NMath User's Guide

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Contents

Part I - Introduction

Chapter 1. Overview

1.1 NMath Premium

1.2 Product Components

1.3 Software Requirements

1.4 NMath Assemblies

1.5 NMath License Key

1.6 NMath Configuration

1.7 Building and Deploying NMath Applications

1.8 Web Applications

1.9 Very Large Objects

1.10 Documentation

1.11 Visualization

1.12 Technical Support

Part II - The Core Namespace

Chapter 2. The Core Namespace

Chapter 3. Complex Number Types

3.1 Creating Complex Numbers

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

Chapter 4. Viewing Data

4.1 DataBlock Classes

4.2 Slices and Ranges

Chapter 5. Vector Classes

5.1 Class Names

5.2 Creating Vectors

5.3 Value Operations on Vectors

5.4 Logical Operations on Vectors

5.5 Arithmetic Operations on Vectors

5.6 Functions of Vectors

5.7 Generic Functions

5.8 Vector Enumeration

Chapter 6. Matrix Classes

6.1 Class Names

6.2 Creating Matrices

6.3 Value Operations on Matrices

6.4 Logical Operations on Matrices

6.5 Arithmetic Operations on Matrices

6.6 Vector Views

6.7 Functions of Matrices

6.8 Generic 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

7.4 Static Methods

Chapter 8. Least Squares

8.1 Class Names

8.2 Creating Least Squares Solutions

8.3 Using Least Squares Solutions

8.4 Nonnegative Least Squares Solutions

Chapter 9. Random Number Generators

9.1 Scalar Random Number Generators

9.2 Vectorized Random Number Generators

Chapter 10. Fourier Transforms, Convolution and Correlation

10.1 Fast Fourier Transforms

10.2 Convolution and Correlation

Chapter 11. Discrete Wavelet Transforms

11.1 Creating Wavelets

11.2 Computing Discrete Wavelet Transforms

Chapter 12. Histograms

12.1 Creating Histograms

12.2 Adding Data to Histograms

12.3 Value Operations of Histograms

12.4 Displaying Histograms

Chapter 13. Calculus

13.1 Encapsulating Functions

13.2 Numerical Integration

13.3 Differentiation

13.4 Polynomials

13.5 Function Interpolation

Chapter 14. Signal Processing

14.1 Moving Window Filtering

14.2 Savitzky-Golay Filtering

14.3 Savitzky-Golay Peak Finding

14.4 Rule-Based Peak Finding

Chapter 15. Special Functions

15.1 Special Functions

Part III - The Matrix Namespace

Chapter 16. The Matrix Namespace

Chapter 17. Structured Sparse Matrix Types

17.1 Lower Triangular Matrices

17.2 Upper Triangular Matrices

17.3 Symmetric Matrices

17.4 Hermitian Matrices

17.5 Banded Matrices

17.6 Tridiagonal Matrices

17.7 Symmetric Banded Matrices

17.8 Hermitian Banded Matrices

Chapter 18. Using The Structured Sparse Matrix Classes

18.1 Creating Matrices

18.2 Value Operations on Matrices

18.3 Logical Operations on Matrices

18.4 Arithmetic Operations on Matrices

18.5 Vector Views

18.6 Functions of Matrices

18.7 Generic Functions

Chapter 19. General Sparse Vectors and Matrices

19.1 Sparse Vectors

19.2 Sparse Matrices

19.3 Sparse Matrix Factorizations

Chapter 20. Structured Sparse Matrix Factorizations

20.1 Factorization Classes

20.2 Creating Factorizations

20.3 Using Factorizations

Chapter 21. Decompositions

21.1 QR Decompositions

21.2 Singular Value Decompositions

Chapter 22. Least Squares Solutions

22.1 Ordinary Least Squares Methods

22.2 Creating Ordinary Least Squares Objects

22.3 Using Ordinary Least Squares Objects

22.4 Weighted Least Squares

22.5 Iteratively Reweighted Least Squares

Chapter 23. EigenValue Problems

23.1 Eigenvalue Classnames

23.2 Using the Eigenvalue Classes

23.3 Using the Eigenvalue Server Classes

Part IV - The Analysis Namespace

Chapter 24. The Analysis Namespace

Chapter 25. Encapsulating Multivariate Functions

25.1 Creating Multivariate Functions

25.2 Evaluating Multivariate Functions

25.3 Algebraic Manipulation of Multivariate Functions

Chapter 26. Minimizing Univariate Functions

26.1 Bracketing a Minimum

26.2 Minimizing Functions Without Calculating the Derivative

26.3 Minimizing Derivable Functions

Chapter 27. Minimizing Multivariate Functions

27.1 Minimizing Functions Without Calculating the Derivative

27.2 Minimizing Derivable Functions

Chapter 28. Simulated Annealing

28.1 Temperature

28.2 Annealing Schedules

28.3 Minimizing Functions by Simulated Annealing

28.4 Annealing History

Chapter 29. Linear Programming

29.1 Encapsulating LP Problems

29.2 Solving LP Problems

Chapter 30. Nonlinear and Quadratic Programming

30.1 Objective and Constraint Function Classes

30.2 Nonlinear Programming

30.3 Quadratic Programming

30.4 Constrained Least Squares

Chapter 31. Fitting Polynomials

31.1 Creating PolynomialLeastSquares

31.2 Properties of PolynomialLeastSquares

Chapter 32. Nonlinear Least Squares

32.1 Nonlinear Least Squares Interfaces

32.2 Trust-Region Minimization

32.3 Levenberg-Marquardt Minimization

32.4 Nonlinear Least Squares Curve Fitting

32.5 Nonlinear Least Squares Surface Fitting

Chapter 33. Finding Roots of Univariate Functions

33.1 Finding Function Roots Without Calculating the Derivative

33.2 Finding Function Roots of Derivable Functions

Chapter 34. Integrating Multivariable Functions

34.1 Creating TwoVariableIntegrators

34.2 Integrating Functions of Two Variables

Chapter 35. Differential Equations

35.1 Encapsulating Differential Equations

35.2 Solving Differential Equations

35.3 Dormand–Prince Method

35.4 Stiff Equations

Part V - Miscellaneous Topics

Chapter 36. Serialization

36.1 Binary Serialization

36.2 SOAP Serialization

36.3 XML Serialization

Chapter 37. Database Integration

37.1 Creating ADO.NET Objects from Vectors and Matrices

37.2 Creating Vector and Matrices from ADO.NET Objects

Chapter 38. Error Handling

38.1 Exception Types

Chapter 39. NMath Premium

39.1 Supported Features

39.2 NMath Premium Assemblies

39.3 NMath Premium Licensing

39.4 Bridge Management

39.5 GPU Logging

39.6 Bridge Tuning

39.7 Reusing Bridges

39.8 Bridge Visualization

39.9 Overriding Bridge Routing

Index


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