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

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

Implementation of pointwise consistently rounded polynomial composition.

Documentation

enclCompose

Arguments

:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b])

=> Int

max degree for result

-> Int

max approx size for result

-> ERChebPoly box b

f

-> varid

variable v to substitute in f

-> (ERChebPoly box b, ERChebPoly box b)

enclosure of a function f_v to substitute for v that maps [-1,1] into [-1,1]

-> (ERChebPoly box b, ERChebPoly box b)

lower bound and upper bound

Compose a polynomial and an enclosure, producing a correcly rounded enclosure, assuming the second polynomial maps [-1,1] into [-1,1].

enclComposeMany

Arguments

:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b])

=> Int

max degree for result

-> Int

max approx size for result

-> ERChebPoly box b

-> Map varid (ERChebPoly box b, ERChebPoly box b)

variables to substitute and the enclosures to substitute for each of them respectively

-> (ERChebPoly box b, ERChebPoly box b)

lower bound (negated) and upper bound

Compose two polynomials, rounding upwards provided the second polynomial maps [-1,1] into [-1,1].