AERN-RnToRm-0.4: polynomial function enclosures (PFEs) approximating exact real functionsSource codeContentsIndex
Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Elementary
Portabilityportable
Stabilityexperimental
Maintainermik@konecny.aow.cz
Description

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

Implementation of elementary functions applied to polynomials.

Synopsis
chplSqrt :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> EffortIndex -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
chplExp :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> EffortIndex -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
chplPow :: (ERRealBase b, Integral i, DomainBox box varid Int, Ord box) => Int -> ERChebPoly box b -> i -> ERChebPoly box b
chplLog :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> EffortIndex -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
chplSine :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> EffortIndex -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
chplCosine :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> EffortIndex -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
sincosTaylorAux :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Bool -> (ERChebPoly box b, ERChebPoly box b) -> Int -> Int -> (b, b) -> ((ERChebPoly box b, ERChebPoly box b), Int, (b, b))
chplAtan :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> EffortIndex -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
chplRecip :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> EffortIndex -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
Documentation
chplSqrtSource
:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Intmaximum polynomial degree
-> EffortIndex??
-> ERChebPoly box b
-> (ERChebPoly box b, ERChebPoly box b)
Approximate the pointwise square root of a polynomial by another polynomial from below and from above.
chplExpSource
:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Intmaximum polynomial degree
-> EffortIndexminimum approx Taylor degree
-> ERChebPoly box b
-> (ERChebPoly box b, ERChebPoly box b)
Approximate the pointwise exponential of a polynomial by another polynomial from below and from above.
chplPowSource
:: (ERRealBase b, Integral i, DomainBox box varid Int, Ord box)
=> Intmaximum polynomial degree
-> ERChebPoly box b
-> i
-> ERChebPoly box b
Approximate the pointwise integer power of a polynomial by another polynomial from above.
chplLogSource
:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Intmaximum polynomial degree
-> EffortIndex??
-> ERChebPoly box b
-> (ERChebPoly box b, ERChebPoly box b)
Approximate the pointwise natural logarithm of a polynomial by another polynomial from below and from above.
chplSineSource
:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Intmaximum polynomial degree
-> EffortIndexhow hard to try (determines Taylor degree and granularity)
-> ERChebPoly box b
-> (ERChebPoly box b, ERChebPoly box b)

Approximate the pointwise sine of a polynomial by another polynomial from below and from above.

Assuming the polynomial range is [-pi2, pi2].

chplCosineSource
:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Intmaximum polynomial degree
-> EffortIndexhow hard to try (determines Taylor degree and granularity)
-> ERChebPoly box b
-> (ERChebPoly box b, ERChebPoly box b)

Approximate the pointwise sine of a polynomial by another polynomial from below and from above.

Assuming the polynomial range is [-pi2, pi2].

sincosTaylorAuxSource
:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Bool
-> (ERChebPoly box b, ERChebPoly box b)
-> Inthow far to go in the Taylor series
-> Intdegree of the term now being constructed
-> (b, b)
-> ((ERChebPoly box b, ERChebPoly box b), Int, (b, b))Bounds for the series result and information about the first discarded term, from which some bound on the uniform error can be deduced.
chplAtanSource
:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Intmaximum polynomial degree
-> EffortIndex??
-> ERChebPoly box b
-> (ERChebPoly box b, ERChebPoly box b)
Approximate the pointwise natural logarithm of a polynomial by another polynomial from below and from above.
chplRecipSource
:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box)
=> Intmaximum polynomial degree
-> EffortIndexminimum approx degree
-> ERChebPoly box b
-> (ERChebPoly box b, ERChebPoly box b)
Approximate the pointwise cosine of a polynomial by another polynomial from below and from above using the tau method as described in [Mason & Handscomb 2003, p 62].
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