Name: GaussQuadIntegration
Version: 0.1
Stability: Experimental
Author: Grigory Sarnitsky
Maintainer: Grigory Sarnitsky
License: BSD3
License-file: LICENSE
Build-type: Simple
Cabal-version: >=1.2
Category: Math
Synopsis: Non-adaptive Gaussian quadrature for numeric integraton
Description:
This package provides means for numeric integration with a Gaussian quadrature. Precisely, it incorporates non-adaptive approximation for definite integrals using 128-, 256-, 512- and 1024-point Gaussian quadrature rule.
For example, to find the approximation of an integral with a 256-point rule:
.
> ╭ a
> │ f(x) dx = nIntegrate256 f a b
> ╯ b
.
> > nIntegrate256 (\x -> x^999) 0 1
> 9.999999999999887e-4
.
The type of a function here is not confined only by Double -> Double, indeed one can use any instance of Fractional:
.
> > nIntegrate256 (\x -> x^999 :: Fixed Prec50) 0 1
> 0.00100000000000000000000000000000000000000000000009
.
128 and 256 rules are given with the accuracy of 50 digits, 512 --- with 35 digits (roughly quad), all of them were computed by myself. 1024-point rule was taken from the Gauss-Legendre Quadrature C\/C++ library by Pavel Holoborodko () and goes with the accuracy of 25 decimal digits (fixed point).
Library
hs-source-dirs: src
Exposed-modules: Math.GaussianQuadratureIntegration
other-modules: Math.GaussianQuadratureRules
build-depends: base >= 3 && < 6