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Overview

To get you started right away with creating your own statistical applications using the Extreme Optimization Numerical Libraries for .NET, we are providing these QuickStart Samples. See our Sample Applications page for some real-life applications.

• Mathematics
• Linear Algebra
• Statistics

New! Check out the samples for our new features: arbitrary precision numbers (C#, VB.NET), generic algorithms (C#, VB.NET), 2d numerical integration (C#, VB.NET), and generalized linear models (C#, VB.NET).

Also check out our samples about polynomials in F#, numerical integration in F#, optimization in F#, Fourier Transforms in F#, continuous distributions in F# and discrete distributions in F#.

Mathematics

General

Project	Description
Complex Numbers in C# Complex Numbers in VB.NET Complex Numbers in Managed C++	Illustrates working with complex numbers using the DoubleComplex structure.
Big Numbers in C# Big Numbers in VB.NET	Illustrates working with arbitrary precision integers, rational numbers, and floating-point numbers.
Elementary Functions in C# Elementary Functions in VB.NET Elementary Functions in Managed C++	Illustrates calling extended elementary functions available from the ElementaryFunctions class.
Fourier Transforms in C# Fourier Transforms in VB.NET Fourier Transforms in F#	Illustrates how to compute the discrete Fourier transform of real and complex signals.
Function Delegates in C# Function Delegates in VB.NET	Illustrates the use of the delegates representing mathematical functions.
Prime Numbers in C# Prime Numbers in VB.NET	Illustrates working with prime numbers using the methods of the NumberTheory class.

Calculus

Project	Description
Numerical Differentiation in C# Numerical Differentiation in VB.NET	Illustrates the calculation of numerical derivatives using the NumericalDifferentiator class.
Basic Integration in C# Basic Integration in VB.NET Basic Integration in F#	Illustrates numerical integration of functions.
Advanced Integration in C# Advanced Integration in VB.NET	Illustrates more advanced numerical integration using the AdaptiveIntegrator class.
N-D Integration in C# N-D Integration in VB.NET	Illustrates numerical integration of functions in higher dimensions.

Curves

Project	Description
Constant Curve in C# Constant Curve in VB.NET	Illustrates the use of the Constant class in the Extreme.Mathematics.Curves namespace.
LineCurve in C# LineCurve in VB.NET	Illustrates the use of the Line class to represent linear relationships between two variables.
QuadraticCurve in C# QuadraticCurve in VB.NET	Illustrates the use of the Quadratic class to represent quadratic curves.
BasicPolynomials in C# BasicPolynomials in VB.NET BasicPolynomials in F#	Illustrates some basic operations on polynomials using the Polynomial class.
AdvancedPolynomials in C# AdvancedPolynomials in VB.NET	Illustrates more advanced uses of the Polynomial class.
ChebyshevExpansions in C# ChebyshevExpansions in VB.NET	Illustrates creating and working with Chebyshev approximations using the ChebyshevSeries class.

Curve Fitting and Interpolation

Project	Description
Piecewise Curves in C# Piecewise Curves in VB.NET	Illustrates interpolation using piecewise constant and piecewise linear curves.
Cubic Splines in C# Cubic Splines in VB.NET	Illustrates interpolation using natural and clamped cubic splines.
Linear Curve Fitting in C# Linear Curve Fitting in VB.NET	Illustrates curve fitting of polynomials and arbitrary linear functions using linear least squares.
Nonlinear Curve Fitting in C# Nonlinear Curve Fitting in VB.NET	Illustrates curve fitting of nonlinear functions using nonlinear least squares.

Solving Equations

Project	Description
Root Bracketing Solvers in C# Root Bracketing Solvers in VB.NET	Illustrates solving equations using root bracketing algorithms, including the bisection method, the method of false position (regula falsi) and the Dekker-Brent algorithm.
Newton Equation Solver in C# Newton Equation Solver in VB.NET	Illustrates solving equations using the Newton-Raphson method.
Nonlinear Systems in C# Nonlinear Systems in VB.NET	Illustrates solving systems of non-linear equations using the Newton-Raphson method.

Optimization

Project	Description
Optimization in 1D in C# Optimization in 1D in VB.NET	Illustrates one-dimensional optimization using the Brent and Golden Section optimizer classes.
Optimization in N-D in C# Optimization in N-D in VB.NET Optimization in N-D in F#	Illustrates multi-dimensional optimization using the quasi-Newton and Nelder-Mead optimizer classes.
Linear Programming in C# Linear Programming in VB.NET	Illustrates optimization with linear constraints using the LinearProgram and related classes.

Generic Arithmetic

Project	Description
Generic Algorithms in C# Generic Algorithms in VB.NET	Illustrates how to implement algorithms using generic arithmetic.

Linear Algebra

Vectors

Project	Description
Basic Vectors in C# Basic Vectors in VB.NET	Illustrates basic vector operations using the Vector class.
Vector Operations in C# Vector Operations in VB.NET	Illustrates operations on vectors: accessing components, arithmetic operations, norms.

Matrices

Project	Description
Basic Matrices in C# Basic Matrices in VB.NET	Illustrates basic matrix operations using the Matrix class.
Matrix-Vector Operations in C# Matrix-Vector Operations in VB.NET	Illustrates operations on matrices and vectors.
Accessing Matrix Components in C# Accessing Matrix Components in VB.NET	Illustrates different ways to access the components of a matrix, including iterating through the rows and columns of a matrix and working with submatrices.
Triangular Matrices in C# Triangular Matrices in VB.NET	Illustrates using the TriangularMatrix class working with triangular matrices, solving triangular systems, and more.
Symmetric Matrices in C# Symmetric Matrices in VB.NET	Illustrates the use of the SymmetricMatrix class for working with symmetric matrices.
Band Matrices in C# Band Matrices in VB.NET	Illustrates the use of the BandMatrix class for working with general and symmetric band matrices.
Sparse Matrices in C# Sparse Matrices in VB.NET	Illustrates using the sparse vector and matrix classes .

Solving Equations and Least Squares

Project	Description
Linear Equations in C# Linear Equations in VB.NET	Illustrates solving systems of simultaneous linear equations.
Structured Linear Equations in C# Structured Linear Equations in VB.NET	Illustrates solving systems of simultaneous linear equations with special structure.
Matrix Decompositions in C# Matrix Decompositions in VB.NET	Illustrates matrix decompositions (LU, QR, and Cholesky decomposition).
Least Squares in C# Least Squares in VB.NET	Illustrates solving linear least squares problems.

Statistics

General

Project	Description
Histograms in C# Histograms in VB.NET	Illustrates the use of the Histogram class.
Sorting and Filtering in C# Sorting and Filtering in VB.NET	Illustrates the Filter class and related methods for sorting and filtering data.

Probability Distributions

Project	Description
Continuous Distributions in C# Continuous Distributions in VB.NET Continuous Distributions in F#	Illustrates how to use the classes that implement continuous probability distributions.
Discrete Distributions in C# Discrete Distributions in VB.NET Discrete Distributions in F#	Illustrates how to use the classes that implement discrete probability distributions.

Analysis of Variance

Project	Description
One-Way ANOVA in C# One-Way ANOVA in VB.NET	Illustrates how to use the OneWayAnovaModel class to perform a one-way analysis of variance.
Two-Way ANOVA in C# Two-Way ANOVA in VB.NET	Illustrates how to use the TwoWayAnovaModel class to perform a two-way analysis of variance.
Repeated Measures ANOVA in C# Repeated Measures ANOVA in VB.NET	Illustrates how to use the OneWayRAnovaModel class to perform a one-way analysis of variance with repeated measures.

Regression Analysis

Project	Description
Simple Regression in C# Simple Regression in VB.NET	Illustrates the use of the SimpleRegressionModel class to perform simple linear regression.
Multiple Regression in C# Multiple Regression in VB.NET	Illustrates the use of the LinearRegressionModel class to perform multiple linear regression.
Polynomial Regression in C# Polynomial Regression in VB.NET	Illustrates how to use the PolynomialRegressionModel class (Extreme.Statistics namespace) to perform a polynomial regression.
Logistic Regression in C# Logistic Regression in VB.NET	Illustrates how to use the LogisticRegressionModel class (Extreme.Statistics namespace) to perform logistic regression.
Generalized Linear Models C# Generalized Linear Models VB.NET	Illustrates how to use the GeneralizedLinearModel class to create generalized linear models used in Poisson regression and probit regression.

Time Series Analysis

Project	Description
Simple Time Series in C# Simple Time Series in VB.NET	Illustrates the use of the TimeSeriesCollection class to perform simple time series analysis computations.
Variable Transforms in C# Variable Transforms in VB.NET	Illustrates transformations of numerical variables by showing how to compute several financial indicators.
ARIMA Models in C# ARIMA Models in VB.NET	Illustrates the use of the TimeSeriesCollection class to perform simple time series analysis computations.

Multivariate Analysis

Project	Description
Principal Component Analysis in C# Principal Component Analysis in VB.NET	Illustrates how to perform a Principal Component Analysis (PCA) on a set of data.
Cluster Analysis in C# Cluster Analysis in VB.NET	Illustrates how to perform hierarchical cluster analysis and K-means cluster analysis.

Hypothesis Tests

Project	Description
Mean Tests in C# Mean Tests in VB.NET	Illustrates how to use the one sample z test and t test to test the mean of one or two samples.
Variance Tests in C# Variance Tests in VB.NET	Illustrates the use of the Chi Square test and F test for the variance of one or two samples.
Goodness-Of-Fit Tests in C# Goodness-Of-Fit Tests in VB.NET	Illustrates the Chi Square, Kolmogorov-Smirnov and Anderson-Darling tests for goodness-of-fit.
Homogeneity of Variances Tests in C# Homogeneity Of Variances Tests in VB.NET	Illustrates how to use Bartlett's test and Levene's test to verify that a set of samples have the same variance.

Random numbers and Quasi-Random Sequences

Project	Description
Random Number Generators in C# Random Number Generators in VB.NET	Illustrates the use of classes that implement pseudo-random number generators.
Non-Uniform Random Numbers in C# Non-Uniform Random Numbers in VB.NET	Illustrates ways of obtaining random numbers from a non-uniform distribution.
Quasi-Random Sequences in C# Quasi-Random Sequences in VB.NET	Illustrates the use of quasi-random sequences in multi-dimensional numerical integration.