Guide to Scientific Computing in C++

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front-matter
Guide to Scientific Computing in C++
Preface
Contents
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Chapter 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
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Chapter 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
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Chapter 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 Reading from the Command Line
3.5 Tips: Controlling Output Format
3.6 Exercises
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Chapter 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 Exercises
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Chapter 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
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Chapter 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
6.2.4.1 Using Makefiles to Compile 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
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Chapter 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
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Chapter 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 Tips: Template Compilation
8.5 Exercises
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Chapter 9: Errors and Exceptions
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 Tips: Test-Driven Development
9.6 Exercises
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Chapter 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
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Chapter 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
11.4.1.1 Blocking and Buffered Sends
11.4.2 Collective Communication
11.4.2.1 Barrier
11.4.2.2 Combined Send and Receive
11.4.2.3 Broadcast and Reduce
11.4.2.4 Scatter and Gather
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
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Chapter 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
12.1.3.1 Model Problem 1
12.1.3.2 Model Problem 2
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
back-matter
Appendix 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.2.1.1 Gaussian Elimination Without Pivoting
A.2.1.2 LU Decomposition
A.2.1.3 Gaussian Elimination with Pivoting
A.2.2 The Thomas Algorithm
A.2.3 The Conjugate Gradient Method
Appendix 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
Appendix C Solutions to Exercises
C.1 Matrix and Linear System Classes
C.2 ODE Solver Library
Further Reading
Mathematical Methods and Linear Algebra
C++ Programming
The Message-Passing Interface (MPI)
Index