mathnetnumerics Wiki & Documentation Rss Feed

Updated Wiki: Home

cdrnet — Mon, 04 Feb 2013 20:58:41 GMT

Math.NET Numerics

Numerics is the numerical foundation of the Math.NET project, aiming to provide methods and algorithms for numerical computations in science, engineering and every day use. Covered topics include special functions, linear algebra, probability models, random numbers, interpolation, integral transforms and more.

Math.NET Numerics targets Microsoft .Net 4.0 and Mono, and in addition to a purely managed implementation also supports native hardware optimization.

Math.NET Numerics Website

Please report issues over at GitHub instead of here. Thanks.

Updated Wiki: Documentation

cdrnet — Mon, 04 Feb 2013 11:34:12 GMT

Math.NET Numerics Documentation

Math.NET Numerics is an opensource numerical library for .Net, Silverlight, Metro and Mono. This topic lists documentation that will help you use the toolkit in your own application. In addition to the user guide, there's also a condensed API Reference available, or if you prefer examples the sample code project may give you some ideas.

API Reference
C# Code Samples: sources or as NuGet source package
F# Code Samples: sources or as NuGet source package

User Guide

Advanced Topics

Precision
Parallel Execution
Native Linear Algebra Providers (MKL, ACML)

Blog Posts & Other Resources

Updated Wiki: Documentation

cdrnet — Mon, 04 Feb 2013 11:33:33 GMT

Math.NET Numerics Documentation

API Reference
C# Code Samples: sources or as NuGet source package
F# Code Samples: sources or as NuGet source package

User Guide

Advanced Topics

Precision
Parallel Execution
Native Linear Algebra Providers (MKL, ACML)

Blog Posts & Other Resources

Updated Wiki: Native Providers

cdrnet — Mon, 04 Feb 2013 11:30:08 GMT

Native Linear Algebra Providers

Math.NET Numerics currently supports two native providers Intel's Math Kernel Library (MKL) and AMD's Core Math Library (ACML).

See also Math.NET Numerics With Native Linear Algebra

MKL (Windows)

Install MKL on your system (we are using v10.3 Update 2).
Open the NativeWrappers.sln in VS 2010 under \src\NativeWrappers\Windows .
Open the Configuration Manager and select either the 32-bit or 64-bit solution platform.
Right click on the MKLWrapper project and update the MKL include directory under C/C++/General and the library directory under Linker/General to point to your MKL installation.
Right click on the MKLWrapper project and click rebuild.
There will be two DLLs in the output directory: Math.NET.Numerics.MKL.dll and libiomp5md.dll. The output directory will be either \src\NativeWrappers\Windows\Win32\Release or \src\NativeWrappers\Windows\x64\release.
Copy the two DLLs from #6 to the same directory as MathNet.Numerics.dll.
Tell the Math.NET Numerics library to use the MKL provider by adding this line to your code:

MathNet.Numerics.Control.LinearAlgebraProvider =
   new MathNet.Numerics.Algorithms.LinearAlgebra.Mkl.MklLinearAlgebraProvider();

ACML (Windows)

Install the Intel Fortran version of ACML on your system (we are using v4.4) - http://developer.amd.com/cpu/Libraries/acml/Pages/default.aspx
Open the NativeWrappers.sln in VS 2010 under \src\NativeWrappers\Windows .
Open the Configuration Manager and select either the 32-bit or 64-bit solution platform.
Right click on the ACMLWrapper project and update the ACML include directory under C/C++/General and the library directory under Linker/General to point to your ACML installation.
Right click on the ACMLWrapper project and click rebuild.
There will be one DLL in the output directory: Math.NET.Numerics.ACML.dll. The output directory will be either \src\NativeWrappers\Windows\Win32\Release or \src\NativeWrappers\Windows\x64\release.
Copy the DLL from #6 to the same directory as MathNet.Numerics.dll.
Copy these DLLS from your ACML installation to the same directory as MathNet.Numerics: libacmlmpdll.dll, libifcoremd.dll, libiomp5md.dll, and libmmd.dll
Tell the Math.NET Numerics library to use the ACML provider by adding this line to your code:

MathNet.Numerics.Control.LinearAlgebraProvider =
   new MathNet.Numerics.Algorithms.LinearAlgebra.Acml.AcmlLinearAlgebraProvider();

Note: The ACML wrapper dynamically links the ACML libraries. If you have the Intel Fortran Complier installed you can statically link them.

Updated Wiki: Home

cdrnet — Mon, 21 Jan 2013 12:35:10 GMT

Math.NET Numerics

Math.NET Numerics Website

Please report issues over at GitHub instead of here. Thanks.

Updated Wiki: Home

cdrnet — Mon, 21 Jan 2013 12:34:58 GMT

Math.NET Numerics

Math.NET Numerics Website

Please report issues over at GitHub instead of here. Thanks.

Updated Wiki: Home

cdrnet — Mon, 21 Jan 2013 12:34:48 GMT

Math.NET Numerics

Math.NET Numerics Website

Please report issues over at GitHub instead of here. Thanks.

Updated Wiki: Special Functions

cdrnet — Fri, 28 Dec 2012 10:53:50 GMT

Special Functions

Factorial

Factorial: Factorial
Logarithmic Factorial: FactorialLn
Binomial Coefficient: Binomial
Logarithmic Binomial Coefficient: BinomialLn
Multinomial Coefficient: Multinomial

Code Sample:

double x = SpecialFunctions.Factorial(14);
// x will now have the value 87178291200.0

double y = SpecialFunctions.Factorial(31);
// y will now have the value 8.2228386541779224E+33

Gamma

Commonly used gamma-related functions in literature:

GAMMA(a) = int(exp(-t)t^(a-1), t=0..infinity)
gamma(a,x) = int(exp(-t)t^(a-1),t=0..x)  
Gamma(a,x) = int(exp(-t)t^(a-1),t=x..infinity)  
P(a,x) = gamma(a,x)/GAMMA(a)  
Q(a,x) = Gamma(a,x)/GAMMA(a)

Gamma: Gamma = a -> GAMMA(a)
Logarithmic Gamma: GammaLn = a -> ln(abs(GAMMA(a))
Lower Incomplete Gamma (Unregularized): GammaLowerIncomplete = (a,x) -> gamma(a,x)
Upper Incomplete Gamma (Unregularized): GammaUpperIncomplete = (a,x) -> Gamma(a,x)
Lower Incomplete Regularized Gamma: GammaLowerRegularized = (a,x) -> P(a,x)
Upper Incomplete Regularized Gamma: GammaUpperRegularized = (a,x) -> Q(a,x)

Digamma (Psi)

Digamma (Psi): DiGamma
Inverse Digamma: DiGammaInv

Euler Beta

Beta: Beta
Logarithmic Beta: BetaLn
Lower Incomplete Beta (Unregularized): BetaIncomplete
Lower Incomplete Regularized Beta: BetaRegularized

Error Function

Error Function: Erf
Complementary Error Function: Erfc
Inverse Error Function: ErfInv
Inverse Complementary Error Function: ErfcInv

Code Sample:

double x = 0.9;
double res = SpecialFunctions.Erf(x);
// res will now have the value 0.7969082124

Logistic (Sigmoid)

Logistic Function: Logistic
Logit Function (inverse of Logistic): Logit

Harmonic Numbers

t'th Harmonic Number: Harmonic
Generalized Harmonic Number of order n of m: GeneralHarmonic

Bessel and Struve Functions

Modified Bessel function of the first kind, order 0 and 1: I0(x), I1(x)
Modified Bessel function of the second kind, order 0 and 1: K0(x), K1(x), plus exponentially scaled versions of them
Modified Struve function of order 0 and 1: L0(x), L1(x)
Modified Bessel minus modified Struve: I0(x)-L0(x), I1(x)-L1(x)

Various Numerically Stable Functions

x -> exp(x)-1: ExponentialMinusOne
(a,b) -> sqrt(a^2 + b^2): Hypotenuse (also for complex numbers)

Updated Wiki: References

cdrnet — Mon, 03 Dec 2012 19:50:33 GMT

References - Math.NET in the wild

On this page we try to collect an excerpt of the "social" graph of the Math.NET Numerics project. What other code or projects contributed in some way to Math.NET? Where is it used in the wild?

Direct Contributions

Maintainers

Christoph Rüegg: @cdrnet
Jurgen Van Gael: @jvangael
Marcus Cuda: @cuda (previously)

Contributors

Alexander Karatarakis
Andriy Bratiychuk
Hani Nedhat
Gustavo Guerra
Much more, for a full compilation see Contributors at ohloh.com, or git shortlog -s.

Indirect Contributions and Inspiration

Contributors via dnAnalytics and Math.NET Iridium (both merged into Numerics)

Patrick van der Valde
Joannès Vermorel
Matthew Kitchin
Rana Ian
Andrew Kurochka
Thaddaeus Parker

Contributors via other opensource projects

ALGLIB by Sergey Bochkanov (with permission before license changed - thanks!)
Boost by John Maddock
Cephes Math Library by Stephen L. Moshier

Where Math.NET is used

Excerpt of some projects and works where Math.NET is used or referenced today, or has been in the past. Please let us know if you'd like your work listed here as well, or if you'd prefer we remove it.

Opensource Projects and Code Snippets

MyMediaLite (lightweight, multi-purpose library of recommender system algorithms)
mathlib.net
lightfieldretrieval
STANLY - STAtic Network anaLYzer
MikeSheWrapper (hydrological modeling)
FermiSim (studying Fermi paradox via simulation of models for space colonisation)
KD-Trees for .NET
MatrixRecommendation
Optical Disk Experiment Analyzer
BarStructures (Dynamic analysis of the bar structures)
Sound Fingerprinting
Affine Transformations
Danny Asher (F#)
Signal Browser
FIIT RoboCup 3D

Articles & Tutorials

Getting Started with Math.NET and F# Programming
Tutorial: Using Math.NET Numerics in F# MSDN Magazine | MSDN Library
Overview: Introduction to Numerical Computing in F# MSDN Magazine
Linear regression in C#
Non Linear Curve Fitting

Thesis & Papers

TODO: find links, verify

Detecting falls and poses in image silhouettes, Master's Thesis in Complex Adaptive Systems, Niklas Schräder, Chalmers University of Technology, Gothenburg, Sweden, 2011
SoundLog, Master's Thesis in Information and Software Engineering, André Filipe Mateus Ferreira, Instituto Superior Técnico, Universidade Técnica de Lisboa
ACCELEROMETERS USABILITY FOR DANGER TILT OFF-HIGHWAY VEHICLES AND SIGNAL FILTRATION WITH KALMAN FILTER, Ondrej LÍŠKA, Kamil ŽIDEK, Technical University of Kosice, SjF, Department of biomedical engineering automation and measuring, Journal of applied science in the thermodynamics and fluid mechanics Vol. 4, No. 2/2010, ISSN 1802-9388
Fast evaluation of Greeks in Monte Carlo calculations with the Adjoint Method, Bachelor Thesis, Ivan Kuliš, Fachbereich Informatik und Mathematik, Institut für Mathematik, Johann Wolfgang Goethe Universität, Frankfurt am Main, 14.09.2011
3DMapping for Robotic Search and Rescue, Peter Nelson, New College, 28 May 2011
Quantitative structure-property relationship modeling algorithms, challenges and IT solutions, Thesis, Ondrej Skrehota, FACULTY OF INFORMATIC, MASARYK UNIVERSITY, 2010
Seismic Performance Assessment of Buildings Volume 2 – Implementation Guide, ATC-58-1 75% Draft, APPLIED TECHNOLOGY COUNCIL, 201 Redwood Shores Parkway, Suite 240, Redwood City, California 94065, prepared for U.S. DEPARTMENT OF HOMELAND SECURITY (DHS) FEDERAL EMERGENCY MANAGEMENT AGENCY
Use of Mobile Phones as Intelligent Sensors for Sound Input Analysis and Sleep State Detection, Ondrej Krejcar, Jakub Jirka, Dalibor Janckulik, Sensors 2011, 11, 6037-6055, ISSN 1424-8220, 2011
Design of a Wireless Acquisition System for a Digital Stethoscope, Bachelor Thesis, Justin Miller, Faculty of Engineering & Surveying, University of Southern Queensland, ENG4112 Research Project, 2010
Konzeption und Umsetzung einer RIA zur untersuchungsbegleitenden Erfassung von RNFLT-Scans und Untersuchung von Klassifikatoren für die diagnostische Unterstützung bei neurodegenerativen Erkrankungen am Beispiel der Multiplen Sklerose, Diplomarbeit, Sebastian Bischoff, Fachbereich Informatik und Medien, Fachhochschule Brandenburg, 1.11.2009
Ka`imiolakai ROV, Team Limawa, Kapi´olani Community College
Prototipo de una aplicación informática para gestión y mantenimiento de recursos pesquero, Silvia Rodríguez Rodríguez, José Juan Castro Hernández, 2010
Elastic Properties of Growing 2D Foam, Master's Thesis, Michael Schindlberger, Physical Systems Biology Group, University of Zurich, August 2011

University Course Work

Uni Muenster, Computer Vision und Mustererkennung (SS 2011)

Updated Wiki: References

cdrnet — Mon, 03 Dec 2012 19:49:57 GMT

References - Math.NET in the wild

On this page we try to collect an excerpt of the "social" graph of the Math.NET Numerics project. What other code or projects contributed in some way to Math.NET? Where is it used in the wild?

Direct Contributions

Maintainers

Christoph Rüegg: @cdrnet
Jurgen Van Gael: @jvangael
Marcus Cuda: @cuda (previously)

Contributors

Alexander Karatarakis
Andriy Bratiychuk
Hani Nedhat
Gustavo Guerra
Much more, for a full compilation see Contributors at ohloh.com, or git shortlog -s.

Indirect Contributions and Inspiration

Contributors via dnAnalytics and Math.NET Iridium (both merged into Numerics)

Patrick van der Valde
Joannès Vermorel
Matthew Kitchin
Rana Ian
Andrew Kurochka
Thaddaeus Parker

Contributors via other opensource projects

ALGLIB by Sergey Bochkanov (with permission before license changed - thanks!)
Boost by John Maddock
Cephes Math Library by Stephen L. Moshier

Where Math.NET is used

Opensource Projects and Code Snippets

MyMediaLite (lightweight, multi-purpose library of recommender system algorithms)
mathlib.net
lightfieldretrieval
STANLY - STAtic Network anaLYzer
MikeSheWrapper (hydrological modeling)
FermiSim (studying Fermi paradox via simulation of models for space colonisation)
KD-Trees for .NET
MatrixRecommendation
Optical Disk Experiment Analyzer
BarStructures (Dynamic analysis of the bar structures)
Sound Fingerprinting
Affine Transformations
Danny Asher (F#)
Signal Browser
FIIT RoboCup 3D

Articles & Tutorials

Getting Started with Math.NET and F# Programming
Tutorial: Using Math.NET Numerics in F# MSDN Magazine | MSDN Library
Overview: Introduction to Numerical Computing in F# MSDN Magazine
Linear regression in C#
Non Linear Curve Fitting

Thesis & Papers

TODO: find links, verify

Detecting falls and poses in image silhouettes, Master's Thesis in Complex Adaptive Systems, Niklas Schräder, Chalmers University of Technology, Gothenburg, Sweden, 2011
SoundLog, Master's Thesis in Information and Software Engineering, André Filipe Mateus Ferreira, Instituto Superior Técnico, Universidade Técnica de Lisboa
ACCELEROMETERS USABILITY FOR DANGER TILT OFF-HIGHWAY VEHICLES AND SIGNAL FILTRATION WITH KALMAN FILTER, Ondrej LÍŠKA, Kamil ŽIDEK, Technical University of Kosice, SjF, Department of biomedical engineering automation and measuring, Journal of applied science in the thermodynamics and fluid mechanics Vol. 4, No. 2/2010, ISSN 1802-9388
Fast evaluation of Greeks in Monte Carlo calculations with the Adjoint Method, Bachelor Thesis, Ivan Kuliš, Fachbereich Informatik und Mathematik, Institut für Mathematik, Johann Wolfgang Goethe Universität, Frankfurt am Main, 14.09.2011
3DMapping for Robotic Search and Rescue, Peter Nelson, New College, 28 May 2011
Quantitative structure-property relationship modeling algorithms, challenges and IT solutions, Thesis, Ondrej Skrehota, FACULTY OF INFORMATIC, MASARYK UNIVERSITY, 2010
Seismic Performance Assessment of Buildings Volume 2 – Implementation Guide, ATC-58-1 75% Draft, APPLIED TECHNOLOGY COUNCIL, 201 Redwood Shores Parkway, Suite 240, Redwood City, California 94065, prepared for U.S. DEPARTMENT OF HOMELAND SECURITY (DHS) FEDERAL EMERGENCY MANAGEMENT AGENCY
Use of Mobile Phones as Intelligent Sensors for Sound Input Analysis and Sleep State Detection, Ondrej Krejcar, Jakub Jirka, Dalibor Janckulik, Sensors 2011, 11, 6037-6055, ISSN 1424-8220, 2011
Design of a Wireless Acquisition System for a Digital Stethoscope, Bachelor Thesis, Justin Miller, Faculty of Engineering & Surveying, University of Southern Queensland, ENG4112 Research Project, 2010
Konzeption und Umsetzung einer RIA zur untersuchungsbegleitenden Erfassung von RNFLT-Scans und Untersuchung von Klassifikatoren für die diagnostische Unterstützung bei neurodegenerativen Erkrankungen am Beispiel der Multiplen Sklerose, Diplomarbeit, Sebastian Bischoff, Fachbereich Informatik und Medien, Fachhochschule Brandenburg, 1.11.2009
Ka`imiolakai ROV, Team Limawa, Kapi´olani Community College
Prototipo de una aplicación informática para gestión y mantenimiento de recursos pesquero, Silvia Rodríguez Rodríguez, José Juan Castro Hernández, 2010
Elastic Properties of Growing 2D Foam, Master's Thesis, Michael Schindlberger, Physical Systems Biology Group, University of Zurich, 2011

University Course Work

Uni Muenster, Computer Vision und Mustererkennung (SS 2011)

Updated Wiki: Probability Distributions

cdrnet — Sat, 01 Dec 2012 01:24:11 GMT

Probability Distributions

In MathNet.Numerics.Distributions we provide a wide range of probability distributions. Once parametrized, they can be used to sample non-uniform random numbers or investigate their statistical properties.

All the distributions implement a basic set of operations such as computing the mean, standard deviation, density, etc. Because it is often numerically more stable and faster to compute quantities in the log domain, we also provide a selection of them, including Density, in the logarithmic domain with the "Ln" suffix, .e.g. DensityLn.

using MathNet.Numerics.Distributions;
var gamma = new Gamma(2.0, 1.5);
var mean = gamma.Mean;
var variance = gamma.Variance;
var entropy = gamma.Entropy;
// ...
var a = gamma.Density(2.3); // pdf
var b = gamma.DensityLn(2.3); // ln(pdf)
var c = gamma.CumulativeDistribution(0.7); // cdf

Parametrizing the Distributions

There are many ways to parameterize a distribution in the literature. When using the default constructor, study carefully which parameters it requires. If they do not suite your needs, there will likely be static method which can construct the distribution for you with the parameters of your choice. For example, to construct a normal distribution with mean 0.0 and standard deviation 2.0 you can use var n = new Normal(0.0, 2.0); . However, if you'd rather parameterize the normal distribution using a mean and precision, one can use the following code instead: var n = Normal.WithMeanPrecision(0.0,0.5);

var gamma = Gamma.WithShapeScale(2.0, 0.75);

Random Number Sampling

Each distribution provides methods to generate random numbers from that distribution. These random variate generators work by accessing the distribution's member RandomSource (which is a subclass of System.Random, see Random Numbers for details) to provide uniform random numbers. By default, this member is an instance of System.Random but one can easily replace this with more sophisticated random number generators from MathNet.Numerics.Random. Each distribution class has two static and two class methods: for each pair (static and class), one of them generates a single sample, the other will generate an IEnumerable<T> of samples. The static methods allow random number generation without instantiating the actual class.

using MathNet.Numerics.Random;
var gamma = new Gamma(2.0, 1.5);
gamma.RandomSource = new MersenneTwister();
double a = gamma.Sample();
double[] b = gamma.Samples().Take(100).ToArray();

Alternative using static methods (note that no intermediate value caching is possible this way and parameters must be validated on each call):

var rnd = new MersenneTwister();
double a = Gamma.Sample(rnd, 2.0, 1.5);
double[] b = Gamma.Samples(rnd, 2.0, 1.5).Take(10).ToArray();

Probability Distributions in F#

The F# extensions provide a few simple helper functions in the MathNet.Numerics.Distributions namespace to assign a specific random source to a distribution: withRandom, withSystemRandom, withCryptoRandom and withMersenneTwister:

let rnd = Random.xorshift ()
let normal = Normal.WithMeanVariance(3.0, 1.5) |> withRandom rnd
let gamma = new Gamma(2.0, 1.5) |> withMersenneTwister
let cauchy = new Cauchy() |> withRandom (Random.mrg32k3aWith 10 false)

let samples = cauchy.Samples() |> Seq.take 100 |> List.ofSeq
let samples2 = Cauchy.Samples(rnd, 1.0, 3.0) |> Seq.take 20 |> List.ofSeq

Discrete Distributions

All discrete distributions implement the IDiscreteDistribution and IDistribution intefaces.

Continuous Distributions

All continuous distributions implement the IContinuousDistribution and IDistribution intefaces.

Multivariate Distributions

There is no shared interface for the multivariate distributions: as their domains can be quite different it would be hard to come up with a simple and clean but still useful unifying interface.

Updated Wiki: Probability Distributions

cdrnet — Fri, 30 Nov 2012 22:39:53 GMT

Probability Distributions

using MathNet.Numerics.Random;
using MathNet.Numerics.Distributions;
var gamma = new Gamma(2.0, 1.5);
var mean = gamma.Mean;
var variance = gamma.Variance;
var entropy = gamma.Entropy;
// ...
var a = gamma.Density(2.3); // pdf
var b = gamma.DensityLn(2.3); // ln(pdf)
var c = gamma.CumulativeDistribution(0.7); // cdf

Parametrizing the Distributions

var gamma = Gamma.WithShapeScale(2.0, 0.75);

Random Number Sampling

var gamma = new Gamma(2.0, 1.5);
gamma.RandomSource = new MersenneTwister();
double a = gamma.Sample();
double[] b = gamma.Samples().Take(100).ToArray();

Alternative using static methods (note that no intermediate value caching is possible this way and parameters must be validated on each call):

var rnd = new MersenneTwister();
double a = Gamma.Sample(rnd, 2.0, 1.5);
double[] b = Gamma.Samples(rnd, 2.0, 1.5).Take(10).ToArray();

Probability Distributions in F#

let rnd = Random.xorshift ()
let normal = Normal.WithMeanVariance(3.0, 1.5) |> withRandom rnd
let gamma = new Gamma(2.0, 1.5) |> withMersenneTwister
let cauchy = new Cauchy() |> withRandom (Random.mrg32k3aWith 10 false)

let samples = cauchy.Samples() |> Seq.take 100 |> List.ofSeq
let samples2 = Cauchy.Samples(rnd, 1.0, 3.0) |> Seq.take 20 |> List.ofSeq

Discrete Distributions

All discrete distributions implement the IDiscreteDistribution and IDistribution intefaces.

Continuous Distributions

All continuous distributions implement the IContinuousDistribution and IDistribution intefaces.

Multivariate Distributions

There is no shared interface for the multivariate distributions: as their domains can be quite different it would be hard to come up with a simple and clean but still useful unifying interface.

Updated Wiki: Probability Distributions

cdrnet — Fri, 30 Nov 2012 22:38:40 GMT

Probability Distributions

using MathNet.Numerics.Random;
using MathNet.Numerics.Distributions;
var gamma = new Gamma(2.0, 1.5);
var mean = gamma.Mean;
var variance = gamma.Variance;
var entropy = gamma.Entropy;
// ...
var a = gamma.Density(2.3); // pdf
var b = gamma.DensityLn(2.3); // ln(pdf)
var c = gamma.CumulativeDistribution(0.7); // cdf

Random Number Sampling

using MathNet.Numerics.Random;
using MathNet.Numerics.Distributions;
var gamma = new Gamma(2.0, 1.5);
gamma.RandomSource = new MersenneTwister();
double a = gamma.Sample();
double[] b = gamma.Samples().Take(100).ToArray();

Alternative using static methods (note that no intermediate value caching is possible this way and parameters must be validated on each call):

var rnd = new MersenneTwister();
double a = Gamma.Sample(rnd, 2.0, 1.5);
double[] b = Gamma.Samples(rnd, 2.0, 1.5).Take(10).ToArray();

Parametrizing the Distributions

var gamma = Gamma.WithShapeScale(2.0, 0.75);

Probability Distributions in F#

let rnd = Random.xorshift ()
let normal = Normal.WithMeanVariance(3.0, 1.5) |> withRandom rnd
let gamma = new Gamma(2.0, 1.5) |> withMersenneTwister
let cauchy = new Cauchy() |> withRandom (Random.mrg32k3aWith 10 false)

let samples = cauchy.Samples() |> Seq.take 100 |> List.ofSeq
let samples2 = Cauchy.Samples(rnd, 1.0, 3.0) |> Seq.take 20 |> List.ofSeq

Discrete Distributions

All discrete distributions implement the IDiscreteDistribution and IDistribution intefaces.

Continuous Distributions

All continuous distributions implement the IContinuousDistribution and IDistribution intefaces.

Multivariate Distributions

There is no shared interface for the multivariate distributions: as their domains can be quite different it would be hard to come up with a simple and clean but still useful unifying interface.

Updated Wiki: Probability Distributions

cdrnet — Fri, 30 Nov 2012 22:38:20 GMT

Probability Distributions

using MathNet.Numerics.Random;
using MathNet.Numerics.Distributions;
var gamma = new Gamma(2.0, 1.5);
var mean = gamma.Mean;
var variance = gamma.Variance;
var entropy = gamma.Entropy;
// ...
var a = gamma.Density(2.3); // pdf
var b = gamma.DensityLn(2.3); // ln(pdf)
var c = gamma.CumulativeDistribution(0.7); // cdf

Random Number Sampling

using MathNet.Numerics.Random;
using MathNet.Numerics.Distributions;
var gamma = new Gamma(2.0, 1.5);
gamma.RandomSource = new MersenneTwister();
double a = gamma.Sample();
double[] b = gamma.Samples().Take(100).ToArray();

Alternative using static methods (note that no intermediate value caching is possible this way and parameters must be validated on each call):

var rnd = new MersenneTwister();
double a = Gamma.Sample(rnd, 2.0, 1.5);
double[] b = Gamma.Samples(rnd, 2.0, 1.5).Take(10).ToArray();

Parametrizing the Distributions

var gamma = Gamma.WithShapeScale(2.0, 0.75);

Probability Distributions in F#

let rnd = Random.xorshift ()
let normal = Normal.WithMeanVariance(3.0, 1.5) |> withRandom rnd
let gamma = new Gamma(2.0, 1.5) |> withMersenneTwister
let cauchy = new Cauchy() |> withRandom (Random.mrg32k3aWith 10 false)

let samples = cauchy.Samples() |> Seq.take 100 |> List.ofSeq
let samples2 = Cauchy.Samples(rnd, 1.0, 3.0) |> Seq.take 20 |> List.ofSeq

Discrete Distributions

All discrete distributions implement the IDiscreteDistribution and IDistribution intefaces.

Continuous Distributions

All continuous distributions implement the IContinuousDistribution and IDistribution intefaces.

Multivariate Distributions

There is no shared interface for the multivariate distributions: as their domains can be quite different it would be hard to come up with a simple and clean but still useful unifying interface.

Updated Wiki: Probability Distributions

cdrnet — Fri, 30 Nov 2012 22:15:06 GMT

Probability Distributions

using MathNet.Numerics.Random;
using MathNet.Numerics.Distributions;
var gamma = new Gamma(2.0, 1.5);
var mean = gamma.Mean;
var variance = gamma.Variance;
var entropy = gamma.Entropy;
// ...
var a = gamma.Density(2.3); // pdf
var b = gamma.DensityLn(2.3); // ln(pdf)
var c = gamma.CumulativeDistribution(0.7); // cdf

Random Number Sampling

using MathNet.Numerics.Random;
using MathNet.Numerics.Distributions;
var gamma = new Gamma(2.0, 1.5);
gamma.RandomSource = new MersenneTwister();
double a = gamma.Sample();
double[] b = gamma.Samples().Take(100).ToArray();

Alternative using static methods (note that no intermediate value caching is possible this way and parameters must be validated on each call):

var rnd = new MersenneTwister();
double a = Gamma.Sample(rnd, 2.0, 1.5);
double[] b = Gamma.Samples(rnd, 2.0, 1.5).Take(10).ToArray();

Parametrizing the Distributions

var gamma = Gamma.WithShapeScale(2.0, 0.75);

Discrete Distributions

All discrete distributions implement the IDiscreteDistribution and IDistribution intefaces.

Continuous Distributions

All continuous distributions implement the IContinuousDistribution and IDistribution intefaces.

Multivariate Distributions

There is no shared interface for the multivariate distributions: as their domains can be quite different it would be hard to come up with a simple and clean but still useful unifying interface.

Updated Wiki: Probability Distributions

cdrnet — Fri, 30 Nov 2012 22:03:35 GMT

Probability Distributions

Random Number Sampling

Parametrizing the Distributions

Discrete Distributions

All discrete distributions implement the IDiscreteDistribution and IDistribution intefaces.

Continuous Distributions

All continuous distributions implement the IContinuousDistribution and IDistribution intefaces.

Multivariate Distributions

There is no shared interface for the multivariate distributions: as their domains can be quite different it would be hard to come up with a simple and clean but still useful unifying interface.

Updated Wiki: Random Numbers

cdrnet — Fri, 30 Nov 2012 21:49:01 GMT

Random Number Generation

The .Net Framwork comes with two (pseudo) random number sources: System.Random and System.Security.Cryptography.RNGCryptoServiceProvider. The former is commonly used throughout the .Net space for general purpose uniform random number generation, the latter in selected cases where random data is needed for cryptoghraphic applications and more "randomness" is required, at the cost of being slower. If you're not sure which one to choose, where randomness is not critical we suggest to simply use System.Random, or MersenneTwister if it turns out to be too slow.

Math.NET Numerics provides a whole set of alternative pseudo random number generators (RNG). Yet, in order to stay fully compatible with other code expecting a traditional System.Random instance, all our providers derive from System.Random (via our AbstractRandomNumberGenerator class) and can thus be used directly in place of System.Random.

using MathNet.Numerics.Random;
var mersenneTwister = new MersenneTwister(42);
double a = mersenneTwister.NextDouble();
decimal b = mersenneTwister.NextDecimal();
long c = mersenneTwiser.NextFullRangeInt64();

Random Number Generators

Namespace: MathNet.Numerics.Random

MersenneTwister: Mersenne Twister 19937 generator
Xorshift: Multiply-with-carry XOR-shift generator
Mcg31m1: Multiplicative congruental generator using a modulus of 2^31-1 and a multiplier of 1132489760
Mcg59: Multiplicative congruental generator using a modulus of 2^59 and a multiplier of 13^13
WH1982: Wichmann-Hill's 1982 combined multiplicative congruental generator
WH2006: Wichmann-Hill's 2006 combined multiplicative congruental generator
Mrg32k3a: 32-bit combined multiple recursive generator with 2 components of order 3
Palf: Parallel Additive Lagged Fibonacci generator
SystemCryptoRandomNumberGenerator: Generator using the RNGCryptoServiceProvider of the .Net framework. Note: Not available in portable builds

Seeding and thread safety

All generator constructors optionally accept two parameters: an integer for seeding and a boolean to enable thread-safety if needed. An exception is the crypto generator, where a custom seed would defeat its purpose.

If you create two instances of the same generator and seed, they will generate exactly the same number sequence. If no seed is provided, most generator fall back to a time-based seed, which is dangerous when creating multiple generators in quick succession (since time resolution is limited, some can end up with the same seed). It is therefore essential to reuse generators instead of creating new ones every time a random number is needed, or at least to have a single random source to generate random seeds for each.

For performance and design reasons, generators are not thread-safe out of the box. However, since sharing generators is recommended, thread-safe number generation can optionally be enabled with the second, boolean constructor parameter.

Non-Standard Ranges

Often you don't need a random number between 0 and 1 but in a different range, or e.g. a random integer of the full integer type range. Generating such random numbers correctly is non-trivial if the distribution should remain uniform (including at 0, min, max etc.). That's why we also provide a set of extension methods (in addition to Next and NextDouble) defined directly on System.Random, so the can be used not only on our custom RNGs but even with System.Random instances:

NextInt64: Returns a 64-bit signed integer greater than or equal to 0 and less than Int64.MaxValue. This is therefore the equivalent of the Next method but for 64-bit integers instead of 32-bit integers. Distributed uniformly.
NextFullRangeInt32: Returns a 32-bit signed integer of the full range, including 0, negative numbers, Int32.MinValue and Int32.MaxValue. Distributed uniformly.
NextFullRangeInt64: Returns a 64-bit signed integer of the full range, including 0, negative numbers, Int64.MinValue and Int64.MaxValue. Distributed uniformly.
NextDecimal: Returns a decimal floating point number greater than or equal to 0.0 and less than 1.0. Distributed uniformly.

Non-Uniform Random Numbers

If you need to generate non-uniform random numbers, you can combine any of these generators with our probability distributions, see Probability Distributions.

Random Numbers in F#

The F# extensions provide a Random module in the MathNet.Numerics.Random namespace that tries to make using our random number generators in F# a bit simpler and more idiomatic.

Random.seed (): generates a GUID based seed
Random.timeSeed (): generates a time-based seed

Random.system(), Random.systemWith seed
Random.crypto(), Random.cryptoWith threadSafe
Random.mersenneTwister(), Random.mersenneTwisterWith seed threadSafe
Random.xorshift(), Random.xorshiftWith seed threadSafe
Random.wh1982(), Random.wh1982With seed threadSafe
Random.wh2006(), Random.wh2006With seed threadSafe
Random.palf(), Random.palfWith seed threadSafe
Random.mcg59(), Random.mcg59With seed threadSafe
Random.mcg31m1(), Random.mcg31m1With seed threadSafe
Random.mrg32k3a(), Random.mrg32k3aWith seed threadSafe

Updated Wiki: Documentation

cdrnet — Fri, 30 Nov 2012 21:44:39 GMT

Math.NET Numerics Documentation

API Reference
C# Code Samples: sources or as NuGet source package
F# Code Samples: sources or as NuGet source package

User Guide

Advanced Topics

Precision
Parallel Execution
Native Linear Algebra Providers (MKL, ACML)

Updated Wiki: Random Numbers

cdrnet — Fri, 30 Nov 2012 21:43:29 GMT

Random Number Generation

The .Net Framwork comes with two (pseudo) random number sources: System.Random and System.Security.Cryptography.RNGCryptoServiceProvider. The former is commonly used throughout the .Net space for general purpose random number generation, the latter in selected cases where random data is needed for cryptoghraphic applications and more "randomness" is required, at the cost of being slower. If you're not sure which one to choose, where randomness is not critical we suggest to simply use System.Random, or MersenneTwister if it turns out to be too slow.

Math.NET Numerics provides a whole set of alternative pseudo random number generators (RNG). Yet, in order to stay fully compatible with other code expecting a traditional System.Random instance, all our providers derive from System.Random (via our AbstractRandomNumberGenerator class) and can thus be used directly in place of System.Random.

Random Number Generators

Namespace: MathNet.Numerics.Random

MersenneTwister: Mersenne Twister 19937 generator
Xorshift: Multiply-with-carry XOR-shift generator
Mcg31m1: Multiplicative congruental generator using a modulus of 2^31-1 and a multiplier of 1132489760
Mcg59: Multiplicative congruental generator using a modulus of 2^59 and a multiplier of 13^13
WH1982: Wichmann-Hill's 1982 combined multiplicative congruental generator
WH2006: Wichmann-Hill's 2006 combined multiplicative congruental generator
Mrg32k3a: 32-bit combined multiple recursive generator with 2 components of order 3
Palf: Parallel Additive Lagged Fibonacci generator
SystemCryptoRandomNumberGenerator: Generator using the RNGCryptoServiceProvider of the .Net framework. Note: Not available in portable builds

Seeding and thread safety

Non-Standard Ranges

NextInt64: Returns a 64-bit signed integer greater than or equal to 0 and less than Int64.MaxValue. This is therefore the equivalent of the Next method but for 64-bit integers instead of 32-bit integers. Distributed uniformly.
NextFullRangeInt32: Returns a 32-bit signed integer of the full range, including 0, negative numbers, Int32.MinValue and Int32.MaxValue. Distributed uniformly.
NextFullRangeInt64: Returns a 64-bit signed integer of the full range, including 0, negative numbers, Int64.MinValue and Int64.MaxValue. Distributed uniformly.
NextDecimal: Returns a decimal floating point number greater than or equal to 0.0 and less than 1.0. Distributed uniformly.

Non-Uniform Random Numbers

If you need to generate non-uniform random numbers, you can combine any of these generators with our probability distributions, see Probability Distributions.

Random Numbers in F#

The F# extensions provide a Random module in the MathNet.Numerics.Random namespace that tries to make using our random number generators in F# a bit simpler and more idiomatic.

Random.seed (): generates a GUID based seed
Random.timeSeed (): generates a time-based seed

Random.system(), Random.systemWith seed
Random.crypto(), Random.cryptoWith threadSafe
Random.mersenneTwister(), Random.mersenneTwisterWith seed threadSafe
Random.xorshift(), Random.xorshiftWith seed threadSafe
Random.wh1982(), Random.wh1982With seed threadSafe
Random.wh2006(), Random.wh2006With seed threadSafe
Random.palf(), Random.palfWith seed threadSafe
Random.mcg59(), Random.mcg59With seed threadSafe
Random.mcg31m1(), Random.mcg31m1With seed threadSafe
Random.mrg32k3a(), Random.mrg32k3aWith seed threadSafe

Updated Wiki: Random Numbers

cdrnet — Fri, 30 Nov 2012 21:28:41 GMT

Random Number Generation

The .Net Framwork comes with two (pseudo) random number sources: System.Random and System.Security.Cryptography.RNGCryptoServiceProvider. The former is commonly used throughout the .Net space for general purpose random number generation, the latter in selected cases where random data is needed for cryptoghraphic applications and more "randomness" is required, at the cost of being slower. If you're not sure which one to choose, where randomness is not critical we suggest to simply use System.Random, or MersenneTwister if it turns out to be too slow.

Math.NET Numerics provides a whole set of alternative pseudo random number generators (RNG). Yet, in order to stay fully compatible with other code expecting a traditional System.Random instance, all our providers derive from System.Random (via our AbstractRandomNumberGenerator class) and can thus be used directly in place of System.Random.

Random Number Generators

Namespace: MathNet.Numerics.Random

MersenneTwister: Mersenne Twister 19937 generator
Xorshift: Multiply-with-carry XOR-shift generator
Mcg31m1: Multiplicative congruental generator using a modulus of 2^31-1 and a multiplier of 1132489760
Mcg59: Multiplicative congruental generator using a modulus of 2^59 and a multiplier of 13^13
WH1982: Wichmann-Hill's 1982 combined multiplicative congruental generator
WH2006: Wichmann-Hill's 2006 combined multiplicative congruental generator
Mrg32k3a: 32-bit combined multiple recursive generator with 2 components of order 3
Palf: Parallel Additive Lagged Fibonacci generator
SystemCryptoRandomNumberGenerator: Generator using the RNGCryptoServiceProvider of the .Net framework. Note: Not available in portable builds

Seeding and thread safety

Non-Standard Ranges

NextInt64: Returns a 64-bit signed integer greater than or equal to 0 and less than Int64.MaxValue. This is therefore the equivalent of the Next method but for 64-bit integers instead of 32-bit integers. Distributed uniformly.
NextFullRangeInt32: Returns a 32-bit signed integer of the full range, including 0, negative numbers, Int32.MinValue and Int32.MaxValue. Distributed uniformly.
NextFullRangeInt64: Returns a 64-bit signed integer of the full range, including 0, negative numbers, Int64.MinValue and Int64.MaxValue. Distributed uniformly.
NextDecimal: Returns a decimal floating point number greater than or equal to 0.0 and less than 1.0. Distributed uniformly.

Non-Uniform Random Numbers

If you need to generate non-uniform random numbers, you can combine any of these generators with our probability distributions, see Probability Distributions.