AERN-RnToRm-0.4.2: polynomial function enclosures (PFEs) approximating exact real functionsSource codeContentsIndex
Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.Bounds
Portabilityportable
Stabilityexperimental
Maintainermik@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
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)
chplThinTimesEncl :: (ERRealBase b, DomainBox box varid Int, Ord box) => Int -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b) -> (ERChebPoly box b, ERChebPoly box b)
chplSquare :: (ERRealBase b, DomainBox box varid Int, Ord box) => Int -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
Documentation
chplUpperBoundAffineSource
:: (ERRealBase b, DomainBox box varid Int, Ord box)
=> EffortIndexhow hard to try
-> ERChebPoly box b
-> b
Find an upper bound on a polynomial over the unit domain [-1,1]^n.
chplUpperBoundAffineCornersSource
:: (ERRealBase b, DomainBox box varid Int, Ord box, DomainBoxMappable boxb boxbb varid b [(b, b)], Num varid, Enum varid)
=> EffortIndexhow hard to try
-> ERChebPoly box b
-> b
Find a close upper bound on an affine polynomial over the unit domain [-1,1]^n.
chplUpperBoundQuadrSource
:: (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)
=> EffortIndexhow 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.
chplMaxSource
:: (ERRealBase b, DomainBox box varid Int, Ord box)
=> Intmaximum 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
chplNonnegSource
:: (ERRealBase b, DomainBox box varid Int, Ord box)
=> Intmaximum 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.
chplNonnegCubicSource
:: (ERRealBase b, DomainBox box varid Int, Ord box)
=> Intmaximum polynomial degree
-> ERChebPoly box b
-> (ERChebPoly box b, ERChebPoly box b)
A version of chplNonneg using a cubic approximation.
chplThinTimesEnclSource
:: (ERRealBase b, DomainBox box varid Int, Ord box)
=> Intmaximum polynomial degree
-> ERChebPoly box b
-> (ERChebPoly box b, ERChebPoly box b)
-> (ERChebPoly box b, ERChebPoly box b)
Multiply a thin enclosure by a non-thin enclosure
chplSquareSource
:: (ERRealBase b, DomainBox box varid Int, Ord box)
=> Intmaximum polynomial degree
-> ERChebPoly box b
-> (ERChebPoly box b, ERChebPoly box b)
Safely multiply a polynomial by itself.
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