Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Eval

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

Implementation of various evaluation functions related to polynomials.

Documentation

chplEval :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)]) => boxb -> ERChebPoly box b -> (b, b)

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 -> 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

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)

Substitute several variables in a polynomial with real number approximations, rounding downwards and upwards.

chplCompose

Arguments

:: (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].