Preface... 1 The Boost C++ Libraries Overview... 5 Math Toolkit: Special Functions Math Toolkit: Orthogonal Functions... 29

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1 Preface... 1 Goals of this Book... 1 Structure of the Book... 1 For whom is this Book?... 1 Using the Boost Libraries... 2 Practical Hints and Guidelines... 2 What s Next? The Boost C++ Libraries Overview Library Classification Essential Libraries Supporting Libraries Math Toolkit: Special Functions Introduction and Objectives An Overview of the Math Toolkit Special Functions Gamma Functions Gamma Function Incomplete Gamma Functions and their Inverses Beta and Error Functions Incomplete Beta Functions and their Inverses Factorials and Binomial Coefficients The Error Function and its Inverse Bessel Functions Elliptic Integral Functions Elliptic Integrals of the First, Second and Third Kinds Complete Elliptic Integrals Other Functions Zeta Function Exponential Integrals Inverse Hyperbolic Functions Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Rounding, Truncation and Integer Conversions Applications and Relationships with STL and Boost Summary and Conclusions Math Toolkit: Orthogonal Functions Introduction and Objectives An Introduction to Orthogonal Polynomials Common Properties Laguerre and Hermite Polynomials Spherical Harmonics Chebychev Polynomials Computing the Roots of Bessel Functions Statistics Distributions Summary and Conclusions Date and Time Introduction and Objectives Overview of Concepts and Functionality Gregorian Time Date... 44

2 ii Table of Contents Date Duration Date Period Date Iterators Creating User-defined Utilities A generic Date Iterator using Boost Variant General Schedules of Date Period International Money Market (IMM) Dates in Trading Systems Posix Time System Local Time Date Generators and Algorithms Date/Time I/O and Serialisation Set-Like Operations Application Areas Summary and Conclusions Some Building Block Data Structures and Libraries Introduction and Objectives Timer Library Uuid (Universally Unique Identifiers) Creating Uuids Other Functionality Dynamic Bitset and STL Bitsets Boolean Operations Type Conversions dynamic_bitset Applications of Dynamic Bitsets Circular Buffer The Boost Circular Buffer Class Using Circular Buffer: Producer-Consumer Pattern Summary and Conclusions Matrix Algebra in Boost Part I: ublas Data Structures Introduction and Objectives BLAS (Basic Linear Algebra Subprograms) BLAS Level BLAS Level BLAS Level Dense Vectors Creating and Accessing Dense Vectors Special Dense Vectors Sparse Vectors Mapped Vector Compressed Vector Coordinate Vector Dense Matrices Creating and Accessing Dense Matrices Special Dense Matrices Other Kinds of Matrices Sparse Matrices Triangular Matrices Triangular Adaptor Summary and Conclusions... 95

3 iii 7 Matrix Algebra in Boost Part II: Advanced Features and Applications Introduction and Objectives Patterned Matrices Symmetric Matrices Hermitian Matrices Banded Matrices Vector and Matrix Proxies Vector Range Vector Slice Matrix Proxies: Rows and Columns Matrix Views: What are Options? Vector Expressions Matrix Expressions Applying ublas: Solving Linear Systems of Equations Conjugate Gradient Method (CGM) LU Decomposition Cholesky Decomposition Applications of ublas Summary and Conclusions An Introduction to Network Programming Concepts and Protocols Introduction and Objectives Overview of OSI and TCP/IP Protocols and Services Internet Addresses Some Special IP Addresses Internet Addresses in Boost Implementing Endpoints Domain Name System (DNS) Client-Server Model of Interaction Connectionless and Connection-Oriented Servers The Socket Interface Protocol for Acknowledgement and Retransmission Summary and Conclusions Boost ASIO: Synchronous Operations Introduction Testing Network Applications and Troubleshooting DNS Reverse DNS Buffers UDP Example: UDP Echo Server Example: UDP Echo Client TCP Example: TCP Echo Server Example: TCP Echo Client Using Socket IOStreams to improve Ease of Use Summary and Conclusions Boost ASIO: Asynchronous Operations Introduction Timers Synchronous Deadline Timer

4 iv Table of Contents Asynchronous Deadline Timer Binding Arguments Binding to Member Functions Thread Pooling and Synchronising Threads Asynchronous UDP Server Asynchronous TCP Server The ASyncEchoServer Class The ASyncConnection Class Thread-Pooled Asynchronous TCP Server CRC Checksums and Time-outs Message and CRC Heartbeats and Time-outs Sending messages Echo Client Implementation Summary and Conclusions Boost Interprocess: IPC Mechanisms Introduction and Objectives Persistence of IPC Mechanisms Shared Memory Memory Mapped File Advanced Mapped Regions Pointers in Mapped Regions Static Members in Mapped Regions Managed Memory Segments Managed Shared Memory Managed Memory Mapped File Allocating Memory Fragments in Managed Memory Allocating Objects in Managed Memory Synchronisation of Object Construction and Retrieving Composite Objects Synchronising Composite Object Creation Using Allocators Other Allocators STL Compatible Containers Managed External Buffer and Managed Heap Memory Other Managed Segment Functionality Summary and Conclusions Boost Interprocess II: Process Synchronisation Introduction and Objectives Mutexes Mutex Operations Named Mutex Anonymous Mutex Scoped Lock Condition Variables Message Queue Semaphores Upgradable Mutexes Introduction to Upgradable Mutexes Upgradable Mutexes in Boost Interprocess

5 v Lock Transfer Summary and Conclusions Interval Arithmetic Introduction and Objectives What is Interval Analysis, Interval Arithmetic, Interval Mathematics? Interval Arithmetic: Mathematical Foundations Boost Interval Library: Functionality and Initial Examples Application: Matrix Computations with Intervals Function Evaluation in Interval Advanced Functions and Related Data Structures Solution of Nonlinear Equations Summary and Conclusions User-defined Memory Allocation: Boost Pool Introduction and Objectives Dynamic Memory Allocation in C++ and STL Allocator Requirements Pool Concepts Simple Segregated Storage Concept Pool Singleton Pool Object Pool Pool Allocator and Fast Pool Allocator Summary and Conclusions An Introduction to Graph Theory and Graph Algorithms Introduction and Objectives Directed and Undirected Graphs; Terms and Definitions Further Properties of Graphs and Digraphs Paths and Connectivity Special Types of Graphs Graph Data Structures Operations on Graphs Minimum Spanning Tree (MST) Problems Depth-First and Breadth-First Searches in Graphs Shortest Path Problems Connected Components Applications of Graph Theory Project Planning Some Specific Graphs Eulerian, de Bruijn and Hamiltonian Digraphs Random Graphs Flow Networks Summary and Conclusions The Boost Graph Library Data Structures and Fundamental Algorithms Introduction and Objectives An Overview of the Functionality in BGL Boost Property Map Library Boost Property Map Category Tags and Traits Property Map Types An Introduction to Data Structures in BGL Auxiliary Classes

6 vi Table of Contents 16.6 Minimum Spanning Tree (MST) Algorithms Kruskal Algorithm Prim Algorithm Shortest Path Algorithms Dijkstra s Algorithm Bellman-Ford Algorithm Summary and Conclusions The Boost Graph Library (BGL) Advanced Algorithms Introduction and Objectives More Shortest-Path Algorithms Floyd-Warshall Algorithm Johnson Algorithm Transitive Closure Connected Component Algorithms Connected Components Biconnected Components and Articulation Points Incremental Connected Components Strong Components Graph Structure Comparison Isomorphic Graphs Extending Algorithms with Visitor Basic Graph Algorithms Other Graph Algorithms in BGL Sparse Matrix Ordering Algorithms Random Graphs Summary and Conclusions Interval Container Library Introduction and Objectives Overview of the ICL What Kinds of Intervals? Statically Bound Interval Types Modelling Intervals by Parameter Variation Intervals and Temporal Types Interval Sets and Interval Maps Interval Combining Styles Splitting Interval Containers Separating Interval Containers Iterators for Interval Sets and Maps Some 101 Examples Applying ICL to Managements Information Systems (MIS) Daily Planning Summary and Conclusions Boost Functional Factory Introduction and Objectives An Overview of GOF Patterns Strengths and Limitations of GOF Patterns An Example: Traditional Windows Factories Boost Functional Factory Function Factory with Smart Pointers R-Value Arguments

7 vii 19.7 Allocators Value Factory Factory with Algorithms Summary and Conclusions Bibliography Index Book Registration Form Boost Volume II User Agreement

Thomas H. Cormen Charles E. Leiserson Ronald L. Rivest. Introduction to Algorithms

Thomas H. Cormen Charles E. Leiserson Ronald L. Rivest Introduction to Algorithms Preface xiii 1 Introduction 1 1.1 Algorithms 1 1.2 Analyzing algorithms 6 1.3 Designing algorithms 1 1 1.4 Summary 1 6