F# for Numerics

All the numerical methods you will ever need in a single beautifully-integrated F# library with an elegant functional interface: Easy to use! Spectral methods including the Fast Fourier Transform (FFT). Interpolation, curve fitting and regression. Local and global function minimization and maximization. Mean, median, mode, variance, standard deviation, Shannon entropy and other statistical quantities. Matrix factorizations including eigenvalues and eigenvectors. Numerical integration and differentiation. This library leverages the awesome power of Microsoft's F# programming language for technical computing, allowing you to solve your problems quickly and easily.

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If you have any comments or suggestions about our F# for Numerics library or would just like to know about updates, please register your interest.

Special Offers Subscribe to our beta release schemes for F# for Visualization and F# for Numerics at the same time and get 20% off! + = For a limited time only, buy the F# for Numerics and F# for Visualization libraries and a one year subscription to the F#.NET Journal and get 25% off! + + =

Full feature list

When complete, this library will implement the following functionality:

General features

• Automatic parallelization to exploit multicore systems.
• Custom run-time compilation for the best possible performance on any given problem.
• Seamless integration with the F# for Visualization library

Functional methods

• Special functions.
• Interpolation and extrapolation.
• Random number generation over many distributions.
• Numerical integration of one- and multi-dimensional functions.
• Root finding.
• Local function minimization or maximization either with or without derivatives.
• Global function minimization or maximization using Monte-Carlo methods.

Spectral methods

• Fast Fourier transforms.
• Easy-to-use frequency interpretations.
• Convolutions.
• Newland transform.
• Short-time and Windowed Fourier transforms.
• Discrete and continuous wavelet transforms.

Vectors, matrices and linear algebra

• Determinant.
• Matrix inversion.
• Eigenvalues and eigenvectors.
• Cholesky decomposition.
• QR decomposition.
• LU decomposition.
• Singular value decomposition.

Statistics

• Mean, median and modal averages.
• Variance and standard deviation.
• Skew and Kurtosis.
• Entropies.
• Curve fitting and regression.

Current features

The beta release already provides many useful numerical methods:

• Linear, cubic spline and Lagrange polynomial function interpolation.
• Physical constants
• 1D and 2D Fast Fourier transforms: O(n log n) for any n.
• Mersenne Twister random number generator.
• Random number generation over six numeric types and over the Normal (Gaussian) distribution.
• Special functions: sinc, Gamma (both real and complex), error, Gaussian, probit, kronecker and heaviside functions.
• Numerical derivative of one-dimensional functions, gradient of multidimensional functions.
• Local function minimization: gradient descent.
• Cholesky decomposition of single- and double-precision real matrices.
• Linear solving using LU decomposition with partial pivoting of single- and double-precision real, double-precision complex and arbitrary-precision rational matrices.
• Inverse of single- and double-precision real, double-precision complex and arbitrary-precision rational matrices.
• Determinant of single- and double-precision real, double-precision complex and arbitrary-precision rational matrices.
• Arbitrary-precision Hilbert matrix generator.
• Numerically stable mean, median, mode, variance and standard deviation.
• Shannon entropy.

On-line documentation

The HTML documentation for the current beta release of F# for Numerics is now available on-line here.

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