|
Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Bounds | Portability | portable | Stability | experimental | Maintainer | mik@konecny.aow.cz |
|
|
|
Description |
Internal module for Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.
Implementation of various functions related to the bounds of polynomials.
|
|
Synopsis |
|
chplUpperBound :: (ERRealBase b, DomainBox box varid Int, Ord box) => EffortIndex -> ERChebPoly box b -> b | | chplLowerBound :: (ERRealBase b, DomainBox box varid Int, Ord box) => EffortIndex -> ERChebPoly box b -> b | | chplBounds :: (ERRealBase b, DomainBox box varid Int, Ord box) => EffortIndex -> ERChebPoly box b -> (b, b) | | chplBoundsAffine :: (ERRealBase b, DomainBox box varid Int, Ord box) => EffortIndex -> ERChebPoly box b -> (b, b) | | chplUpperBoundQuadr :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box, DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b], DomainBoxMappable boxra boxra varid (ERInterval b) (ERInterval b), DomainIntBox boxra varid (ERInterval b), Num varid, Enum varid) => EffortIndex -> ERChebPoly box b -> b | | chplMax :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> ERChebPoly box b -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b) | | chplMin :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> ERChebPoly box b -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b) | | chplNonneg :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b) | | chplNonnegCubic :: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box) => Int -> Int -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b) | | chplTimesLoHi :: (ERRealBase b, DomainBox box varid Int, Ord box) => ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b, b) -> (ERChebPoly box b, ERChebPoly box b, b) |
|
|
Documentation |
|
|
|
|
|
|
|
|
|
|
|
:: (ERRealBase b, DomainBox box varid Int, Ord box) | | => EffortIndex | how hard to try
| -> ERChebPoly box b | | -> (b, b) | | Find bounds on a polynomial over the unit domain [-1,1]^n.
Fast but inaccurate method, in essence
taking the maximum of the upper affine reduction.
|
|
|
|
:: (ERRealBase b, RealFrac b, DomainBox box varid Int, Ord box, DomainBoxMappable boxra boxras varid (ERInterval b) [ERInterval b], DomainBoxMappable boxra boxra varid (ERInterval b) (ERInterval b), DomainIntBox boxra varid (ERInterval b), Num varid, Enum varid) | | => EffortIndex | how hard to try looking for peaks
| -> ERChebPoly box b | | -> b | | Find a close upper bound on a quadratic polynomial over the
unit domain [-1,1]^n.
Much slower and somewhat more accurate method, in essence
taking the maximum of the upper quadratic reduction.
!!! Not yet properly tested !!!
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Multiply a polynomial by an enclosure (with non-negated lower bound).
|
|
Produced by Haddock version 2.4.2 |