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 Applications
NMath License Management
Deploying NMath Applications
1.4 Documentation
This Manual
1.5 Visualization
1.6 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 Scalar Random Number Generators
Underlying Uniform Generators
Generating Random Numbers
Random Seeds
9.2 Vectorized Random Number Generators
Generating Random Numbers
Successive Random Numbers
Independent Streams
Quasirandom Numbers

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 14. The Matrix Namespace

Chapter 15. Structured Sparse Matrix Types

15.1 Lower Triangular Matrices
15.2 Upper Triangular Matrices
15.3 Symmetric Matrices
15.4 Hermitian Matrices
15.5 Banded Matrices
15.6 Tridiagonal Matrices
15.7 Symmetric Banded Matrices
15.8 Hermitian Banded Matrices

Chapter 16. Using The Structured Sparse Matrix Classes

16.1 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
16.2 Value Operations on Matrices
Accessing and Modifying Matrix Values
Resizing a Matrix
16.3 Logical Operations on Matrices
16.4 Arithmetic Operations on Matrices
16.5 Vector Views
16.6 Functions of Matrices
Matrix Transposition
Matrix Inner Products
Matrix Norms
Trigonometric and Transcendental Functions
Absolute Value
Complex Matrix Functions
16.7 Generic Functions

Chapter 17. General Sparse Vectors and Matrices

17.1 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
17.2 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
17.3 Sparse Matrix Factorizations
Factorization Classes
Creating Factorizations
Using Factorizations

Chapter 18. Structured Sparse Matrix Factorizations

18.1 Factorization Classes
18.2 Creating Factorizations
18.3 Using Factorizations
Solving for Right-Hand Sides
Computing Inverses, Determinants, and Condition Numbers

Chapter 19. Decompositions

19.1 QR Decompositions
Creating QR Decompositions
Using QR Decompositions
Reusing QR Decompositions
19.2 Singular Value Decompositions
Creating Singular Value Decompositions
Using Singular Value Decompositions
Reusing Singular Value Decompositions

Chapter 20. Least Squares Solutions

20.1 Ordinary Least Squares Methods
Least Squares Using Cholesky Factorization
Least Squares Using QR Decomposition
Least Squares Using SVD
20.2 Creating Ordinary Least Squares Objects
20.3 Using Ordinary Least Squares Objects
Testing for Goodness
Solving Least Squares Problems
Retrieving Information About the Original Matrix
20.4 Weighted Least Squares
20.5 Iteratively Reweighted Least Squares
Convergence Functions
Weighting Functions

Chapter 21. EigenValue Problems

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

Part IV - The Analysis Namespace

Chapter 22. The Analysis Namespace

Chapter 23. Encapsulating Multivariate Functions

23.1 Creating Multivariate Functions
23.2 Evaluating Multivariate Functions
23.3 Algebraic Manipulation of Multivariate Functions

Chapter 24. Minimizing Univariate Functions

24.1 Bracketing a Minimum
24.2 Minimizing Functions Without Calculating the Derivative
24.3 Minimizing Derivable Functions

Chapter 25. Minimizing Multivariate Functions

25.1 Minimizing Functions Without Calculating the Derivative
25.2 Minimizing Derivable Functions

Chapter 26. Simulated Annealing

26.1 Temperature
26.2 Annealing Schedules
Linear Annealing Schedules
Custom Annealing Schedules
26.3 Minimizing Functions by Simulated Annealing
26.4 Annealing History

Chapter 27. Linear Programming

27.1 Solving LP Problems

Chapter 28. Nonlinear and Quadratic Programming

28.1 Objective and Constraint Function Classes
Objective Function Classes
Constraint Function Classes
28.2 Nonlinear Programming
Encapsulating the Problem
Adding Bounds and Constraints
Solving the Problem
Advanced Options
28.3 Quadratic Programming
Encapsulating the Problem
Adding Bounds and Constraints
Solving the Problem

Chapter 29. Fitting Polynomials

29.1 Creating PolynomialLeastSquares
29.2 Properties of PolynomialLeastSquares

Chapter 30. Nonlinear Least Squares

30.1 Nonlinear Least Squares Interfaces
Minimization
Minimization Results
Implementations
30.2 Trust-Region Minimization
Constructing a TrustRegionMinimizer
Minimization
Linear Bound Constraints
Minimization Results
30.3 Levenberg-Marquardt Minimization
Constructing a LevenburgMarquardtMinimizer
Minimization
Minimization Results
30.4 Nonlinear Least Squares Curve Fitting
Generalized One Variable Functions
Encapsulating One Variable Functions
Predefined Functions
Constructing a OneVariableFunctionFitter
Fitting Data
Fit Results
30.5 Nonlinear Least Squares Surface Fitting
Generalized Multivariable Functions
Encapsulating Generalized Multivariable Functions
Constructing a MultiVariableFunctionFitter
Fitting Data
Fit Results

Chapter 31. Finding Roots of Univariate Functions

31.1 Finding Function Roots Without Calculating the Derivative
31.2 Finding Function Roots of Derivable Functions

Chapter 32. Integrating Multivariable Functions

32.1 Creating TwoVariableIntegrators
32.2 Integrating Functions of Two Variables

Chapter 33. Differential Equations

33.1 Encapsulating Differential Equations
33.2 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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