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

Portability	portable
Stability	experimental
Maintainer	mik@konecny.aow.cz

Description

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

Implementation of selected operations working on pairs of polynomials understood as function enclosures. These are needed to define composition and some elementary operations.

Synopsis

enclThin :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)

enclConst :: (ERRealBase b, DomainBox box varid Int, Ord box) => b -> (ERChebPoly box b, ERChebPoly box b)

enclRAConst :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERInterval b -> (ERChebPoly box b, ERChebPoly box b)

enclMultiply :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)

enclSquare :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)

enclScaleNonneg :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => b -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)

enclScale :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> b -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)

enclRAScale :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> ERInterval b -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)

chplScaleRA :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> ERInterval b -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)

enclEvalTs :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> (ERChebPoly box b, ERChebPoly box b) -> [(ERChebPoly box b, ERChebPoly box b)]

enclThinTimes :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)

Documentation

enclThin :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)

Source

enclConst :: (ERRealBase b, DomainBox box varid Int, Ord box) => b -> (ERChebPoly box b, ERChebPoly box b)

Source

enclRAConst :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERInterval b -> (ERChebPoly box b, ERChebPoly box b)

Source

enclMultiply

Source

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)

enclSquare

Source

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)

enclScaleNonneg

Source

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> b	ratio to scale by
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)
Multiply an enclosure by a scalar assuming the enclosure is non-negative on the whole unit domain.

enclScale

Source

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> b	ratio to scale by
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)
Multiply an enclosure by a scalar.

enclRAScale

Source

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> ERInterval b
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)

chplScaleRA

Source

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> ERInterval b	lower and upper bounds on the ratio to scale by
-> ERChebPoly box b
-> (ERChebPoly box b, ERChebPoly box b)
Multiply a polynomial by a scalar interval, returning an enclosure.

enclEvalTs

Source

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	max degree for result
-> Int	max approx size for result
-> (ERChebPoly box b, ERChebPoly box b)	bounds of a polynomial enclosure to evaluate
-> [(ERChebPoly box b, ERChebPoly box b)]
Evaluate the Chebyshev polynomials of the first kind applied to a given polynomial, yielding a list of polynomial enclosures.

enclThinTimes

Source

:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Int	maximum polynomial degree
-> Int	maximum term count
-> ERChebPoly box b
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)
Multiply a polynomial by an enclosure using min/max

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