Portability | portable |
---|---|
Stability | experimental |
Maintainer | mik@konecny.aow.cz |
Internal module for Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.
Implementation of elementary functions applied to polynomials.
- enclSqrt :: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) => Int -> Int -> EffortIndex -> Int -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)
- enclExp :: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) => Int -> Int -> EffortIndex -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)
- enclPow :: (Integral i, ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) => Int -> Int -> (ERChebPoly box b, ERChebPoly box b) -> i -> (ERChebPoly box b, ERChebPoly box b)
- enclLog :: (ERRealBase b, DomainBox box varid Int, Ord box) => Int -> Int -> EffortIndex -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)
- enclSine :: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) => Int -> Int -> EffortIndex -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)
- enclCosine :: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) => Int -> Int -> EffortIndex -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)
- sincosTaylorAux :: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) => Int -> Int -> Bool -> (ERChebPoly box b, ERChebPoly box b) -> Int -> Int -> ERInterval b -> ((ERChebPoly box b, ERChebPoly box b), Int, ERInterval b)
- enclAtan :: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) => Int -> Int -> EffortIndex -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)
Documentation
:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) | |
=> Int | maximum polynomial degree |
-> Int | maximum term count |
-> EffortIndex | for calls to other ER functions |
-> Int | how many times to iterate |
-> (ERChebPoly box b, ERChebPoly box b) | |
-> (ERChebPoly box b, ERChebPoly box b) |
Approximate the pointwise square root of a polynomial enclosure.
:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) | |
=> Int | maximum polynomial degree |
-> Int | maximum term count |
-> EffortIndex | used to derive minimum approx Taylor degree |
-> (ERChebPoly box b, ERChebPoly box b) | |
-> (ERChebPoly box b, ERChebPoly box b) |
Approximate the pointwise exponential of a polynomial enclosure.
:: (Integral i, ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) | |
=> Int | maximum polynomial degree |
-> Int | maximum term count |
-> (ERChebPoly box b, ERChebPoly box b) | |
-> i | |
-> (ERChebPoly box b, ERChebPoly box b) | lower (negated) and upper bound |
Approximate the pointwise integer power of an enclosure.
:: (ERRealBase b, DomainBox box varid Int, Ord box) | |
=> Int | maximum polynomial degree |
-> Int | maximum term count |
-> EffortIndex | ?? |
-> (ERChebPoly box b, ERChebPoly box b) | |
-> (ERChebPoly box b, ERChebPoly box b) |
Approximate the pointwise natural logarithm of an enclosure.
:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) | |
=> Int | maximum polynomial degree |
-> Int | maximum term count |
-> EffortIndex | how hard to try (determines Taylor degree and granularity) |
-> (ERChebPoly box b, ERChebPoly box b) | |
-> (ERChebPoly box b, ERChebPoly box b) |
Approximate the pointwise sine of an enclosure.
Assuming the polynomial range is [-pi2, pi2].
:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) | |
=> Int | maximum polynomial degree |
-> Int | maximum term count |
-> EffortIndex | how hard to try (determines Taylor degree and granularity) |
-> (ERChebPoly box b, ERChebPoly box b) | |
-> (ERChebPoly box b, ERChebPoly box b) |
Approximate the pointwise cosine of an enclosure.
Assuming the polynomial range is [-pi2, pi2].
:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) | |
=> Int | maximum polynomial degree |
-> Int | maximum term count |
-> Bool | is sine ? |
-> (ERChebPoly box b, ERChebPoly box b) | |
-> Int | how far to go in the Taylor series |
-> Int | degree of the term now being constructed |
-> ERInterval b | the coefficient of the term now being constructed |
-> ((ERChebPoly box b, ERChebPoly box b), Int, ERInterval b) | Bounds for the series result and information about the first discarded term, from which some bound on the uniform error can be deduced. |
:: (ERRealBase b, DomainBox box varid Int, Ord box, Show varid, DomainIntBox boxra varid (ERInterval b), DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b]) | |
=> Int | maximum polynomial degree |
-> Int | maximum term count |
-> EffortIndex | how far to go in the Euler's series |
-> (ERChebPoly box b, ERChebPoly box b) | |
-> (ERChebPoly box b, ERChebPoly box b) |
Approximate the pointwise arcus tangens of an enclosure.