Guide to Scientific Computing in C++

Preface to the Second Edition
Preface to the First Edition
Contents
1 Getting Started
	1.1 A Brief Introduction to C++
		1.1.1 C++ is ``Object-Oriented\'\'
		1.1.2 Why You Should Write Scientific Programs in C++
		1.1.3 Why You Should Not Write Scientific Programs in C++
		1.1.4 Scope of This Book
	1.2 A First C++ Program
	1.3 Compiling a C++ Program
		1.3.1 Integrated Development Environments
		1.3.2 Compiling at the Command Line
		1.3.3 Compiler Flags
	1.4 Variables
		1.4.1 Basic Numerical Variables
		1.4.2 Other Numerical Variables
		1.4.3 Mathematical Operations on Numerical Variables
		1.4.4 Division of Integers
		1.4.5 Arrays
		1.4.6 ASCII Characters
		1.4.7 Boolean Variables
		1.4.8 Strings
	1.5 Simple Input and Output
		1.5.1 Basic Console Output
		1.5.2 Keyboard Input
	1.6 The assert Statement
	1.7 Tips: Debugging Code
	1.8 Exercises
2 Flow of Control
	2.1 The if Statement
		2.1.1 A Single if Statement
		2.1.2 Example: Code for a Single if Statement
		2.1.3 if--else Statements
		2.1.4 Multiple if Statements
		2.1.5 Nested if Statements
		2.1.6 Boolean Variables
	2.2 Logical and Relational Operators
	2.3 The while Statement
	2.4 Loops Using the for Statement
		2.4.1 Example: Calculating the Scalar Product of Two Vectors
	2.5 The switch Statement
	2.6 Tips: Loops and Branches
		2.6.1 Tip 1: A Common Novice Coding Error
		2.6.2 Tip 2: Counting from Zero
		2.6.3 Tip 3: Equality Versus Assignment
		2.6.4 Tip 4: Never Ending while Loops
		2.6.5 Tip 5: Comparing Two Floating Point Numbers
	2.7 Exercises
3 File Input and Output
	3.1 Redirecting Console Output to File
	3.2 Writing to File
		3.2.1 Setting the Precision of the Output
	3.3 Reading from File
	3.4 Checking Input and Output are Successful
	3.5 Reading from the Command Line
	3.6 Tips: Controlling Output Format
	3.7 Exercises
4 Pointers
	4.1 Pointers and the Computer\'s Memory
		4.1.1 Addresses
		4.1.2 Pointer Variables
		4.1.3 Example Use of Pointers
		4.1.4 Warnings on the Use of Pointers
	4.2 Dynamic Allocation of Memory for Arrays
		4.2.1 Vectors
		4.2.2 Matrices
		4.2.3 Irregularly Sized Matrices
	4.3 Tips: Pointers
		4.3.1 Tip 1: Pointer Aliasing
		4.3.2 Tip 2: Safe Dynamic Allocation
		4.3.3 Tip 3: Every new Has a delete
	4.4 Modern C++ Memory Management
		4.4.1 The unique_ptr Smart Pointer
		4.4.2 The shared_ptr Smart Pointer
	4.5 Exercises
5 Blocks, Functions and Reference Variables
	5.1 Blocks
	5.2 Functions
		5.2.1 Simple Functions
		5.2.2 Returning Pointer Variables from a Function
		5.2.3 Use of Pointers as Function Arguments
		5.2.4 Sending Arrays to Functions
		5.2.5 Example: A Function to Calculate the Scalar Product of Two Vectors
	5.3 Reference Variables
	5.4 Default Values for Function Arguments
	5.5 Function Overloading
	5.6 Declaring Functions Without Prototypes
	5.7 Function Pointers
	5.8 Recursive Functions
	5.9 Modules
	5.10 Tips: Code Documentation
	5.11 Exercises
6 An Introduction to Classes
	6.1 The Raison d\'Être for Classes
		6.1.1 Problems That May Arise When Using Modules
		6.1.2 Abstraction, Encapsulation and Modularity Properties of Classes
	6.2 A First Example Simple Class: A Class of Books
		6.2.1 Basic Features of Classes
		6.2.2 Header Files
		6.2.3 Setting and Accessing Variables
		6.2.4 Compiling Multiple Files
		6.2.5 Access Privileges
		6.2.6 Including Function Implementations in Header Files
		6.2.7 Constructors and Destructors
		6.2.8 Pointers to Classes
	6.3 The friend Keyword
	6.4 A Second Example Class: A Class of Complex Numbers
		6.4.1 Operator Overloading
		6.4.2 The Class of Complex Numbers
	6.5 Some Additional Remarks on Operator Overloading
	6.6 Tips: Coding to a Standard
	6.7 Exercises
7 Inheritance and Derived Classes
	7.1 Inheritance, Extensibility and Polymorphism
	7.2 Example: A Class of E-books Derived from a Class of Books
	7.3 Access Privileges for Derived Classes
	7.4 Classes Derived from Derived Classes
	7.5 Run-Time Polymorphism
	7.6 The Abstract Class Pattern
	7.7 Tips: Using a Debugger
	7.8 Exercises
8 Templates
	8.1 Templates to Control Dimensions and Verify Sizes
	8.2 Templates for Polymorphism
	8.3 A Brief Survey of the Standard Template Library
		8.3.1 Vectors
		8.3.2 Sets
	8.4 A Survey of Some New Functionality in Modern C++
		8.4.1 The auto Type
		8.4.2 Some Useful Container Types with Unified Functionality
		8.4.3 Range-based for Loops
		8.4.4 Mapping Lambda Functions
	8.5 Tips: Template Compilation
	8.6 Exercises
9 Errors, Exceptions and Testing
	9.1 Preconditions
		9.1.1 Example: Two Implementations of a Graphics Function
	9.2 Three Levels of Errors
	9.3 Introducing the Exception
	9.4 Using Exceptions
	9.5 Testing Software
		9.5.1 Unit Testing
		9.5.2 Extending Software
		9.5.3 Black Box Testing
		9.5.4 White Box Testing
		9.5.5 Test Driven Development
	9.6 Tips: Writing Appropriate Tests
	9.7 Exercises
10 Developing Classes for Linear Algebra Calculations
	10.1 Requirements of the Linear Algebra Classes
	10.2 Constructors and Destructors
		10.2.1 The Default Constructor
		10.2.2 The Copy Constructor
		10.2.3 A Specialised Constructor
		10.2.4 Destructor
	10.3 Accessing Private Class Members
		10.3.1 Accessing the Size of a Vector
		10.3.2 Overloading the Square Bracket Operator
		10.3.3 Read-Only Access to Vector Entries
		10.3.4 Overloading the Round Bracket Operator
	10.4 Operator Overloading for Vector Operations
		10.4.1 The Assignment Operator
		10.4.2 Unary Operators
		10.4.3 Binary Operators
	10.5 Functions
		10.5.1 Members Versus Friends
	10.6 Tips: Memory Debugging Tools
	10.7 Exercises
11 An Introduction to Parallel Programming Using MPI
	11.1 Distributed Memory Architectures
	11.2 Installing MPI
	11.3 A First Program Using MPI
		11.3.1 Essential MPI Functions
		11.3.2 Compiling and Running MPI Code
	11.4 Basic MPI Communication
		11.4.1 Point-to-Point Communication
		11.4.2 Collective Communication
	11.5 Example MPI Applications
		11.5.1 Summation of Series
		11.5.2 Parallel Linear Algebra
	11.6 Tips: Debugging a Parallel Program
		11.6.1 Tip 1: Make an Abstract Program
		11.6.2 Tip 2: Datatype Mismatch
		11.6.3 Tip 3: Intermittent Deadlock
		11.6.4 Tip 4: Almost Collective Communication
	11.7 Exercises
12 Designing Object-Oriented Numerical Libraries
	12.1 Developing the Library for Ordinary Differential Equations
		12.1.1 Model Problems
		12.1.2 Finite Difference Approximation to Derivatives
		12.1.3 Application of Finite Difference Methods to Boundary Value Problems
		12.1.4 Concluding Remarks on Boundary Value Problems  in One Dimension
	12.2 Designing a Library for Solving Boundary Value Problems
		12.2.1 The Class SecondOrderOde
		12.2.2 The Class BoundaryConditions
		12.2.3 The Class FiniteDifferenceGrid
		12.2.4 The Class BvpOde
		12.2.5 Using the Class BvpOde
	12.3 Extending the Library to Two Dimensions
		12.3.1 Model Problem for Two Dimensions
		12.3.2 Finite Difference Methods for Boundary Value Problems in Two Dimensions
		12.3.3 Setting Up the Linear System for the Model Problem
		12.3.4 Developing the Classes Required
	12.4 Tips: Using Well-Written Libraries
	12.5 Exercises
A Linear Algebra
	A.1 Vectors and Matrices
		A.1.1 Operations Between Vectors and Matrices
		A.1.2 The Scalar Product of Two Vectors
		A.1.3 The Determinant and the Inverse of a Matrix
		A.1.4 Eigenvalues and Eigenvectors of a Matrix
		A.1.5 Vector and Matrix Norms
	A.2 Systems of Linear Equations
		A.2.1 Gaussian Elimination
		A.2.2 The Thomas Algorithm
		A.2.3 The Conjugate Gradient Method
B Other Programming Constructs You Might Meet
	B.1 C Style Output
	B.2 C Style Dynamic Memory Allocation
	B.3 Ternary ?: Operator
	B.4 Using Namespace
	B.5 Structures
	B.6 Multiple Inheritance
	B.7 Class Initialisers
C Solutions to Exercises
	C.1 Matrix and Linear System Classes
	C.2 ODE Solver Library
Further Reading
Index