Data Analysis Mathematics Linear Algebra Statistics

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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

### Data Frames

Illustrates how to create and manipulate data frames using classes in the Extreme.DataAnalysis namespace.

### Indexes and Labels

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

Illustrates how to perform basic data wrangling or data munging operations on data frames using classes in the Extreme.DataAnalysis namespace.

### Manipulating Columns

Illustrates how to transform and manipulate the columns of a data frame.

### Sorting and Filtering

Illustrates how to sort and filter data used for data analysis.

### Grouping and Aggregation

Illustrates how to group data and how to compute aggregates over groups and entire datasets..

### Histograms

Illustrates how to create histograms using the Histogram class in the Extreme.DataAnalysis namespace.

## Mathematics

### General

#### Complex Numbers

Illustrates how to work with complex numbers using the DoubleComplex structure.

#### Elementary Functions

Illustrates how to use additional elementary functions.

#### BigNumbers

Illustrates the basic use of the arbitrary precision classes: BigInteger, BigRational, BigFloat.

#### Prime Numbers

Illustrates working with prime numbers and the IntegerMath class in the Extreme.Mathematics namespace.

#### FFT/Fourier Transforms

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

Illustrates how to write algorithms that are generic over the numerical type of the arguments.

### Calculus

#### Basic Integration

Illustrates the basic numerical integration classes.

#### Higher Dimensional Numerical Integration

Illustrates numerical integration of functions in higher dimensions using classes in the Extreme.Mathematics.Calculus namespace.

#### Numerical Differentiation

Illustrates how to approximate the derivative of a function.

#### Differential Equations

Illustrates integrating systems of ordinary differential equations (ODE's).

### Curves

#### Basic Polynomials

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

Illustrates the basic use of the ChebyshevSeries class .

### Curve Fitting and Interpolation

#### Linear Curve Fitting

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

Illustrates nonlinear least squares curve fitting of predefined and user-defined curves using the NonlinearCurveFitter class.

#### Piecewise Curves

Illustrates working with piecewise constant and piecewise linear curves using classes from the Extreme.Mathematics.Curves namespace.

#### Cubic Splines

Illustrates using natural and clamped cubic splines for interpolation using classes in the Extreme.Mathematics.LinearAlgebra namespace.

### Solving Equations

#### Newton-Raphson Equation Solver

Illustrates the use of the NewtonRaphsonSolver class for solving equations in one variable and related functions for numerical differentiation.

#### Root Bracketing Solvers

Illustrates the use of the root bracketing solvers for solving equations in one variable.

#### Nonlinear Systems

Illustrates the use of the NewtonRaphsonSystemSolver and DoglegSystemSolver classes for solving systems of nonlinear equations.

### Optimization

#### Optimization In One Dimension

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

Illustrates the use of the multi-dimensional optimizer classes in the Extreme.Mathematics.Optimization namespace for optimization in multiple dimensions.

#### Linear Programming

Illustrates solving linear programming (LP) problems using classes in the Extreme.Mathematics.Optimization.LinearProgramming namespace.

#### Mixed Integer Programming

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

Illustrates solving nonlinear programs (optimization problems with linear or nonlinear constraints) using the NonlinearProgram and related classes.

### Random numbers and Quasi-Random Sequences

#### Random Number Generators

Illustrates how to use specialized random number generator classes in the Extreme.Statistics.Random namespace.

#### Non-Uniform Random Numbers

Illustrates how to generate random numbers from a non-uniform distribution.

#### Quasi-Random Sequences

Illustrates how to generate quasi-random sequences like FaurÃ© and Sobol sequences using classes in the Extreme.Statistics.Random namespace.

## Linear Algebra

### Vectors

#### Basic Vectors

Illustrates the basic use of the Vector class for working with vectors.

#### Vector Operations

Illustrates how to perform operations on Vector objects, including construction, element access, arithmetic operations.

### Matrices

#### Basic Matrices

Illustrates the basic use of the Matrix class for working with matrices.

#### Accessing Matrix Components

Illustrates different ways of iterating through the rows and columns of a matrix using classes in the Extreme.Mathematics.LinearAlgebra namespace.

#### Matrix-Vector Operations

Illustrates how to perform operations that involve both matrices and vectors.

#### Triangular Matrices

Illustrates how to work efficiently with upper or lower triangular or trapezoidal matrices.

#### Symmetric Matrices

Illustrates how to work efficiently with symmetric matrices.

#### Band Matrices

Illustrates how to work with the BandMatrix class.

#### Sparse Matrices

Illustrates using sparse vectors and matrices using the classes in the Extreme.Mathematics.LinearAlgebra.Sparse namespace.

#### Matrix Decompositions

Illustrates how compute various decompositions of a matrix using classes in the Extreme.Mathematics.LinearAlgebra namespace.

### Solving Equations and Least Squares

#### Linear Equations

Illustrates how to solve systems of simultaneous linear equations.

#### Structured Linear Equations

Illustrates how to solve systems of simultaneous linear equations that have special structure.

#### Iterative Sparse Solvers

Illustrates the use of iterative sparse solvers and preconditioners for efficiently solving large, sparse systems of linear equations.

#### Least Squares

Illustrates how to solve least squares problems using classes in the Extreme.Mathematics.LinearAlgebra namespace.

## Statistics

### Probability Distributions

#### Discrete Distributions

Illustrates how to use the classes that represent discrete probability distributions in the Extreme.Statistics.Distributions namespace.

#### Continuous Distributions

Illustrates how to use the classes that represent continuous probability distributions in the Extreme.Statistics.Distributions namespace.

### Analysis of Variance

#### One-Way Anova

Illustrates how to use the OneWayAnovaModel class to perform a one-way analysis of variance.

#### Repeated Measures Anova

Illustrates how to use the OneWayRAnovaModel class to perform a one-way analysis of variance with repeated measures.

#### Two-Way Anova

Illustrates how to use the TwoWayAnovaModel class to perform a two-way analysis of variance.

### Regression Analysis

#### Simple Regression

Illustrates how to perform a simple linear regression using the SimpleRegressionModel class.

#### Multiple Linear Regression

Illustrates how to use the LinearRegressionModel class to perform a multiple linear regression.

#### Polynomial Regression

Illustrates how to fit data to polynomials using the PolynomialRegressionModel class.

#### Logistic Regression

Illustrates how to use the LogisticRegressionModel class to create logistic regression models.

#### Generalized Linear Models

Illustrates how to use the GeneralizedLinearModel class to compute probit, Poisson and similar regression models.

### Time Series Analysis

#### Simple Time Series

Illustrates how to perform simple operations on time series data using classes in the Extreme.Statistics.TimeSeriesAnalysis namespace.

#### Variable Transformations

Illustrates how to perform a range of transformations on statistical data.

#### ARIMA Models

Illustrates how to work with ARIMA time series models using classes in the Extreme.Statistics.TimeSeriesAnalysis namespace.

### Multivariate Analysis

#### Cluster Analysis

Illustrates how to use the classes in the Extreme.Statistics.Multivariate namespace to perform hierarchical clustering and K-means clustering.

#### Principal Component Analysis (PCA)

Illustrates how to perform a Principal Components Analysis using classes in the Extreme.Statistics.Multivariate namespace.

#### Factor Analysis (FA)

Illustrates how to perform a Factor Analysis using classes in the Extreme.Statistics.Multivariate namespace.

### Hypothesis Tests

#### Mean Tests

Illustrates how to use various tests for the mean of one or more sanples using classes in the Extreme.Statistics.Tests namespace.

#### Variance Tests

Illustrates how to perform hypothesis tests involving the standard deviation or variance using classes in our .NET statistical library.

#### Goodness-Of-Fit Tests

Illustrates how to test for goodness-of-fit using classes in the Extreme.Statistics.Tests namespace.

#### Homogeneity Of Variances Tests

Illustrates how to test a collection of variables for equal variances using classes in the Extreme.Statistics.Tests namespace.

#### Non-Parametric Tests

Illustrates how to perform non-parametric tests like the Wilcoxon-Mann-Whitney test and the Kruskal-Wallis test.