Data Analysis Mathematics Linear Algebra Statistics
New Version 8.1!

Supports .NET 6.0. Try it for free with our fully functional 60-day trial version. QuickStart Samples

# 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.

## Data Analysis

Project Description
Data Frames in C#
Data Frames in Visual Basic
Data Frames in F#
Illustrates how to create and manipulate data frames using classes in the Extreme.DataAnalysis namespace.
Indexes and Labels in C#
Indexes and Labels in Visual Basic
Indexes and Labels in F#
Illustrates how to use indexes to label the rows and columns of a data frame or matrix, or the elements of a vector.
Data Wrangling in C#
Data Wrangling in Visual Basic
Data Wrangling in F#
Illustrates how to perform basic data wrangling or data munging operations on data frames using classes in the Extreme.DataAnalysis namespace.
Manipulating Columns in C#
Manipulating Columns in Visual Basic
Manipulating Columns in F#
Illustrates how to transform and manipulate the columns of a data frame.
Sorting and Filtering in C#
Sorting and Filtering in Visual Basic
Sorting and Filtering in F#
Sorting and Filtering in IronPython
Illustrates how to sort and filter data used for data analysis.
Grouping and Aggregation in C#
Grouping and Aggregation in Visual Basic
Grouping and Aggregation in F#
Illustrates how to group data and how to compute aggregates over groups and entire datasets..
Histograms in C#
Histograms in Visual Basic
Histograms in F#
Histograms in IronPython
Illustrates how to create histograms using the Histogram class in the Extreme.DataAnalysis namespace.

## Mathematics

### General

Project Description
Complex Numbers in C#
Complex Numbers in Visual Basic
Complex Numbers in F#
Complex Numbers in IronPython
Illustrates how to work with complex numbers using the DoubleComplex structure.
Elementary Functions in C#
Elementary Functions in Visual Basic
Elementary Functions in F#
Elementary Functions in IronPython
Illustrates how to use additional elementary functions.
BigNumbers in C#
BigNumbers in Visual Basic
BigNumbers in F#
BigNumbers in IronPython
Illustrates the basic use of the arbitrary precision classes: BigInteger, BigRational, BigFloat.
Prime Numbers in C#
Prime Numbers in Visual Basic
Prime Numbers in F#
Prime Numbers in IronPython
Illustrates working with prime numbers and the IntegerMath class in the Extreme.Mathematics namespace.
FFT/Fourier Transforms in C#
FFT/Fourier Transforms in Visual Basic
FFT/Fourier Transforms in F#
FFT/Fourier Transforms in IronPython
Illustrates how to compute the forward and inverse Fourier transform of a real or complex signal using classes in the Extreme.Mathematics.SignalProcessing namespace.
Generic Algorithms in C#
Generic Algorithms in Visual Basic
Generic Algorithms in F#
Illustrates how to write algorithms that are generic over the numerical type of the arguments.

### Calculus

Project Description
Basic Integration in C#
Basic Integration in Visual Basic
Basic Integration in F#
Basic Integration in IronPython
Illustrates the basic numerical integration classes.
Higher Dimensional Numerical Integration in C#
Higher Dimensional Numerical Integration in Visual Basic
Higher Dimensional Numerical Integration in F#
Higher Dimensional Numerical Integration in IronPython
Illustrates numerical integration of functions in higher dimensions using classes in the Extreme.Mathematics.Calculus namespace.
Numerical Differentiation in C#
Numerical Differentiation in Visual Basic
Numerical Differentiation in F#
Numerical Differentiation in IronPython
Illustrates how to approximate the derivative of a function.
Differential Equations in C#
Differential Equations in Visual Basic
Differential Equations in F#
Differential Equations in IronPython
Illustrates integrating systems of ordinary differential equations (ODE's).

### Curves

Project Description
Basic Polynomials in C#
Basic Polynomials in Visual Basic
Basic Polynomials in F#
Basic Polynomials in IronPython
Illustrates the basic use of the Polynomial class .
Illustrates more advanced uses of the Polynomial class, including real and complex root finding, calculating least squares polynomials and polynomial arithmetic.
Chebyshev Series in C#
Chebyshev Series in Visual Basic
Chebyshev Series in F#
Chebyshev Series in IronPython
Illustrates the basic use of the ChebyshevSeries class .

### Curve Fitting and Interpolation

Project Description
Linear Curve Fitting in C#
Linear Curve Fitting in Visual Basic
Linear Curve Fitting in F#
Linear Curve Fitting in IronPython
Illustrates how to fit linear combinations of curves to data using the LinearCurveFitter class and other classes in the Extreme.Mathematics.Curves namespace.
Nonlinear Curve Fitting in C#
Nonlinear Curve Fitting in Visual Basic
Nonlinear Curve Fitting in F#
Nonlinear Curve Fitting in IronPython
Illustrates nonlinear least squares curve fitting of predefined and user-defined curves using the NonlinearCurveFitter class.
Piecewise Curves in C#
Piecewise Curves in Visual Basic
Piecewise Curves in F#
Piecewise Curves in IronPython
Illustrates working with piecewise constant and piecewise linear curves using classes from the Extreme.Mathematics.Curves namespace.
Cubic Splines in C#
Cubic Splines in Visual Basic
Cubic Splines in F#
Cubic Splines in IronPython
Illustrates using natural and clamped cubic splines for interpolation using classes in the Extreme.Mathematics.LinearAlgebra namespace.

### Solving Equations

Project Description
Newton-Raphson Equation Solver in C#
Newton-Raphson Equation Solver in Visual Basic
Newton-Raphson Equation Solver in F#
Newton-Raphson Equation Solver in IronPython
Illustrates the use of the NewtonRaphsonSolver class for solving equations in one variable and related functions for numerical differentiation.
Root Bracketing Solvers in C#
Root Bracketing Solvers in Visual Basic
Root Bracketing Solvers in F#
Root Bracketing Solvers in IronPython
Illustrates the use of the root bracketing solvers for solving equations in one variable.
Nonlinear Systems in C#
Nonlinear Systems in Visual Basic
Nonlinear Systems in F#
Nonlinear Systems in IronPython
Illustrates the use of the NewtonRaphsonSystemSolver and DoglegSystemSolver classes for solving systems of nonlinear equations.

### Optimization

Project Description
Optimization In One Dimension in C#
Optimization In One Dimension in Visual Basic
Optimization In One Dimension in F#
Optimization In One Dimension in IronPython
Illustrates the use of the Brent and Golden Section optimizer classes in the Extreme.Mathematics.Optimization namespace for one-dimensional optimization.
Optimization In Multiple Dimensions in C#
Optimization In Multiple Dimensions in Visual Basic
Optimization In Multiple Dimensions in F#
Optimization In Multiple Dimensions in IronPython
Illustrates the use of the multi-dimensional optimizer classes in the Extreme.Mathematics.Optimization namespace for optimization in multiple dimensions.
Linear Programming in C#
Linear Programming in Visual Basic
Linear Programming in F#
Linear Programming in IronPython
Illustrates solving linear programming (LP) problems using classes in the Extreme.Mathematics.Optimization.LinearProgramming namespace.
Mixed Integer Programming in C#
Mixed Integer Programming in Visual Basic
Mixed Integer Programming in F#
Mixed Integer Programming in IronPython
Illustrates how to solve mixed integer programming by solving Sudoku puzzles using the linear programming solver.
Illustrates how to solve optimization problems a quadratic objective function and linear constraints using classes in the Extreme.Mathematics.Optimization namespace.
Nonlinear Programming in C#
Nonlinear Programming in Visual Basic
Nonlinear Programming in F#
Nonlinear Programming in IronPython
Illustrates solving nonlinear programs (optimization problems with linear or nonlinear constraints) using the NonlinearProgram and related classes.

### Random numbers and Quasi-Random Sequences

Project Description
Random Number Generators in C#
Random Number Generators in Visual Basic
Random Number Generators in F#
Random Number Generators in IronPython
Illustrates how to use specialized random number generator classes in the Extreme.Statistics.Random namespace.
Non-Uniform Random Numbers in C#
Non-Uniform Random Numbers in Visual Basic
Non-Uniform Random Numbers in F#
Non-Uniform Random Numbers in IronPython
Illustrates how to generate random numbers from a non-uniform distribution.
Quasi-Random Sequences in C#
Quasi-Random Sequences in Visual Basic
Quasi-Random Sequences in F#
Quasi-Random Sequences in IronPython
Illustrates how to generate quasi-random sequences like FaurÃ© and Sobol sequences using classes in the Extreme.Statistics.Random namespace.

## Linear Algebra

### Vectors

Project Description
Basic Vectors in C#
Basic Vectors in Visual Basic
Basic Vectors in F#
Basic Vectors in IronPython
Illustrates the basic use of the Vector class for working with vectors.
Vector Operations in C#
Vector Operations in Visual Basic
Vector Operations in F#
Vector Operations in IronPython
Illustrates how to perform operations on Vector objects, including construction, element access, arithmetic operations.

### Matrices

Project Description
Basic Matrices in C#
Basic Matrices in Visual Basic
Basic Matrices in F#
Basic Matrices in IronPython
Illustrates the basic use of the Matrix class for working with matrices.
Accessing Matrix Components in C#
Accessing Matrix Components in Visual Basic
Accessing Matrix Components in F#
Accessing Matrix Components in IronPython
Illustrates different ways of iterating through the rows and columns of a matrix using classes in the Extreme.Mathematics.LinearAlgebra namespace.
Matrix-Vector Operations in C#
Matrix-Vector Operations in Visual Basic
Matrix-Vector Operations in F#
Matrix-Vector Operations in IronPython
Illustrates how to perform operations that involve both matrices and vectors.
Triangular Matrices in C#
Triangular Matrices in Visual Basic
Triangular Matrices in F#
Triangular Matrices in IronPython
Illustrates how to work efficiently with upper or lower triangular or trapezoidal matrices.
Symmetric Matrices in C#
Symmetric Matrices in Visual Basic
Symmetric Matrices in F#
Symmetric Matrices in IronPython
Illustrates how to work efficiently with symmetric matrices.
Band Matrices in C#
Band Matrices in Visual Basic
Band Matrices in F#
Band Matrices in IronPython
Illustrates how to work with the BandMatrix class.
Sparse Matrices in C#
Sparse Matrices in Visual Basic
Sparse Matrices in F#
Sparse Matrices in IronPython
Illustrates using sparse vectors and matrices using the classes in the Extreme.Mathematics.LinearAlgebra.Sparse namespace.
Matrix Decompositions in C#
Matrix Decompositions in Visual Basic
Matrix Decompositions in F#
Matrix Decompositions in IronPython
Illustrates how compute various decompositions of a matrix using classes in the Extreme.Mathematics.LinearAlgebra namespace.

### Solving Equations and Least Squares

Project Description
Linear Equations in C#
Linear Equations in Visual Basic
Linear Equations in F#
Linear Equations in IronPython
Illustrates how to solve systems of simultaneous linear equations.
Structured Linear Equations in C#
Structured Linear Equations in Visual Basic
Structured Linear Equations in F#
Structured Linear Equations in IronPython
Illustrates how to solve systems of simultaneous linear equations that have special structure.
Iterative Sparse Solvers in C#
Iterative Sparse Solvers in Visual Basic
Iterative Sparse Solvers in F#
Iterative Sparse Solvers in IronPython
Illustrates the use of iterative sparse solvers and preconditioners for efficiently solving large, sparse systems of linear equations.
Least Squares in C#
Least Squares in Visual Basic
Least Squares in F#
Least Squares in IronPython
Illustrates how to solve least squares problems using classes in the Extreme.Mathematics.LinearAlgebra namespace.

## Statistics

### Probability Distributions

Project Description
Discrete Distributions in C#
Discrete Distributions in Visual Basic
Discrete Distributions in F#
Discrete Distributions in IronPython
Illustrates how to use the classes that represent discrete probability distributions in the Extreme.Statistics.Distributions namespace.
Continuous Distributions in C#
Continuous Distributions in Visual Basic
Continuous Distributions in F#
Continuous Distributions in IronPython
Illustrates how to use the classes that represent continuous probability distributions in the Extreme.Statistics.Distributions namespace.

### Analysis of Variance

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

### Regression Analysis

Project Description
Simple Regression in C#
Simple Regression in Visual Basic
Simple Regression in F#
Simple Regression in IronPython
Illustrates how to perform a simple linear regression using the SimpleRegressionModel class.
Multiple Linear Regression in C#
Multiple Linear Regression in Visual Basic
Multiple Linear Regression in F#
Multiple Linear Regression in IronPython
Illustrates how to use the LinearRegressionModel class to perform a multiple linear regression.
Polynomial Regression in C#
Polynomial Regression in Visual Basic
Polynomial Regression in F#
Polynomial Regression in IronPython
Illustrates how to fit data to polynomials using the PolynomialRegressionModel class.
Logistic Regression in C#
Logistic Regression in Visual Basic
Logistic Regression in F#
Logistic Regression in IronPython
Illustrates how to use the LogisticRegressionModel class to create logistic regression models.
Generalized Linear Models in C#
Generalized Linear Models in Visual Basic
Generalized Linear Models in F#
Illustrates how to use the GeneralizedLinearModel class to compute probit, Poisson and similar regression models.

### Time Series Analysis

Project Description
Simple Time Series in C#
Simple Time Series in Visual Basic
Simple Time Series in F#
Simple Time Series in IronPython
Illustrates how to perform simple operations on time series data using classes in the Extreme.Statistics.TimeSeriesAnalysis namespace.
Variable Transformations in C#
Variable Transformations in Visual Basic
Variable Transformations in F#
Variable Transformations in IronPython
Illustrates how to perform a range of transformations on statistical data.
ARIMA Models in C#
ARIMA Models in Visual Basic
ARIMA Models in F#
ARIMA Models in IronPython
Illustrates how to work with ARIMA time series models using classes in the Extreme.Statistics.TimeSeriesAnalysis namespace.

### Multivariate Analysis

Project Description
Cluster Analysis in C#
Cluster Analysis in Visual Basic
Cluster Analysis in F#
Cluster Analysis in IronPython
Illustrates how to use the classes in the Extreme.Statistics.Multivariate namespace to perform hierarchical clustering and K-means clustering.
Principal Component Analysis (PCA) in C#
Principal Component Analysis (PCA) in Visual Basic
Principal Component Analysis (PCA) in F#
Principal Component Analysis (PCA) in IronPython
Illustrates how to perform a Principal Components Analysis using classes in the Extreme.Statistics.Multivariate namespace.
Factor Analysis (FA) in C#
Factor Analysis (FA) in Visual Basic
Factor Analysis (FA) in F#
Illustrates how to perform a Factor Analysis using classes in the Extreme.Statistics.Multivariate namespace.

### Hypothesis Tests

Project Description
Mean Tests in C#
Mean Tests in Visual Basic
Mean Tests in F#
Mean Tests in IronPython
Illustrates how to use various tests for the mean of one or more sanples using classes in the Extreme.Statistics.Tests namespace.
Variance Tests in C#
Variance Tests in Visual Basic
Variance Tests in F#
Variance Tests in IronPython
Illustrates how to perform hypothesis tests involving the standard deviation or variance using classes in our .NET statistical library.
Goodness-Of-Fit Tests in C#
Goodness-Of-Fit Tests in Visual Basic
Goodness-Of-Fit Tests in F#
Goodness-Of-Fit Tests in IronPython
Illustrates how to test for goodness-of-fit using classes in the Extreme.Statistics.Tests namespace.
Homogeneity Of Variances Tests in C#
Homogeneity Of Variances Tests in Visual Basic
Homogeneity Of Variances Tests in F#
Homogeneity Of Variances Tests in IronPython
Illustrates how to test a collection of variables for equal variances using classes in the Extreme.Statistics.Tests namespace.
Non-Parametric Tests in C#
Non-Parametric Tests in Visual Basic
Non-Parametric Tests in F#
Non-Parametric Tests in IronPython
Illustrates how to perform non-parametric tests like the Wilcoxon-Mann-Whitney test and the Kruskal-Wallis test.