mathnet/mathnet-numerics

Features

• Linear Algebra Libraries - Provides a complete framework for matrix and vector operations, decompositions, and solving linear equation systems.
• Numerical Libraries - Provides a comprehensive suite of optimized algorithms for matrix operations and scientific mathematical calculations.
• Pseudo-Random Number Generators - Produces pseudo-random number sequences across various probability distributions for simulations.
• Random Sequence Generation - Generates large arrays or infinite sequences of random numbers in a single operation for high performance.
• Random Variate Sampling - Generates single or bulk non-uniform random numbers from specified probability distributions.
• Correlation Coefficient Calculators - Computes Pearson's and Spearman's correlation coefficients and generates correlation matrices for vectors.
• Covariance Calculators - Estimates the joint variability of two random variables using sample or population covariance.
• Data Interpolation - Estimates unknown values between known data points using various mathematical interpolation methods.
• Definite Integration - Calculates the definite integral of a function by approximating the area under a curve.
• Iterative Solvers - Provides iterative numerical solvers for finding roots and solving ordinary differential equations.
• Linear System Solvers - Implements direct and iterative linear solvers for solving systems of linear equations.
• Mathematical Optimization Solving - Provides numerical solutions for linear, quadratic, and nonlinear programs to find function minimums and maximums.
• Matrix and Vector Construction - Constructs dense, sparse, and diagonal matrices and vectors from various input sources and distributions.
• Matrix Arithmetic Operations - Executes addition, subtraction, multiplication, and division between matrices, vectors, and scalars.
• Matrix Decompositions - Implements essential matrix decompositions including LU, QR, Cholesky, and SVD for solving linear systems.
• Native Provider Acceleration - Supports swapping managed code for platform-native binary libraries to accelerate computationally intensive linear algebra.
• Numerical Differentiation - Computes numerical derivatives, Jacobians, and Hessians to analyze the rate of change of functions.
• Numerical Integration Engines - Implements numerical integration rules such as Gauss-Kronrod and Simpson's rule.
• Numerical Integration Tools - Implements algorithms for calculating definite integrals and performing numerical integration across multiple dimensions.
• Numerical Integration Routines - Calculates definite integrals and function derivatives using approximation algorithms.
• Special Function Calculators - Evaluates complex mathematical special functions including Gamma, Beta, and Bessel functions.
• Distribution Function Calculators - Evaluates empirical cumulative distribution functions and their inverses for given sample sets.
• Distribution Statistics - Computes statistical properties of probability distributions, including mean, variance, and entropy.
• Statistical Analysis Libraries - Provides a comprehensive set of tools for calculating basic descriptive statistics like mean, minimum, and maximum.
• Numerical Quadrature - Implements numerical integration using Gauss-Kronrod and Simpson rules.
• Quantile and Percentile Calculators - Calculates quartiles, percentiles, and arbitrary quantiles to divide sorted data into equal groups.
• Root-Finding Algorithms - Implements iterative root-finding methods, such as bisection, to determine where a function equals zero.
• Population and Sample Variance Calculators - Calculates variance and standard deviation for both entire populations and unbiased sample estimates.
• Spline Interpolators - Provides linear, cubic, and quadratic spline interpolation for estimating values between known data points.
• Trigonometric Functions - Provides a comprehensive suite of standard, inverse, hyperbolic, and inverse hyperbolic trigonometric functions.
• Linear Regression - Calculates best-fitting parameters for linear relationships using least squares for lines and polynomials.
• Linear Combination Fitting - Determines optimal parameters for models defined as linear combinations of custom functions.
• Weighted Regression - Adjusts the influence of specific data points using a weight matrix to reduce overall error.
• Quantile Rank Estimators - Determines the probability tau of a specific value relative to the provided sample distribution.
• Curve Fitting - Implements linear and non-linear regression to fit curves to datasets and estimate unknown values.
• Fourier Transforms - Provides Fourier and Hartley mathematical transforms to convert signals between different domains.
• Data Ranking Utilities - Assigns a rank to each sample in a set with configurable strategies for handling ties.
• Descriptive Statistics Summaries - Produces five-number summaries containing the minimum, quartiles, median, and maximum.
• Ordinary Differential Equation Solving - Implements numerical solvers for ordinary differential equations, including Runge-Kutta and Adams-Bashforth methods.
• Scalar-Valued Function Optimization - Provides optimization of scalar-valued objective functions using algorithms such as BFGS and Golden Section search.
• Exponential Integral Calculators - Calculates generalized exponential integrals for given orders and values.
• Factorial Calculators - Computes factorials and binomial coefficients, including logarithmic versions to prevent overflow.
• Greatest Common Divisor Algorithms - Implements the Euclidean algorithm to find the greatest common divisor and linear combination coefficients.
• Histogram Generators - Groups sample data into buckets to analyze the distribution of numerical values.
• Stable Numerical Formulations - Implements numerically stable formulations for hypotenuse and exponential minus one to prevent precision loss.
• Multi-Dimensional Integration - Performs integration over one or two dimensions using weighted abscissas and nodes across specified intervals.
• Least Common Multiple Calculators - Calculates the least common multiple for sets of two or more integers.
• Integer Property Verifiers - Provides algorithms to verify integer properties, such as determining if a number is even or odd.
• Power-of-Two Identifications - Includes bitwise logic and algorithms to identify perfect squares and powers of two.
• Mathematical Constants - Provides high-precision values for common mathematical constants including Pi, Euler's number, and the Golden Ratio.
• Bessel Function Implementations - Evaluates modified Bessel and Struve functions of various orders.
• Log-Domain Calculations - Evaluates distribution functions in the logarithmic domain to prevent numerical underflow.
• Error Function Implementations - Evaluates the error function, complementary error function, and their respective inverses.
• Order Statistics - Retrieves the k-th smallest value from a dataset using efficient sorting or lookup methods.
• Smooth Function Integration - The library applies fixed-order Gauss-Legendre rules to find the exact integral of polynomials and functions with a known order.
• Sparse Matrix Storage - Provides distinct storage strategies for sparse and dense matrices to optimize memory usage.
• Vector Distance Metrics - Computes distances between high-dimensional vectors using Euclidean, Manhattan, Chebyshev, Minkowski, and Hamming metrics.
• Data Science and Analytics - Numerical computation and algorithms.

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