Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Integration
 Portability portable Stability experimental Maintainer mik@konecny.aow.cz
Description

Internal module for Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.

Implementation of safely rounded integration of polynomials and other related functions.

Synopsis
 chplIntegrate :: (ERRealBase b, DomainBox box varid Int, Ord box) => varid -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b) chplVolumeAboveZero :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)]) => [varid] -> ERChebPoly box b -> (b, b) chplDifferentiate :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERChebPoly box b -> varid -> ERChebPoly box b
Documentation
 chplIntegrate Source
 :: (ERRealBase b, DomainBox box varid Int, Ord box) => varid variable to integrate by -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b) Approximate from below and from above the integral of a polynomial. Based on the following formulas for Chebyshev polynomials: \int T_n(x)dx = T_{n+1}(x)/2(n+1) - T_{n-1}(x)/2(n-1) \int T_1(x)dx = T_2(x)/4 + 1/4 \int T_0(x)dx = T_1(x)
 chplVolumeAboveZero :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)]) => [varid] -> ERChebPoly box b -> (b, b) Source
measure the volume between a polynomial and the zero axis on [-1,1]^n
 chplDifferentiate Source
 :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERChebPoly box b -> varid variable to differentiate over -> ERChebPoly box b Differentiate a polynomial using one of its variables.