Applications and libraries/Mathematics

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This page contains a list of libraries and tools in a certain category. For a comprehensive list of such pages, see Applications and libraries.

Libraries for numerical algorithms and mathematics

Linear algebra

GSLHaskell

High level functional interface to standard linear algebra computations and other numerical algorithms based on the GNU Scientific Library.

Wrapper to CLAPACK

Digital Signal Processing

Modules for matrix manpulation, digital signal processing, spectral estimation, and frequency estimation.

Index-aware linear algebra

Frederik Eaton's library for statically checked matrix manipulation in Haskell

Indexless linear algebra algorithms by Jan Skibinski, see below

other

Geometric Algorithms

A small Haskell library, containing algorithms for two-dimensional convex hulls, triangulations of polygons, Voronoi-diagrams and Delaunay-triangulations, the QEDS data structure, kd-trees and range-trees.

Papers by Jerzy Karczmarczuk

Some interesting uses of Haskell in mathematics, including functional differentiation, power series, continued fractions.

DoCon - Algebraic Domain Constructor

A Computer Algebra System

Decimal arithmetic library

An implementation of real decimal arithmetic, for cases where the binary floating point is not acceptable (for example, money).

HaskellMath

The HaskellMath library is a sandbox for experimenting with mathematics algorithms. So far I've implemented a few quantitative finance models (Black Scholes, Binomial Trees, etc) and basic linear algebra functions. Next I might work on either computer algebra or linear programming. All comments welcome!

Numeric Prelude

Experimental revised framework for numeric type classes.

Exact real arithmetic

is an interesting area: it is a deep connection between numeric methods and deep theoretic fondations of algorithms (and mathematics). Its topic: computable real numbers raise a lot of interesting questions rooted in mathematical analysis, arithmetic, but also computability theory (see numbers-as-programs approaches). Computable reals can be achieved by many approaches -- it is not one single theory.

Adaptive Simulated Annealing

A Haskell interface to Lester Ingber's adaptive simulating annealing code.

Number Theory Library

Andrew Bromage's Haskell number theory library, providing operations on primes, fibonacci sequences and combinatorics.

Hmm: Haskell Metamath

Hmm is a small Haskell library to parse and verify Metamath databases.

Probabilistic Functional Programming

The PFP library is a collection of modules for Haskell that facilitates probabilistic functional programming, that is, programming with stochastic values. The probabilistic functional programming approach is based on a data type for representing distributions. A distribution represent the outcome of a probabilistic event as a collection of all possible values, tagged with their likelihood. A nice aspect of this system is that simulations can be specified independently from their method of execution. That is, we can either fully simulate or randomize any simulation without altering the code which defines it.

Mirror of the following numeric modules by Jan Skibinski

• Numerics with fractions(via Internet Archive since 10/06/2003).
• Roots of polynomials(via Internet Archive since 10/06/2003). It implements the well known Laguerre's method for finding complex roots of polynomials.
• Indexless linear algebra algorithms(via Internet Archive since 10/06/2003). Orthogonalization, solution of linear equations, eigenvalues and eigenvectors.
• State vector evolution(via Internet Archive since 10/06/2003)
• Short study of fuzzy oscillator(via Internet Archive since 10/06/2003)
• N-dimensional tensors(via Internet Archive since 10/06/2003)

Sinc function

Boolean

A general boolean algebra class and some instances for Haskell.

HODE

HODE is a binding to the Open Dynamics Engine. ODE is an open source, high performance library for simulating rigid body dynamics.