 | AERN-RnToRm-0.3.0.3: polynomial function enclosures (PFEs) approximating exact real functions | Source code | Contents | Index |
| Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Elementary |
|
Internal module for Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.
Implementation of elementary functions applied to polynomials.
| 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) |
| chplSineCosine :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Bool -> 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) |
| chplSqrt | Source |
| :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) | |
| => Int | maximum 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. | |
| chplExp | Source |
| :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) | |
| => Int | maximum polynomial degree |
| -> EffortIndex | minimum 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. | |
| chplPow | Source |
| :: (ERRealBase b, Integral i, DomainBox box varid Int, Ord box) | |
| => Int | maximum polynomial degree |
| -> ERChebPoly box b | |
| -> i | |
| -> ERChebPoly box b | |
| Approximate the pointwise integer power of a polynomial by another polynomial from above. | |
| chplLog | Source |
| :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) | |
| => Int | maximum 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. | |
| chplSineCosine | Source |
| :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) | |
| => Bool | True iff sine, False iff cosine |
| -> Int | maximum polynomial degree |
| -> EffortIndex | minimum approx Taylor degree |
| -> ERChebPoly box b | |
| -> (ERChebPoly box b, ERChebPoly box b) | |
| Approximate the pointwise sine of a polynomial by another polynomial from below and from above. | |
| chplRecip | Source |
| :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) | |
| => Int | maximum polynomial degree |
| -> EffortIndex | minimum 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]. | |