Polynom.hs

{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}
{-|
    Module      :  Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom
    Description :  polynoms in the Chebyshev basis of the 1st kind
    Copyright   :  (c) 2007-2008 Michal Konecny
    License     :  BSD3

    Maintainer  :  mik@konecny.aow.cz
    Stability   :  experimental
    Portability :  portable
    
    Arithmetic of multivariate polynomials 
    represented by their coefficients it the Chebyshev basis.
    
    The polynomials are never to be used outside the domain @[-1,1]^n@.
    
    All operations are rounded in such a way that the resulting polynomial
    is a /point-wise upper or lower bound/ of the exact result. 
-}
module Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom
(
    ERChebPoly(..), TermKey
)
where

import Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Basic
import Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Field
import Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Eval
import Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Bounds
import Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Integration
import Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Elementary

import qualified Data.Number.ER.RnToRm.UnitDom.Base as UFB
import qualified Data.Number.ER.Real.Base as B
import Data.Number.ER.Real.Approx.Interval
import Data.Number.ER.Real.DomainBox (VariableID(..), DomainBox, DomainBoxMappable, DomainIntBox)

{- code for testing purpose, to be deleted later -}
import Data.Number.ER.Real.DefaultRepr
import Data.Number.ER.Real.DomainBox.IntMap
type P = ERChebPoly (Box Int) B
x0 = chplVar 0 :: P
x1 = chplVar 1 :: P
x2 = chplVar 2 :: P
x3 = chplVar 3 :: P
x4 = chplVar 4 :: P
p1 = x1 * x1 * x1 + x1 * (x2 + 2) * (x3 - 3)
{- end of code for testing purposes -}


instance 
    (B.ERRealBase rb, RealFrac rb,
     DomainBox box varid Int, Ord box,
     DomainBoxMappable boxb boxbb varid rb [(rb,rb)],
     DomainBoxMappable boxra boxras varid (ERInterval rb) [ERInterval rb],
     DomainIntBox boxra varid (ERInterval rb)) =>
    (UFB.ERUnitFnBase boxb boxra varid rb (ERInterval rb) (ERChebPoly box rb))
    where
    check = chplCheck
    getGranularity = chplGetGranularity
    setMinGranularity = chplSetMinGranularity
    setGranularity = chplSetGranularity
    const = chplConst
    affine = chplAffine
    scale = chplScale
    scaleApprox (ERInterval ratioDown ratioUp) = chplScaleApprox (ratioDown, ratioUp) 
--    Arity = chplGetArity
    getDegree = chplGetDegree
    reduceDegree = chplReduceDegree
    volumeAboveZero = chplVolumeAboveZero
    integrate = chplIntegrate
    upperBound = chplUpperBoundAffine
--    upperBound = chplUpperBoundQuadr
    nonneg = chplNonneg
    recip = chplRecip
    max = chplMax
    sqrt = chplSqrt
    exp = chplExp
    log = chplLog
    sin = chplSine
    cos = chplCosine
    atan = chplAtan
    eval = chplEval
    evalApprox ufb x = chplEvalApprox (\ b -> ERInterval b b) ufb x
    partialEvalApprox substitutions ufb = 
        chplPartialEvalApprox (UFB.raEndpoints ufb) substitutions ufb
    raEndpoints _ (ERInterval l h) = (l,h)
    raEndpoints _ ERIntervalAny = (- B.plusInfinity, B.plusInfinity)
    raFromEndpoints _ (l,h) = normaliseERInterval (ERInterval l h)
    compose = chplCompose