators Storing generated values

When iterators behave as lists

Generator expression Zipping iterators

Iterator objects Infinite iterations

The while loop Recursion

Summary Exercises

10. Error Handling

What are exceptions?

Basic principles

Raising exceptions Catching exceptions

User-defined exceptions Context managers - the with statement

Finding Errors: Debugging

Bugs The stack The Python debugger Overview - debug commands Debugging in IPython

Summary

11. Namespaces, Scopes, and Modules

Namespace Scope of a variable Modules

Introduction Modules in IPython

The IPython magic command

The variable __name__ Some useful modules

Summary

12. Input and Output

File handling

Interacting with files Files are iterable File modes

NumPy methods

savetxt loadtxt

Pickling Shelves Reading and writing Matlab data files Reading and writing images Summary

13. Testing

Manual testing Automatic testing

Testing the bisection algorithm

Using unittest package

Test setUp and tearDown methods

Parameterizing tests Assertion tools Float comparisons Unit and functional tests Debugging Test discovery Measuring execution time

Timing with a magic function Timing with the Python module timeit Timing with a context manager

Summary Exercises

14. Comprehensive Examples

Polynomials

Theoretical background Tasks

The polynomial class Newton polynomial Spectral clustering Solving initial value problems Summary Exercises

15. Symbolic Computations - SymPy

What are symbolic computations?

Elaborating an example in SymPy

Basic elements of SymPy

Symbols - the basis of all formulas Numbers Functions

Undefined functions

Elementary Functions

Lambda - functions

Symbolic Linear Algebra

Symbolic matrices

Examples for Linear Algebra Methods in SymPy Substitutions Evaluating symbolic expressions

Example: A study on the convergence order of Newton's Method

Converting a symbolic expression into a numeric function

A study on the parameter dependency of polynomial coefficients

Summary

References

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