| Portability | portable |
|---|---|
| Stability | experimental |
| Maintainer | mik@konecny.aow.cz |
Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Bounds
Description
Internal module for Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.
Implementation of various functions related to the bounds of polynomials.
- chplUpperBoundAffine :: (ERRealBase b, DomainBox box varid Int, Ord box) => EffortIndex -> ERChebPoly box b -> b
- chplUpperBoundAffineCorners :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)], Num varid, Enum varid) => EffortIndex -> ERChebPoly box 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, DomainBox box varid Int, Ord box) => Int -> ERChebPoly box b -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
- chplNonneg :: (ERRealBase b, DomainBox box varid Int, Ord box) => Int -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
- chplNonnegCubic :: (ERRealBase b, DomainBox box varid Int, Ord box) => Int -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
Documentation
Arguments
| :: (ERRealBase b, DomainBox box varid Int, Ord box) | |
| => EffortIndex | how hard to try |
| -> ERChebPoly box b | |
| -> b |
Find an upper bound on a polynomial over the unit domain [-1,1]^n.
chplUpperBoundAffineCornersSource
Arguments
| :: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)], Num varid, Enum varid) | |
| => EffortIndex | how hard to try |
| -> ERChebPoly box b | |
| -> b |
Find a close upper bound on an affine polynomial over the unit domain [-1,1]^n.
Arguments
| :: (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.
Arguments
| :: (ERRealBase b, DomainBox box varid Int, Ord box) | |
| => Int | maximum polynomial degree |
| -> ERChebPoly box b | |
| -> ERChebPoly box b | |
| -> (ERChebPoly box b, ERChebPoly box b) |
Approximate from below and from above the pointwise maximum of two polynomials
Arguments
| :: (ERRealBase b, DomainBox box varid Int, Ord box) | |
| => Int | maximum polynomial degree |
| -> ERChebPoly box b | |
| -> (ERChebPoly box b, ERChebPoly box b) |
Approximate the function max(0,p(x)) by a polynomial from below and from above.
Arguments
| :: (ERRealBase b, DomainBox box varid Int, Ord box) | |
| => Int | maximum polynomial degree |
| -> ERChebPoly box b | |
| -> (ERChebPoly box b, ERChebPoly box b) |
A version of chplNonneg using a cubic approximation.