Scientific Computing with Python: High-performance scientific computing with NumPy, SciPy, and pandas

Cover
Title Page
Copyright and Credits
Contributors
Acknowledgement
Preface
Table of Contents
Chapter 1: Getting Started
	1.1 Installation and configuration instructions
		1.1.1 Installation
		1.1.2 Anaconda
		1.1.3 Spyder
		1.1.4 Configuration
		1.1.5 Python shell
		1.1.6 Executing scripts
		1.1.7 Getting help
		1.1.8 Jupyter – Python notebook
	1.2 Program and program flow
		1.2.1 Comments
		1.2.2 Line joining
	1.3 Basic data types in Python
		1.3.1 Numbers
		1.3.2 Strings
		1.3.3 Variables
		1.3.4 Lists
			Operations on lists
		1.3.6 Boolean expressions
	1.4 Repeating statements with loops
		1.4.1 Repeating a task
		1.4.2 break and else
	1.5 Conditional statements
	1.6 Encapsulating code with functions
	1.7 Understanding scripts and modules
		1.7.1 Simple modules – collecting functions
		1.7.2 Using modules and namespaces
	1.8 Python interpreter
	Summary
Chapter 2: Variables and Basic Types
	2.1 Variables
	2.2 Numeric types
		2.2.1 Integers
			Plain integers
		2.2.2 Floating-point numbers
			Floating-point representation
			Infinite and not a number
			Underflow – Machine epsilon
			Other float types in NumPy
		2.2.3 Complex numbers
			Complex numbers in mathematics
			The j notation
			Real and imaginary parts
	2.3 Booleans
		2.3.1 Boolean operators
		2.3.2 Boolean casting
			Automatic Boolean casting
		2.3.3 Return values of and and or
		2.3.4 Booleans and integers
	2.4 Strings
		2.4.1 Escape sequences and raw strings
		2.4.2 Operations on strings and string methods
		2.4.3 String formatting
	2.5 Summary
	2.6 Exercises
Chapter 3: Container Types
	3.1 Lists
		3.1.1 Slicing
			Strides
		3.1.2 Altering lists
		3.1.3 Belonging to a list
		3.1.4 List methods
			In-place operations
		3.1.5 Merging lists – zip
		3.1.6 List comprehension
	3.2 A quick glance at the concept of arrays
	3.3 Tuples
		3.3.1 Packing and unpacking variables
	3.4 Dictionaries
		3.4.1 Creating and altering dictionaries
		3.4.2 Looping over dictionaries
	3.5 Sets
	3.6 Container conversions
	3.7 Checking the type of a variable
	3.8 Summary
	3.9 Exercises
Chapter 4: Linear Algebra - Arrays
	4.1 Overview of the array type
		4.1.1 Vectors and matrices
		4.1.2 Indexing and slices
		4.1.3 Linear algebra operations
			Solving a linear system
	4.2 Mathematical preliminaries
		4.2.1 Arrays as functions
		4.2.2 Operations are elementwise
		4.2.3 Shape and number of dimensions
		4.2.4 The dot operations
	4.3 The array type
		4.3.1 Array properties
		4.3.2 Creating arrays from lists
			Array and Python parentheses
	4.4 Accessing array entries
		4.4.1 Basic array slicing
		4.4.2 Altering an array using slices
	4.5 Functions to construct arrays
	4.6 Accessing and changing the shape
		4.6.1 The function shape
		4.6.2 Number of dimensions
		4.6.3 Reshape
			Transpose
	4.7 Stacking
		4.7.1 Stacking vectors
	4.8 Functions acting on arrays
		4.8.1 Universal functions
			Built-in universal functions
			Creation of universal functions
		4.8.2 Array functions
	4.9 Linear algebra methods in SciPy
		4.9.1 Solving several linear equation systems with LU
		4.9.2 Solving a least square problem with SVD
		4.9.3 More methods
	4.10 Summary
	4.11 Exercises
Chapter 5: Advanced Array Concepts
	5.1 Array views and copies
		5.1.1 Array views
		5.1.2 Slices as views
		5.1.3 Generating views by transposing and reshaping
		5.1.4 Array copies
	5.2 Comparing arrays
		5.2.1 Boolean arrays
		5.2.2 Checking for array equality
		5.2.3 Boolean operations on arrays
	5.3 Array indexing
		5.3.1 Indexing with Boolean arrays
		5.3.2 Using the command where
	5.4 Performance and vectorization
		5.4.1 Vectorization
	5.5 Broadcasting
		5.5.1 Mathematical views
			Constant functions
			Functions of several variables
			General mechanism
			Conventions
		5.5.2 Broadcasting arrays
			The broadcasting problem
			Shape mismatch
		5.5.3 Typical examples
			Rescale rows
			Rescale columns
			Functions of two variables
	5.6. Sparse matrices
		5.6.1 Sparse matrix formats
			Compressed sparse row format (CSR)
			Compressed sparse column format (CSC)
			Row-based linked list format (LIL)
			Altering and slicing matrices in LIL format
		5.6.2 Generating sparse matrices
		5.6.3 Sparse matrix methods
	5.7 Summary
Chapter 6: Plotting
	6.1 Making plots with basic plotting commands
		6.1.1 Using the plot command and some of its variants
		6.1.2 Formatting
		6.1.3 Working with meshgrid and contours
		6.1.4 Generating images and contours
	6.2 Working with Matplotlib objects directly
		6.2.1 Creating axes objects
		6.2.2 Modifying line properties
		6.2.3 Making annotations
		6.2.4 Filling areas between curves
		 6.2.5 Defining ticks and tick labels
		6.2.6 Setting spines makes your plot more instructive – a comprehensive example
	6.3 Making 3D plots
	6.4 Making movies from plots
	6.5 Summary
	6.6 Exercises
Chapter 7: Functions
	7.1 Functions in mathematics and functions in Python
	7.2 Parameters and arguments
		7.2.1 Passing arguments – by position and by keyword
		7.2.2 Changing arguments
		7.2.3 Access to variables defined outside the local namespace
		7.2.4 Default arguments
			Beware of mutable default arguments
		7.2.5 Variable number of arguments
	7.3 Return values
	7.4 Recursive functions
	7.5 Function documentation
	7.6 Functions are objects
		7.6.1 Partial application
		7.6.2 Using closures
	7.7 Anonymous functions – the keyword lambda
		7.7.1 The lambda construction is always replaceable
	7.8 Functions as decorators
	7.9 Summary
	7.10 Exercises
Chapter 8: Classes
	8.1 Introduction to classes
		8.1.1 A guiding example: Rational numbers
		8.1.2 Defining a class and making an instance
		8.1.3 The __init__ method
		8.1.4 Attributes and methods
		8.1.5 Special methods
			Reverse operations
			Methods mimicking function calls and iterables
		8.2 Attributes that depend on each other
		8.2.1 The function property
	8.3 Bound and unbound methods
	8.4 Class attributes and class methods
		8.4.1 Class attributes
		8.4.2 Class methods
	8.5 Subclasses and inheritance
	8.6 Encapsulation
	8.7 Classes as decorators
	8.8 Summary
	8.9 Exercises
Chapter 9: Iterating
	9.1 The for statement
	9.2 Controlling the flow inside the loop
	9.3 Iterable objects
		9.3.1 Generators
		9.3.2 Iterators are disposable
		9.3.3 Iterator tools
		9.3.4 Generators of recursive sequences
		9.3.5 Examples for iterators in mathematics
			Arithmetic geometric mean
			Convergence acceleration
	9.4 List-filling patterns
		9.4.1 List filling with the append method
		9.4.2 List from iterators
		9.4.3 Storing generated values
	9.5 When iterators behave as lists
		9.5.1 Generator expressions
		9.5.2 Zipping iterators
	9.6 Iterator objects
	9.7 Infinite iterations
		9.7.1 The while loop
		9.7.2 Recursion
	9.8 Summary
	9.9 Exercises
Chapter 10: Series and Dataframes - Working with Pandas
	10. 1 A guiding example: Solar cells
	10.2 NumPy arrays and pandas dataframes
		10.2.1 Indexing rules
	10.3 Creating and modifying dataframes
		10.3.1 Creating a dataframe from imported data
		10.3.2 Setting the index
		10.3.3 Deleting entries
		10.3.4 Merging dataframes
		10.3.5 Missing data in a dataframe
	10.4 Working with dataframes
		10.4.1 Plotting from dataframes
		10.4.2 Calculations within dataframes
		10.4.3 Grouping data
	10.5 Summary
Chapter 11: Communication by a Graphical User Interface
	11.1 A guiding example to widgets
		11.1.1 Changing a value with a slider bar
			An example with two sliders
	11.2 The button widget and mouse events
		11.2.1 Updating curve parameters with a button
		11.2.2 Mouse events and textboxes
	11.3 Summary
Chapter 12: Error and Exception Handling
	12.1 What are exceptions?
		12.1.1 Basic principles
			Raising exceptions
			Catching exceptions
		12.1.2 User-defined exceptions
		12.1.3 Context managers – the with statement
	12.2 Finding errors: debugging
		12.2.1 Bugs
		12.2.2 The stack
		12.2.3 The Python debugger
		12.2.4 Overview – debug commands
		12.2.5 Debugging in IPython
	12.3 Summary
Chapter 13: Namespaces, Scopes, and Modules
	13.1 Namespaces
	13.2 The scope of a variable
	13.3 Modules
		13.3.1 Introduction
		13.3.2 Modules in IPython
			The IPython magic command – run
		13.3.3 The variable __name__
		13.3.4 Some useful modules
	13.4 Summary
Chapter 14: Input and Output
	14.1 File handling
		14.1.1 Interacting with files
		14.1.2 Files are iterables
		14.1.3 File modes
	14.2 NumPy methods
		14.2.1 savetxt
		14.2.3 loadtxt
	14.3 Pickling
	14.4 Shelves
	14.5 Reading and writing Matlab data files
	14.6 Reading and writing images
	14.7 Summary
Chapter 15: Testing
	15.1 Manual testing
	15.2 Automatic testing
		15.2.1 Testing the bisection algorithm
		15.2.2 Using the unittest module
		15.2.3 Test setUp and tearDown methods
			Setting up testdata when a test case is created
		15.2.4 Parameterizing tests
		15.2.5 Assertion tools
		15.2.6 Float comparisons
		15.2.7 Unit and functional tests
		15.2.8 Debugging
		15.2.9 Test discovery
	15.3 Measuring execution time
		15.3.1 Timing with a magic function
		15.3.2 Timing with the Python module timeit
		15.3.3 Timing with a context manager
	15.4 Summary
	15.5 Exercises
Chapter 16: Symbolic Computations - SymPy
	16.1 What are symbolic computations?
		16.1.1 Elaborating an example in SymPy
	16.2 Basic elements of SymPy
		16.2.1 Symbols – the basis of all formulas
		16.2.2 Numbers
		16.2.3 Functions
			Undefined functions
		16.2.4 Elementary functions
		16.2.5 Lambda functions
	16.3 Symbolic linear algebra
		16.3.1 Symbolic matrices
		16.3.2 Examples for linear algebra methods in SymPy
	16.4 Substitutions
	16. 5 Evaluating symbolic expressions
		16.5.1 Example: A study on the convergence order of Newton's method
		16.5.2 Converting a symbolic expression into a numeric function
			A study on the parameter dependency of polynomial coefficients
	16.6 Summary
Chapter 17: Interacting with the Operating System
	17.1 Running a Python program in a Linux shell
	17.2 The module sys
		17.2.1 Command-line arguments
		17.2.2 Input and output streams
			Redirecting streams
			Building a pipe between a Linux command and a Python script
	17.3 How to execute Linux commands from Python
		17.3.1 The modules subprocess and shlex
			A complete process: subprocess.run
			Creating processes: subprocess.Popen
	17.4 Summary
Chapter 18: Python for Parallel Computing
	18.1 Multicore computers and computer clusters
	18.2 Message passing interface (MPI)
		18.2.1 Prerequisites
	18.3 Distributing tasks to different cores
		18.3.1 Information exchange between processes
		18.3.2 Point-to-point communication
		18.3.3 Sending NumPy arrays
			18.3.4 Blocking and non-blocking communication
		18.3.5 One-to-all and all-to-one communication
			Preparing the data for communication
			The commands – scatter and gather
			A final data reduction operation – the command reduce
			Sending the same message to all
			Buffered data
	18.4 Summary
Chapter 19: Comprehensive Examples
	19.1 Polynomials
		19.1.1 Theoretical background
		19.1.2 Tasks
	19.1.3 The polynomial class
		19.1.4 Usage examples of the polynomial class
		19.1.5 Newton polynomial
	19.2 Spectral clustering
	19.3 Solving initial value problems
	19.4 Summary
	19.5 Exercises
About Packt
Other Books You May Enjoy
References
Index