## What are Extreme Optimization Numerical Libraries for .NET?

The Extreme Optimization Numerical Libraries for .NET are an assortment of general-purpose mathematical and statistical classes designed specifically for Microsoft's Microsoft .NET Framework.

Extreme Optimization Numerical Libraries for .NET is a collection of general-purpose math and statistical courses. It is a complete statistical and technical computing platform built on the Microsoft .NET platform. It includes the math library, vector and matrix library, and a statistics library in a straightforward package.

### Extreme Optimization Numerical Libraries for .NET Great Features:

#### General Features

- Easy to use even for the mathematically not-so-inclined.
- Excellent performance through optimized implementation of the best algorithms.
- Powerful enough to satisfy the most demanding power user.
- Intuitive object model. The objects in the Extreme Optimization Numerical Libraries for .NET and the relationships between them match our everyday concepts.
- Cross-platform. Works out-of-the-box on 32 and 64-bit platforms, .NET versions 1.1, 2.0, 3.0, and 3.5.

#### Math Library Features

- General
- Machine floating-point constants.
- Common mathematical constants.
- It extended elementary functions.
- Algorithm support functions: iteration, tolerance, convergence tests.

- Complex numbers
- Double-precision complex number value type.
- Overloaded operators for all arithmetic operations.
- Static operator functions for languages that don't support operator overloading.
- Extension of functions in the System.Math to the complex argument.
- Support for complex infinity and complex Not-a-Number (NaN).
- Complex vector and matrix classes.

- Numerical integration and differentiation
- Numerical differentiation.
- Numerical integration using Simpson's rule and Romberg's method.
- Non-adaptive Gauss-Kronrod numerical integrator.
- Adaptive Gauss-Kronrod numerical integrator.
- Integration over infinite intervals.
- Optimizations for functions with singularities and discontinuities.
- Six integration rules to choose from, or provide your own.
- Integration in 2 or more dimensions.

- Curve fitting and interpolation
- Interpolation using polynomials, cubic splines, piecewise constant, and linear curves.
- Linear least squares fit using polynomials or arbitrary functions.
- Nonlinear least squares using predefined functions or your own.
- Predefined nonlinear curves: exponential, rational, Gaussian, Lorentz, 4 and 5 parameter logistic.
- I weighted least squares with four predefined weight functions.
- I am scaling curve parameters.
- Constraints on curve parameters.

- Curves
- An object-oriented approach to working with mathematical curves.
- Methods for: evaluation, derivative, definite integral, tangent, roots.
- Many basic types of curves: constants, lines, quadratics, polynomials, cubic splines, Chebyshev approximations, and linear combinations of arbitrary functions.

- Solving equations
- Real and complex roots of polynomials.
- Roots of arbitrary functions: bisection, false positive, Dekker-Brent, and Newton-Raphson methods.
- Systems of simultaneous linear equations.
- Systems of nonlinear equations: Powell's hybrid 'dogleg' method, Newton's method.
- Least squares solutions.

- Optimization
- Optimization in 1 dimension: Brent's algorithm, Golden Section search.
- The quasi-Newton method in N dimensions: BFGS and DFP variants.
- Conjugate gradient method in N dimensions: Fletcher-Reeves and Polak-Ribière variants.
- Powell's conjugate gradient method.
- Downhill Simplex method of Nelder and Mead.
- Levenberg-Marquardt method for nonlinear least squares.
- Line search algorithms: Moré-Thuente, quadratic, unit.
- Linear program solver: Based on the Revised Simplex method.
- Linear program solver: Import from MPS files.

- Signal processing
- Accurate 1D and 2D Fast Fourier Transform.
- Complex 2D Fast Fourier Transform.
- Unique code for factors 2, 3, 4, and 5.
- Real and complex convolution.
- Managed 32bit and 64bit native implementations.

- Special functions
- Over 40 special functions are not included in the standard .NET Framework class library.
- Functions from combinatorics: factorial, combinations, variations, and more.
- Functions from number theory: greatest common divisor, least common multiple, decomposition into prime factors, primality testing.
- Gamma and related functions include incomplete and regularized digamma, beta, and harmonic numbers.
- Hyperbolic and inverse hyperbolic functions for real and complex numbers.
- Ordinary and Modified Bessel functions of the first and second kind.
- Airy functions and their derivatives.
- Exponential integral, sine and cosine integral, and logarithmic integral.

#### Vector and Matrix Library Features

- General
- Single, double, or quad precision absolute or complex components.
- Based on standard BLAS and LAPACK routines.
- 100% managed implementation for security, portability, and small sizes.
- Native, processor-optimized implementation for speed with large sizes based on the Intel® Math Kernel Library.
- Native 64bit support.

- GPU computing
- GPU computing: offload computations to the GPU.
- Data is kept on the GPU as long as possible for optimal performance.

- Vectors
- Dense vectors.
- Band vectors.
- Constant vectors.
- Row, column, and diagonal vectors.
- Vector views.

- Vector Operations
- Basic arithmetic operations.
- Element-wise operations.
- They overloaded arithmetic operators.
- Norms, dot products.
- Most significant and smallest values.
- Functions of vectors (sine, cosine, etc.)

- Matrices
- General matrices.
- Triangular matrices.
- Real symmetric matrices and complex Hermitian matrices.
- Band matrices.
- Diagonal matrices.
- Matrix views.

- Matrix Operations
- Basic arithmetic operations.
- Matrix-vector products.
- They overloaded arithmetic operations.
- Element-wise operations.
- Row and column scaling.
- Norms, rank, condition numbers.
- Singular values, eigenvalues, and eigenvectors.

- Matrix Decompositions
- LU decomposition.
- QR decomposition.
- Cholesky decomposition.
- Singular value decomposition.
- Symmetric eigenvalue decomposition.
- Non-symmetric eigenvalue decomposition.
- Banded LU and Cholesky decomposition.

- Sparse Matrices
- Sparse vectors.
- Sparse matrices.
- Matrices in Compressed Sparse Column format.
- Sparse LU Decomposition.
- Read matrices in Matrix Market format.

- Linear equations and least squares
- Shared API for matrices and decompositions.
- Determinants, inverses, numerical rank, condition numbers.
- Solve equations with one or multiple right-hand sides.
- Least squares solutions using QR or Singular Value Decomposition.
- Moore-Penrose Pseudo-inverse.
- Non-negative least squares (NNLS).

#### Statistics Library Features

- Descriptive Statistics
- Measures of central tendency: mean, median, trimmed mean, harmonic mean, geometric mean.
- Measures of scale: variance, standard deviation, range, interquartile range, absolute deviation from mean and median.
- Higher moments: skewness, kurtosis.

- Probability Distributions
- Probability density function (PDF).
- Cumulative distribution function (CDF).
- Percentile or inverse cumulative distribution function.
- Moments: mean, variance, skewness, and kurtosis.
- Generate random samples from any distribution.
- Parameter estimation for selected distributions.

- Continuous Probability Distributions
- Beta distribution.
- Cauchy distribution.
- Chi-squared distribution.
- Erlang distribution.
- Exponential distribution.
- F distribution.
- Gamma distribution.
- You generalized Pareto distribution.
- Gumbel distribution.
- Laplace distribution.
- Logistic distribution.
- Lognormal distribution.
- Normal distribution.
- Pareto distribution.
- Piecewise distribution.
- Rayleigh distribution.
- Student t distribution.
- She transformed beta distribution.
- She transformed gamma distribution.
- Triangular distribution.
- Uniform distribution.
- Weibull distribution.

- Discrete Probability Distributions
- Bernoulli distribution.
- Binomial distribution.
- Geometric distribution.
- Hypergeometric distribution.
- Negative binomial distribution.
- Poisson distribution.
- Uniform distribution.

- Multivariate Probability Distributions
- Multivariate normal distribution.
- Dirichlet distribution.

- Histograms
- One-dimensional histograms.
- Probability distribution associated with a histogram.

- General Linear Models
- Infrastructure for General Linear Model and Generalized Linear Model calculations.
- Analysis of variance.
- Regression analysis.
- Model-specific hypothesis tests.

- Analysis of variance (ANOVA)
- One and two-way ANOVA.
- One-way ANOVA with repeated measures.

- Regression analysis
- Simple, multiple, and polynomial regression.
- Nonlinear regression.
- Logistic regression.
- You generalized linear models.
- Flexible regression models.
- Variance-covariance matrix, regression matrix.
- Confidence intervals and significance tests for regression parameters.

- Time series analysis
- Treat several observation variables as a unit.
- Change the frequency of the time series.
- Automatically apply predefined aggregators.
- Advanced aggregators: volume weighted average.

- Transformations of Time Series Data
- It lagged time series, sums, and products.
- Change, percent change, growth rate.
- Extrapolated change, percent change, growth rate.
- Period-to-date sums and differences.
- Simple, exponential, weighted moving average.
- Savitsky-Golay smoothing.

- Multivariate Models
- Principal Component Analysis (PCA).
- Hierarchical clustering.
- K-means clustering.

- Statistical tests
- Tests for the mean: one sample z-test, one sample t-test.
- Paired and unpaired two-sample t-test for the difference between two sample means.
- Two Sample z-test for ratios.
- One sample chi-squared test for variance.
- F-test for the ratio of two variances.
- One and two sample Kolmogorov-Smirnov test.
- Anderson-Darling test for normality.
- Chi-squared goodness-of-fit test.
- Bartlett and Levene tests for homogeneity of variances.
- McNemar and Stuart-Maxwell test.

- Random number generation
- Compatible with the .NET Framework's System.Random.
- Four generators with varying quality, period, and speed to suit your application.
- Generate random samples from any distribution.
- Fauré and Halton sequences.
- Shufflers and randomized enumerators.

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