AERN-RnToRm-0.4.2: polynomial function enclosures (PFEs) approximating exact real functionsSource codeContentsIndex
Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Eval
Portabilityportable
Stabilityexperimental
Maintainermik@konecny.aow.cz
Description

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

Implementation of various evaluation functions related to polynomials.

Synopsis
chplEval :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)]) => boxb -> ERChebPoly box b -> (b, b)
chplEvalUp :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)]) => boxb -> ERChebPoly box b -> b
chplEvalDown :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)]) => boxb -> ERChebPoly box b -> b
chebyEvalTsRoundDownUp :: Num v => v -> [(v, v)]
chebyEvalTsExact :: Num v => v -> [v]
chplEvalApprox :: (ERRealBase b, ERApprox ra, DomainBox box varid Int, Ord box, DomainBoxMappable boxra boxras varid ra [ra], DomainIntBox boxra varid ra) => (b -> ra) -> boxra -> ERChebPoly box b -> ra
chplPartialEvalApprox :: (ERRealBase b, ERApprox ra, DomainBox box varid Int, Ord box, DomainBoxMappable boxra boxras varid ra [ra], DomainIntBox boxra varid ra) => (ra -> (b, b)) -> boxra -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
chplCompose :: (ERRealBase b, DomainBox box varid Int, Ord box) => Int -> ERChebPoly box b -> Map varid (ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)
Documentation
chplEval :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)]) => boxb -> ERChebPoly box b -> (b, b)Source
Evaluate a polynomial at a point, consistently rounding upwards and downwards.
chplEvalUp :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)]) => boxb -> ERChebPoly box b -> bSource
chplEvalDown :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)]) => boxb -> ERChebPoly box b -> bSource
chebyEvalTsRoundDownUp :: Num v => v -> [(v, v)]Source
chebyEvalTsExact :: Num v => v -> [v]Source
chplEvalApprox :: (ERRealBase b, ERApprox ra, DomainBox box varid Int, Ord box, DomainBoxMappable boxra boxras varid ra [ra], DomainIntBox boxra varid ra) => (b -> ra) -> boxra -> ERChebPoly box b -> raSource
Evaluate a polynomial at a real number approximation
chplPartialEvalApprox :: (ERRealBase b, ERApprox ra, DomainBox box varid Int, Ord box, DomainBoxMappable boxra boxras varid ra [ra], DomainIntBox boxra varid ra) => (ra -> (b, b)) -> boxra -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)Source
Substitute several variables in a polynomial with real number approximations, rounding downwards and upwards.
chplComposeSource
:: (ERRealBase b, DomainBox box varid Int, Ord box)
=> Int
-> ERChebPoly box b
-> Map varid (ERChebPoly box b)variable to substitute, polynomial to substitute
-> (ERChebPoly box b, ERChebPoly box b)
Compose two polynomials, rounding upwards provided the second polynomial maps [-1,1] into [-1,1].
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