Contents

Chapter 1. Introduction

1.1 Product Features

1.2 Software Requirements

1.3 Namespaces

1.4 Documentation

This Manual

1.5 Technical Support

Chapter 2. Structured Sparse Matrix Types

2.1 Lower Triangular Matrices

2.2 Upper Triangular Matrices

2.3 Symmetric Matrices

2.4 Hermitian Matrices

2.5 Banded Matrices

2.6 Tridiagonal Matrices

2.7 Symmetric Banded Matrices

2.8 Hermitian Banded Matrices

Chapter 3. Using The Structured Sparse Matrix Classes

3.1 Creating Matrices

Creating Default Matrices

Creating Sparse Matrices from General Matrices

Creating Sparse Matrices from Other Sparse Matrices

Creating Sparse Matrices from a Data Vector

Implicit Conversion

Copying Matrices

3.2 Value Operations on Matrices

Accessing and Modifying Matrix Values

Resizing a Matrix

3.3 Logical Operations on Matrices

3.4 Arithmetic Operations on Matrices

3.5 Vector Views

3.6 Functions of Matrices

Matrix Transposition

Matrix Inner Products

Matrix Norms

Trigonometric and Transcendental Functions

Absolute Value

Complex Matrix Functions

3.7 Generic Functions

Chapter 4. Structured Sparse Matrix Factorizations

4.1 Factorization Classes

4.2 Creating Factorizations

4.3 Using Factorizations

Solving for Right-Hand Sides

Computing Inverses, Determinants, and Condition Numbers

Chapter 5. General Sparse Vectors and Matrices

5.1 Sparse Vectors

Storage Format

Creating Sparse Vectors

Accessing and Modifying Sparse Vector Values

Operations on Sparse Vectors

Sparse Vector Functions

Creating Dense Vectors from Sparse Vectors

5.2 Sparse Matrices

Storage Format

Creating Sparse Matrices

Accessing and Modifying Sparse Matrix Values

Operations on Sparse Matrices

Sparse Matrix Functions

Creating Dense Matrices from Sparse Matrices

5.3 Sparse Matrix Factorizations

Factorization Classes

Creating Factorizations

Using Factorizations

Chapter 6. Decompositions

6.1 QR Decompositions

Creating QR Decompositions

Using QR Decompositions

Reusing QR Decompositions

6.2 Singular Value Decompositions

Creating Singular Value Decompositions

Using Singular Value Decompositions

Reusing Singular Value Decompositions

Chapter 7. Least Squares Solutions

7.1 Ordinary Least Squares Methods

Least Squares Using Cholesky Factorization

Least Squares Using QR Decomposition

Least Squares Using SVD

7.2 Creating Ordinary Least Squares Objects

7.3 Using Ordinary Least Squares Objects

Testing for Goodness

Solving Least Squares Problems

Retrieving Information About the Original Matrix

7.4 Weighted Least Squares

7.5 Iteratively Reweighted Least Squares

Convergence Functions

Weighting Functions

Chapter 8. EigenValue Problems

8.1 Eigenvalue Classnames

8.2 Using the Eigenvalue Classes

Constructing Eigenvalue Objects

Testing for Goodness

Retrieving Eigenvalues and Eigenvectors

Retrieving Information About the Original Matrix

Reusing Eigenvalue Decompositions

8.3 Using the Eigenvalue Server Classes

Constructing Eigenvalue Servers

Configuring Eigenvalue Servers

Creating Eigenvalue Objects from a Server

Chapter 9. Serialization

9.1 Binary Serialization

9.2 SOAP Serialization

Index

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