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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 |
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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 |
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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

### Curves

Project | Description |
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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 . |

Advanced Polynomials in C# Advanced Polynomials in Visual Basic Advanced Polynomials in F# Advanced Polynomials in IronPython |
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 |
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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. |

Quadratic Programming in C# Quadratic Programming in Visual Basic Quadratic Programming in F# Quadratic Programming in IronPython |
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 |
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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

### 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 |
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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

### 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. |

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