{-| Module : Data.Number.ER.RnToRm Description : overview of AERN-RnToRm Copyright : (c) Michal Konecny License : BSD3 Maintainer : mik@konecny.aow.cz Stability : experimental Portability : non-portable (requires fenv.h) This module bundles some of the most important functionality of the AERN-RnToRm package. It is intended to be imported *qualified*. AERN-RnToRm provides datatypes and abstractions for approximating functions of type @D -> R^m@ where @D@ is a bounded interval in @R^n@ with non-empty interior. Abstractions are provided via 4 type classes: * 'UFB.ERUnitFnBase': generalises polynomials with floating point coefficients. (/Not exported here, used only internally./) * 'ERFnApprox': generalises functions enclosures on a certain unspecified domain. * 'UFA.ERUnitFnApprox' (extends 'ERFnApprox'): generalises function graph enclosures on the domain @[-1,1]^n@. (/Not exported here, used only internally./) * 'ERFnDomApprox' (extends 'ERFnApprox'): generalises function enclosures over a specified and queriable domain box (instance of class 'DomainBox'). At all levels, all field operations are supported as well as some elementary operations, namely exp, sin and cos. Log and sqrt are planned to be added soon. Implementations of 'UFB.ERUnitFnBase': * 'ERChebPoly' By using the Chebyshev basis on domain @[-1,1]^n@, we gain simple and optimally rounding degree reduction as well as relatively simple handling of rounding in other operations. Implementations of 'UFA.ERUnitFnApprox': * 'ERFnInterval' Implementations of 'ERFnDomApprox': * 'ERFnDomTranslApprox': builds a basic implementation using an instance of 'UFA.ERUnitFnApprox'. * 'ERFnTuple': extends another implementation of 'ERFnDomApprox' to work with lists of functions simultaneously. * 'ERFnDomEdgesApprox': separately enclose a function on its domain box as well as on all the domain's hyper-edges (including the corners) using another implementation of 'ERFnDomApprox'. * 'ERFnPiecewise': allows the domain box to be bisected to an arbitrary finite depth and uses another implementation of 'ERFnDomApprox' to approximate the function on each segment. -} module Data.Number.ER.RnToRm ( module Data.Number.ER.RnToRm.DefaultRepr, module Data.Number.ER.RnToRm.Approx, module Data.Number.ER.Real.DomainBox ) where import Data.Number.ER.RnToRm.DefaultRepr import Data.Number.ER.RnToRm.Approx import Data.Number.ER.Real.DomainBox import qualified Data.Number.ER.RnToRm.UnitDom.Approx as UFA import qualified Data.Number.ER.RnToRm.UnitDom.Base as UFB import qualified Data.Number.ER.Real.Approx as RA import qualified Data.Number.ER.Real.Approx.Elementary as RAEL import Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom import Data.Number.ER.RnToRm.UnitDom.Approx.Interval import Data.Number.ER.RnToRm.Approx.DomTransl import Data.Number.ER.RnToRm.Approx.DomEdges import Data.Number.ER.RnToRm.Approx.Tuple import Data.Number.ER.RnToRm.Approx.PieceWise