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Core

Namespace: MathNet.Numerics

  • Complex Numbers (including trigonometric functions)
  • Quaternions (including exponential functions)

  • Polynomials (fast multiplication and evaluation)
  • Rationals

  • Number class, for safe floating point handling (EpsilonOf, AlmostEqual, AlmostZero, CoerceZero, Increment, Decrement)

  • Mathematical Constants
  • Scientific Constants (2007 CODATA)
  • Scientific Prefixes
  • Various helper and data structure classes

Special Functions

Namespace: MathNet.Numerics
Class: MathNet.Numerics.Fn

  • Hypot (stable sqrt(a^2+b^2))
  • Integer Power
  • Base 2 Integer Power and Logarithm
  • Ceiling/Floor to power of 2

  • Greatest common divisor (gcd), of two or more integers
  • Extended greatest common divisor of two numbers
  • Least common multiple (lcm), of two or more integers

  • Sinus Cardinalis (sinc)

  • Logarithmic Factorial
  • Factorial
  • Logarithmic Binomial Coefficient
  • Binomial Coefficient

  • Logarithmic Gamma
  • Gamma (supports negative numbers as well)
  • Regularized Gamma
  • Inverse Regularized Gamma
  • Digamma (Psi)
  • Logarithmic Beta
  • Beta
  • Regularized Beta
  • Error Function
  • Inverse Error Function
  • Harmonic Number

Trigonometry Functions

Namespace: MathNet.Numerics
Class: MathNet.Numerics.Trig

  • Conversion between degree, radian and grad.
  • Sine, Cosine, Tangent, Cotangent, Secant, Cosecant
  • Inverse: Sine, Cosine, Tangent, Cotangent, Secant, Cosecant
  • Hyperbolic: Sine, Cosine, Tangent, Cotangent, Secant, Cosecant
  • Inverse Hyperbolic: Sine, Cosine, Tangent, Cotangent, Secant, Cosecant

Combinatorics

Namespace: MathNet.Numerics
Class: MathNet.Numerics.Combinatorics

  • Counting: Variations, Variations with repetition, Combinations, Combinations with repetition, Permutations
  • Generate Randomly: Variations, Variations with repetition, Combinations, Combinations with repetition, Permutations
  • Random Shuffling (Random Permutations)
  • Select Random Subset: Variation, Variation with repetition, Combination, Combination with repetition

Probability Distributions

Namespace: MathNet.Numerics.Distributions

Continuous Probability Distributions

Continuous probability distributions support both the probability density function (pdf) and the cumulative distribution function (cdf), as well as the usual probability parameters. Additionally, random numbers can be generated based on the configured probability model parameters and some random number source.

All implementations inherit from the public abstract base class ContinuousDistribution and implement both interfaces IContinuousProbabilityDistribution and IContinuousGenerator.

  • Continuous Uniform Distribution
  • Triangular Distribution
  • Standard Distribution (Gaussian)
  • Normal Distribution (Gaussian with mean and variance)
  • Lognormal Distribution
  • Exponential Distribution
  • Laplace Distribution
  • Gamma Distribution
  • Beta Distribution
  • Student's T Distribution
  • Fisher Snedecor Distribution
  • Erlang Distribution
  • Cauchy Lorentz Distribution
  • Chi Distribution
  • ChiSquared Distribution
  • Pareto Distribution
  • Stable Distribution
  • Rayleigh Distribution

Discrete Probability Distributions

Discrete probability distributions support both the probability mass function (pmf) and the cumulative distribution function (cdf), as well as the usual probability parameters. Additionally, random numbers can be generated based on the configured probability model parameters and some random number source.

All implementations inherit from the public abstract base class DiscreteDistribution and implement both interfaces IDiscreteProbabilityDistribution and IDiscreteGenerator.

  • Discrete Uniform Distribution
  • Arbitrary Distribution
  • Bernoulli Distribution
  • Binomial Distribution
  • Geometric Distribution
  • Hypergeometric Distribution
  • Poisson Distribution
  • Zipf Distribution

Code Sample

StudentsTDistribution dist = new StudentsTDistribution(2);
double a = dist.Variance;
double b = dist.ProbabilityDensity(1);

Random Sources

Namespace: MathNet.Numerics.RandomSources

All implementations inherit the public abstract base class RandomSource.

  • System Random Source
  • Mersenne Twister Random Source
  • Additive Lagged Fibonacci Random Source
  • Xor Shift Random Source

If unsure what to choose, we recommend to simply use SystemRandomSource which internally uses the random source provided by the .Net Framework. Note that random sources should be reused, so be careful to create only one instance (per thread) and share it internally.

Code Sample

MersenneTwisterRandomSource src = new MersenneTwisterRandomSource();
StudentsTDistribution dist = new StudentsTDistribution(src);
double a = dist.NextDouble();

Interpolation

Namespace: MathNet.Numerics.Interpolation

Most interpolation algorithms also support numeric differentiation and integration. A facade class Interpolation is provided for easy access, but if needed the algorithms can also be used directly in the Algorithms sub-namespace. All implementations implement the interface IInterpolationMethod.

  • Rational Pole Free Interpolation, on arbitrary points (Barycentric Algorithm)
  • Polynomial Interpolation, on arbitrary points (Neville Algorithm)
  • Polynomial Interpolation, on equidistant points (Barycentric Algorithm)
  • Polynomial Interpolation, on first kind Chebychev points (Barycentric Algorithm)
  • Polynomial Interpolation, on second kind Chebychev points (Barycentric Algorithm)
  • Rational Interpolation, on arbitrary points (with poles; Bulirsch & Stoer Algorithm)
  • Linear Spline Interpolation, on arbitrary points
  • Cubic Spline Interpolation, with boundary conditions on arbitrary points
  • Natural Cubic Spline Interpolation, on arbitrary points
  • Akima Cubic Spline Interpolation, on arbitrary points
  • Custom Barycentric Interpolation, based on provided barycentric weights
  • Custom Spline Interpolation, based on provided spline coefficients
  • Custom Cubic Hermite Spline Interpolation, based on provided derivatives

If unsure what to choose, we recommend to simply use Interpolation.Create(x,y) which internally uses the barycentric rational pole free interpolation.

Code Sample

double[] t = new double[] { -2.0, -1.0, 0.0, 1.0, 2.0 };
double[] x = new double[] { 1.0, 2.0, -1.0, 0.0, 1.0 };
IInterpolationMethod method = Interpolation.Create(t, x);
double a = method.Interpolate(-0.5);

Linear Algebra

Namespace: MathNet.Numerics.LinearAlgebra

  • Vector, Real and Complex
  • Matrix, Real and Complex
  • LU Decomposition (Real only)
  • QR Decomposition (Real only)
  • Eigenvalue Decomposition (Real only)
  • Singular Value Decomposition (Real only)
  • Cholesky Decomposition (Real only)
  • Solve linear systems on a Least Square (L2) or a Least Absolute Deviation (L1) criterion
  • Common linear algebra operations and properties on matrices and vectors

Integral Transformations

Namespace: MathNet.Numerics.Transformations

  • Real Fast Fourier Transformation
  • Complex Fast Fourier Transformation

The transformation behavior can be configured (scaling, exponent sign, etc). See here for more details and code samples around fast Fourier transformations.

Code Sample

double[] data = new double[] { ... };
double[] freqReal, freqImag;
RealFourierTransformation rft = new RealFourierTransformation();
rft.TransformForward(data, out freqReal, out freqImag);

Math.NET, a mathematical opensource .Net project by Christoph Rüegg and contributors.