| Portability | portable |
|---|---|
| Stability | experimental |
| Maintainer | mik@konecny.aow.cz |
Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Elementary
Description
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)
Documentation
Arguments
| :: (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.
Arguments
| :: (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.
Arguments
| :: (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.
Arguments
| :: (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.
Arguments
| :: (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.
Arguments
| :: (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].