When the radius of the ball is implicitly contributed to by imprecision in the centre (eg if the centre is a polynomial with inexact coefficients), move all that imprecision to the explicit radius, making the centre exact. This may lose some information, but as a ball is equivalent to the original. For MPBall this function is pointless because it is equivalent to the identity.

Instances

IsBall MPBall #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Type Associated Types type CentreType MPBall :: * # Methods centre :: MPBall -> CentreType MPBall # centreAsBallAndRadius :: MPBall -> (MPBall, ErrorBound) # centreAsBall :: MPBall -> MPBall # radius :: MPBall -> ErrorBound # updateRadius :: (ErrorBound -> ErrorBound) -> MPBall -> MPBall # makeExactCentre :: MPBall -> MPBall #

class IsInterval i e where #

Minimal complete definition

fromEndpoints, endpoints

Methods

fromEndpoints :: e -> e -> i #

endpoints :: i -> (e, e) #

Instances

IsInterval MPBall MPFloat #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Type Methods fromEndpoints :: MPFloat -> MPFloat -> MPBall # endpoints :: MPBall -> (MPFloat, MPFloat) #
IsInterval MPBall MPBall #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Type Methods fromEndpoints :: MPBall -> MPBall -> MPBall # endpoints :: MPBall -> (MPBall, MPBall) #

intervalFunctionByEndpoints #

Arguments

:: (IsInterval t t, HasEqCertainly t t)
=> (t -> t)	`fThin`: a version of `f` that works well on thin intervals
-> t -> t	`f` on large intervals

Computes a *monotone* ball function f on intervals using the interval endpoints.

intervalFunctionByEndpointsUpDown #

Arguments

:: IsInterval t e
=> (e -> e)	`fDown`: a version of `f` working on endpoints, rounded down
-> (e -> e)	`fUp`: a version of `f` working on endpoints, rounded up
-> t -> t	`f` on intervals rounding outwards

Computes a *monotone* ball function f on intervals using the interval endpoints.

class CanTestContains dom e where #

Minimal complete definition

contains

Methods

contains #

Arguments

:: dom	dom
-> e	e
-> Bool

Test if e is inside dom.

Instances

CanTestContains MPBall Int #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Type Methods contains :: MPBall -> Int -> Bool #
CanTestContains MPBall Integer #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Type Methods contains :: MPBall -> Integer -> Bool #
CanTestContains MPBall Rational #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Type Methods contains :: MPBall -> Rational -> Bool #
CanTestContains MPBall Dyadic #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Type Methods contains :: MPBall -> Dyadic -> Bool #
CanTestContains MPBall MPBall #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Type Methods contains :: MPBall -> MPBall -> Bool #

class CanMapInside dom e where #

Minimal complete definition

mapInside

Methods

mapInside #

Arguments

:: dom	dom
-> e	e
-> e

Return some value contained in dom. The returned value does not have to equal the given e even if e is already inside dom. All elements of dom should be covered with roughly the same probability when calling this function for evenly distributed e's.

This function is intended mainly for generating values inside dom for randomised tests.

specCanMapInside :: (CanMapInside d e, CanTestContains d e, Arbitrary d, Arbitrary e, Show d, Show e) => T d -> T e -> Spec #

class CanIntersectAsymmetric e1 e2 where #

Minimal complete definition

intersect

Associated Types

type IntersectionType e1 e2 #

Methods

intersect :: e1 -> e2 -> IntersectionType e1 e2 #

Instances

CanIntersectAsymmetric Bool Bool #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType Bool Bool :: * # Methods intersect :: Bool -> Bool -> IntersectionType Bool Bool #
CanIntersectAsymmetric MPBall MPBall #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Comparisons Associated Types type IntersectionType MPBall MPBall :: * # Methods intersect :: MPBall -> MPBall -> IntersectionType MPBall MPBall #
(CanIntersectAsymmetric Bool b, CanEnsureCE es b, CanEnsureCE es (IntersectionType Bool b), SuitableForCE es) => CanIntersectAsymmetric Bool (CollectErrors es b) #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType Bool (CollectErrors es b) :: * # Methods intersect :: Bool -> CollectErrors es b -> IntersectionType Bool (CollectErrors es b) #
(CanIntersectAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (IntersectionType MPBall b), SuitableForCE es) => CanIntersectAsymmetric MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Comparisons Associated Types type IntersectionType MPBall (CollectErrors es b) :: * # Methods intersect :: MPBall -> CollectErrors es b -> IntersectionType MPBall (CollectErrors es b) #
(CanIntersectAsymmetric a b, CanEnsureCN a, IntersectionType a b ~ EnsureCN a, CanEnsureCN (EnsureCN a), CanEnsureCN b, EnsureCN b ~ EnsureCN a) => CanIntersectAsymmetric (Maybe a) (Maybe b) #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType (Maybe a) (Maybe b) :: * # Methods intersect :: Maybe a -> Maybe b -> IntersectionType (Maybe a) (Maybe b) #
(CanIntersectAsymmetric (Maybe a) b, CanEnsureCE es b, CanEnsureCE es (IntersectionType (Maybe a) b), SuitableForCE es) => CanIntersectAsymmetric (Maybe a) (CollectErrors es b) #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType (Maybe a) (CollectErrors es b) :: * # Methods intersect :: Maybe a -> CollectErrors es b -> IntersectionType (Maybe a) (CollectErrors es b) #
(CanIntersectAsymmetric a Bool, CanEnsureCE es a, CanEnsureCE es (IntersectionType a Bool), SuitableForCE es) => CanIntersectAsymmetric (CollectErrors es a) Bool #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType (CollectErrors es a) Bool :: * # Methods intersect :: CollectErrors es a -> Bool -> IntersectionType (CollectErrors es a) Bool #
(CanIntersectAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (IntersectionType a MPBall), SuitableForCE es) => CanIntersectAsymmetric (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Comparisons Associated Types type IntersectionType (CollectErrors es a) MPBall :: * # Methods intersect :: CollectErrors es a -> MPBall -> IntersectionType (CollectErrors es a) MPBall #
(CanIntersectAsymmetric a (Maybe b), CanEnsureCE es a, CanEnsureCE es (IntersectionType a (Maybe b)), SuitableForCE es) => CanIntersectAsymmetric (CollectErrors es a) (Maybe b) #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType (CollectErrors es a) (Maybe b) :: * # Methods intersect :: CollectErrors es a -> Maybe b -> IntersectionType (CollectErrors es a) (Maybe b) #
(CanIntersectAsymmetric e1 e2, SuitableForCE es, CanEnsureCE es e1, CanEnsureCE es e2, CanEnsureCE es (IntersectionType e1 e2)) => CanIntersectAsymmetric (CollectErrors es e1) (CollectErrors es e2) #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType (CollectErrors es e1) (CollectErrors es e2) :: * # Methods intersect :: CollectErrors es e1 -> CollectErrors es e2 -> IntersectionType (CollectErrors es e1) (CollectErrors es e2) #

type CanIntersect e1 e2 = (CanIntersectAsymmetric e1 e2, CanIntersectAsymmetric e1 e2, IntersectionType e1 e2 ~ IntersectionType e2 e1) #

type CanIntersectCNBy e1 e2 = (CanIntersect e1 e2, IntersectionType e1 e2 ~ EnsureCN e1, CanIntersect (EnsureCN e1) e2, IntersectionType (EnsureCN e1) e2 ~ EnsureCN e1) #

type CanIntersectCNSameType e1 = (CanIntersectCNBy e1 e1, CanIntersect (EnsureCN e1) (EnsureCN e1), IntersectionType (EnsureCN e1) (EnsureCN e1) ~ EnsureCN e1) #

class CanUnionAsymmetric e1 e2 where #

Minimal complete definition

union

Associated Types

type UnionType e1 e2 #

Methods

union :: e1 -> e2 -> UnionType e1 e2 #

Instances

CanUnionAsymmetric MPBall MPBall #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Comparisons Associated Types type UnionType MPBall MPBall :: * # Methods union :: MPBall -> MPBall -> UnionType MPBall MPBall #
(CanUnionAsymmetric MPBall b, CanEnsureCE es b, CanEnsureCE es (UnionType MPBall b), SuitableForCE es) => CanUnionAsymmetric MPBall (CollectErrors es b) #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Comparisons Associated Types type UnionType MPBall (CollectErrors es b) :: * # Methods union :: MPBall -> CollectErrors es b -> UnionType MPBall (CollectErrors es b) #
(CanUnionAsymmetric e1 e2, CanEnsureCN e1, CanEnsureCN e2, CanEnsureCN (UnionType e1 e2)) => CanUnionAsymmetric (CN e1) (CN e2) #
Instance details Defined in AERN2.MP.Enclosure Associated Types type UnionType (CN e1) (CN e2) :: * # Methods union :: CN e1 -> CN e2 -> UnionType (CN e1) (CN e2) #
(CanUnionAsymmetric a MPBall, CanEnsureCE es a, CanEnsureCE es (UnionType a MPBall), SuitableForCE es) => CanUnionAsymmetric (CollectErrors es a) MPBall #
Instance details Defined in AERN2.MP.UseMPFR.Ball.Comparisons Associated Types type UnionType (CollectErrors es a) MPBall :: * # Methods union :: CollectErrors es a -> MPBall -> UnionType (CollectErrors es a) MPBall #
(Arrow to, CanUnionAsymmetric e1 e2) => CanUnionAsymmetric (to Accuracy e1) (to Accuracy e2) #
Instance details Defined in AERN2.MP.Enclosure Associated Types type UnionType (to Accuracy e1) (to Accuracy e2) :: * # Methods union :: to Accuracy e1 -> to Accuracy e2 -> UnionType (to Accuracy e1) (to Accuracy e2) #

type CanUnion e1 e2 = (CanUnionAsymmetric e1 e2, CanUnionAsymmetric e1 e2, UnionType e1 e2 ~ UnionType e2 e1) #

type CanUnionCNBy e1 e2 = (CanUnion e1 e2, UnionType e1 e2 ~ EnsureCN e1, CanUnion (EnsureCN e1) e2, UnionType (EnsureCN e1) e2 ~ EnsureCN e1) #

type CanUnionCNSameType e1 = (CanUnionCNBy e1 e1, CanUnion (EnsureCN e1) (EnsureCN e1), UnionType (EnsureCN e1) (EnsureCN e1) ~ EnsureCN e1) #

Orphan instances

(CanUnionCNSameType t, CanEnsureCN t) => HasIfThenElse (Maybe Bool) t #
Instance details Associated Types type IfThenElseType (Maybe Bool) t :: * # Methods ifThenElse :: Maybe Bool -> t -> t -> IfThenElseType (Maybe Bool) t #