NMath User's Guide

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Contents

Part I - Introduction

Chapter 1. Overview

1.1 Product Components
1.2 Software Requirements
1.3 Building and Deploying NMath Applications
Building NMath Application
Deploying NMath Applications
1.4 Documentation
This Manual
1.5 Technical Support

Part II - The Core Namespace

Chapter 2. The Core Namespace

Chapter 3. Complex Number Types

3.1 Creating Complex Numbers
Creating Complex Numbers from Numeric Values
Creating Complex Numbers from Strings
Implicit Conversion
3.2 Value Operations on Complex Numbers
3.3 Logical Operations on Complex Numbers
3.4 Arithmetic Operations on Complex Numbers
3.5 Functions of Complex Numbers
Conjugate, Norm, and Argument
Trigonometric Functions
Transcendental Functions
Absolute Value and Square Root

Chapter 4. Viewing Data

4.1 DataBlock Classes
Class Names
Data Block Properties
Accessing the Underlying Data
4.2 Slices and Ranges
Creating Slices and Ranges
Creating Abstract Subsets
Modifying Ranges and Slices

Chapter 5. Vector Classes

5.1 Class Names
5.2 Creating Vectors
Creating Vectors from Numeric Values
Creating Vectors from Strings
Implicit Conversion
Copying Vectors
New Vector Views
5.3 Value Operations on Vectors
Accessing and Modifying Vector Values
Resizing a Vector
Appending to a Vector
5.4 Logical Operations on Vectors
5.5 Arithmetic Operations on Vectors
5.6 Functions of Vectors
Rounding Functions
Sums, Differences, and Products
Min/Max Functions
Statistical Functions
Trigonometric Functions
Transcendental Functions
Absolute Value and Square Root
Sorting Functions
Complex Vector Functions
5.7 Generic Functions
5.8 Vector Enumeration

Chapter 6. Matrix Classes

6.1 Class Names
6.2 Creating Matrices
Creating Matrices from Numeric Values
Creating Matrices from Strings
Implicit Conversion
Copying Matrices
Matrix Views
6.3 Value Operations on Matrices
Accessing and Modifying Matrix Values
Resizing a Matrix
6.4 Logical Operations on Matrices
6.5 Arithmetic Operations on Matrices
6.6 Vector Views
Row and Column Views
Diagonal Views
Arbitrary Slices
6.7 Functions of Matrices
Matrix Transposition
Matrix Norms
Matrix Inner Products
Matrix Inverse and Pseudoinverse
Rounding Functions
Sums and Differences
Min/Max Functions
Statistical Functions
Trigonometric Functions
Transcendental Functions
Absolute Value and Square Root
Sorting Functions
Complex Matrix Functions
6.8 Generic Functions
Applying Elementwise Functions
Applying Columnwise Functions
6.9 Matrix Enumeration

Chapter 7. Solutions of Linear Systems

7.1 Class Names
7.2 Creating LU Factorizations
7.3 Using LU Factorizations
Component Matrices
Solving for Right-Hand Sides
Computing Inverses, Determinants, and Condition Numbers
7.4 Static Methods

Chapter 8. Least Squares

8.1 Class Names
8.2 Creating Least Squares Solutions
8.3 Using Least Squares Solutions

Chapter 9. Random Number Generators

9.1 Distributions
Uniform Distribution
Beta Distribution
Binomial Distribution
Exponential Distribution
Gamma Distribution
Geometric Distribution
Johnson Distribution
Log-Normal Distribution
Normal Distribution
Pareto Distribution
Poisson Distribution
Triangular Distribution
Weibull Distribution
9.2 Underlying Uniform Generators
9.3 Generating Random Numbers
9.4 Random Seeds

Chapter 10. Fourier Transforms, Convolution and Correlation

10.1 Fast Fourier Transforms
FFT Classes
Creating FFT Instances
Scale Factors
Computing FFTs
Unpacking Real Results
Inverting Real Results
Strided Signals
10.2 Convolution and Correlation
Convolution and Correlation Classes
Creating Convolution and Correlation Instances
Convolution and Correlation Properties
Computing Convolutions and Correlations
Windowing Options

Chapter 11. Histograms

11.1 Creating Histograms
11.2 Adding Data to Histograms
11.3 Value Operations of Histograms
11.4 Displaying Histograms

Chapter 12. Calculus

12.1 Encapsulating Functions
Creating a Function of One Variable
Properties of Functions
Evaluating Functions
Algebraic Manipulation of Functions
12.2 Numerical Integration
Computing Integrals
Romberg Integration
Gauss-Kronrod Integration
12.3 Differentiation
12.4 Polynomials
Creating Polynomials
Properties of Polynomials
Evaluating Polynomials
Algebraic Manipulation of Polynomials
Integration
Differentiation
12.5 Function Interpolation
Linear Spline Interpolation
Cubic Spline Interpolation
Creating Your Own Interpolation Classes

Chapter 13. Signal Processing

13.1 Moving Window Filtering
Creating Moving Window Filter Objects
Moving Window Filter Properties
Filtering Data
13.2 Savitzky-Golay Filtering
Creating Savitzky-Golay Filter Objects
Savitzky-Golay Filter Properties
Filtering Data
13.3 Peak Finding
Creating Peak Finders
Peak Finder Results
Advanced Peak Finder Properties

Part III - The Matrix Namespace

Chapter 12. The Matrix Namespace

Chapter 13. Structured Sparse Matrix Types

13.1 Lower Triangular Matrices
13.2 Upper Triangular Matrices
13.3 Symmetric Matrices
13.4 Hermitian Matrices
13.5 Banded Matrices
13.6 Tridiagonal Matrices
13.7 Symmetric Banded Matrices
13.8 Hermitian Banded Matrices

Chapter 14. Using The Structured Sparse Matrix Classes

14.1 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
14.2 Value Operations on Matrices
Accessing and Modifying Matrix Values
Resizing a Matrix
14.3 Logical Operations on Matrices
14.4 Arithmetic Operations on Matrices
14.5 Vector Views
14.6 Functions of Matrices
Matrix Transposition
Matrix Inner Products
Matrix Norms
Trigonometric and Transcendental Functions
Absolute Value
Complex Matrix Functions
14.7 Generic Functions

Chapter 15. Structured Sparse Matrix Factorizations

15.1 Factorization Classes
15.2 Creating Factorizations
15.3 Using Factorizations
Solving for Right-Hand Sides
Computing Inverses, Determinants, and Condition Numbers

Chapter 16. General Sparse Vectors and Matrices

16.1 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
16.2 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
16.3 Sparse Matrix Factorizations
Factorization Classes
Creating Factorizations
Using Factorizations

Chapter 17. Decompositions

17.1 QR Decompositions
Creating QR Decompositions
Using QR Decompositions
Reusing QR Decompositions
17.2 Singular Value Decompositions
Creating Singular Value Decompositions
Using Singular Value Decompositions
Reusing Singular Value Decompositions

Chapter 18. Least Squares Solutions

18.1 Ordinary Least Squares Methods
Least Squares Using Cholesky Factorization
Least Squares Using QR Decomposition
Least Squares Using SVD
18.2 Creating Ordinary Least Squares Objects
18.3 Using Ordinary Least Squares Objects
Testing for Goodness
Solving Least Squares Problems
Retrieving Information About the Original Matrix
18.4 Weighted Least Squares
18.5 Iteratively Reweighted Least Squares
Convergence Functions
Weighting Functions

Chapter 19. EigenValue Problems

19.1 Eigenvalue Classnames
19.2 Using the Eigenvalue Classes
Constructing Eigenvalue Objects
Testing for Goodness
Retrieving Eigenvalues and Eigenvectors
Retrieving Information About the Original Matrix
Reusing Eigenvalue Decompositions
19.3 Using the Eigenvalue Server Classes
Constructing Eigenvalue Servers
Configuring Eigenvalue Servers
Creating Eigenvalue Objects from a Server

Part IV - The Analysis Namespace

Chapter 20. The Analysis Namespace

Chapter 21. Encapsulating Multivariate Functions

21.1 Creating Multivariate Functions
21.2 Evaluating Multivariate Functions
21.3 Algebraic Manipulation of Multivariate Functions

Chapter 22. Minimizing Univariate Functions

22.1 Bracketing a Minimum
22.2 Minimizing Functions Without Calculating the Derivative
22.3 Minimizing Derivable Functions

Chapter 23. Minimizing Multivariate Functions

23.1 Minimizing Functions Without Calculating the Derivative
23.2 Minimizing Derivable Functions

Chapter 24. Simulated Annealing

24.1 Temperature
24.2 Annealing Schedules
Linear Annealing Schedules
Custom Annealing Schedules
24.3 Minimizing Functions by Simulated Annealing
24.4 Annealing History

Chapter 25. Linear Programming

25.1 Solving LP Problems

Chapter 26. Fitting Polynomials

26.1 Creating PolynomialLeastSquares
26.2 Properties of PolynomialLeastSquares

Chapter 27. Nonlinear Least Squares

27.1 Nonlinear Least Squares Interfaces
Minimization
Minimization Results
Implementations
27.2 Trust-Region Minimization
Constructing a TrustRegionMinimizer
Minimization
Linear Bound Constraints
Minimization Results
27.3 Levenberg-Marquardt Minimization
Constructing a LevenburgMarquardtMinimizer
Minimization
Minimization Results
27.4 Nonlinear Least Squares Curve Fitting
Generalized One Variable Functions
Encapsulating One Variable Functions
Predefined Functions
Constructing a OneVariableFunctionFitter
Fitting Data
Fit Results
27.5 Nonlinear Least Squares Surface Fitting
Generalized Multivariable Functions
Encapsulating Generalized Multivariable Functions
Constructing a MultiVariableFunctionFitter
Fitting Data
Fit Results

Chapter 28. Finding Roots of Univariate Functions

28.1 Finding Function Roots Without Calculating the Derivative
28.2 Finding Function Roots of Derivable Functions

Chapter 29. Integrating Multivariable Functions

29.1 Creating TwoVariableIntegrators
29.2 Integrating Functions of Two Variables

Chapter 30. Differential Equations

30.1 Encapsulating Differential Equations
30.2 Solving Differential Equations
Constructing RungeKuttaSolver Instances
Solving First Order Initial Value Problems

Part V - Miscellaneous Topics

Chapter 30. Serialization

30.1 Binary Serialization
30.2 SOAP Serialization
30.3 XML Serialization

Chapter 31. Database Integration

31.1 Creating ADO.NET Objects from Vectors and Matrices
31.2 Creating Vector and Matrices from ADO.NET Objects

Chapter 32. Error Handling

32.1 Exception Types

Index


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