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

Instances details

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

ballFunctionUsingLipschitz Source #

Arguments

:: (IsBall t, HasEqCertainly t t)
=> (t -> t)	`fThin`: a version of `f` that works well on thin balls
-> (t -> ErrorBound)	`fLip`: a Lipschitz function of `f` over large balls
-> t -> t	`f` on large balls

Computes a ball function f on the centre and updating the error bound using a Lipschitz constant.

class IsInterval i where Source #

Associated Types

type IntervalEndpoint i Source #

Methods

endpoints :: i -> (IntervalEndpoint i, IntervalEndpoint i) Source #

fromEndpoints :: IntervalEndpoint i -> IntervalEndpoint i -> i Source #

Instances

Instances details

IsInterval MPBall Source #
Instance details Defined in AERN2.MP.Ball.Type Associated Types type IntervalEndpoint MPBall Source # Methods endpoints :: MPBall -> (IntervalEndpoint MPBall, IntervalEndpoint MPBall) Source # fromEndpoints :: IntervalEndpoint MPBall -> IntervalEndpoint MPBall -> MPBall Source #
IsInterval t => IsInterval (CN t) Source #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntervalEndpoint (CN t) Source # Methods endpoints :: CN t -> (IntervalEndpoint (CN t), IntervalEndpoint (CN t)) Source # fromEndpoints :: IntervalEndpoint (CN t) -> IntervalEndpoint (CN t) -> CN t Source #

endpointL :: IsInterval i => i -> IntervalEndpoint i Source #

endpointR :: IsInterval i => i -> IntervalEndpoint i Source #

fromEndpointsAsIntervals :: (IsInterval i, CanMinMaxSameType (IntervalEndpoint i)) => i -> i -> i Source #

endpointsAsIntervals :: IsInterval i => i -> (i, i) Source #

endpointLAsInterval :: IsInterval i => i -> i Source #

endpointRAsInterval :: IsInterval i => i -> i Source #

intervalFunctionByEndpoints Source #

Arguments

:: (IsInterval t, CanMinMaxSameType (IntervalEndpoint 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 Source #

Arguments

:: IsInterval t
=> (IntervalEndpoint t -> IntervalEndpoint t)	`fDown`: a version of `f` working on endpoints, rounded down
-> (IntervalEndpoint t -> IntervalEndpoint t)	`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 CanPlusMinus t1 t2 where Source #

Associated Types

type PlusMinusType t1 t2 Source #

type PlusMinusType t1 t2 = t1

Methods

plusMinus :: t1 -> t2 -> PlusMinusType t1 t2 Source #

Operator for constructing or enlarging enclosures such as balls or intervals

Instances

Instances details

CanBeErrorBound t => CanPlusMinus Int t Source #
Instance details Defined in AERN2.MP.Ball.Conversions Associated Types type PlusMinusType Int t Source # Methods plusMinus :: Int -> t -> PlusMinusType Int t Source #
CanBeErrorBound t => CanPlusMinus Integer t Source #
Instance details Defined in AERN2.MP.Ball.Conversions Associated Types type PlusMinusType Integer t Source # Methods plusMinus :: Integer -> t -> PlusMinusType Integer t Source #
CanBeErrorBound t => CanPlusMinus Rational t Source #
Instance details Defined in AERN2.MP.Ball.Conversions Associated Types type PlusMinusType Rational t Source # Methods plusMinus :: Rational -> t -> PlusMinusType Rational t Source #
CanBeErrorBound t => CanPlusMinus MPFloat t Source #
Instance details Defined in AERN2.MP.Ball.Conversions Associated Types type PlusMinusType MPFloat t Source # Methods plusMinus :: MPFloat -> t -> PlusMinusType MPFloat t Source #
CanBeErrorBound t => CanPlusMinus Dyadic t Source #
Instance details Defined in AERN2.MP.Ball.Conversions Associated Types type PlusMinusType Dyadic t Source # Methods plusMinus :: Dyadic -> t -> PlusMinusType Dyadic t Source #
CanBeErrorBound t => CanPlusMinus MPBall t Source #
Instance details Defined in AERN2.MP.Ball.Conversions Associated Types type PlusMinusType MPBall t Source # Methods plusMinus :: MPBall -> t -> PlusMinusType MPBall t Source #
CanBeErrorBound t => CanPlusMinus (CN MPBall) t Source #
Instance details Defined in AERN2.MP.Ball.Conversions Associated Types type PlusMinusType (CN MPBall) t Source # Methods plusMinus :: CN MPBall -> t -> PlusMinusType (CN MPBall) t Source #

(+-) :: CanPlusMinus t1 t2 => t1 -> t2 -> PlusMinusType t1 t2 infixl 6 Source #

Operator for constructing or enlarging enclosures such as balls or intervals

class CanTestContains dom e where Source #

Methods

contains Source #

Arguments

:: dom	dom
-> e	e
-> Bool

Test if e is inside dom.

Instances

Instances details

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

class CanMapInside dom e where Source #

Methods

mapInside Source #

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 Source #

class CanIntersectAsymmetric e1 e2 where Source #

A set intersection (usually partial)

Associated Types

type IntersectionType e1 e2 Source #

type IntersectionType e1 e2 = CN e1

Methods

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

Instances

Instances details

CanIntersectAsymmetric Bool Bool Source #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType Bool Bool Source # Methods intersect :: Bool -> Bool -> IntersectionType Bool Bool Source #
CanIntersectAsymmetric Kleenean Kleenean Source #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType Kleenean Kleenean Source # Methods intersect :: Kleenean -> Kleenean -> IntersectionType Kleenean Kleenean Source #
CanIntersectAsymmetric MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type IntersectionType MPBall MPBall Source # Methods intersect :: MPBall -> MPBall -> IntersectionType MPBall MPBall Source #
CanIntersectAsymmetric (CN Bool) (CN b) => CanIntersectAsymmetric Bool (CN b) Source #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType Bool (CN b) Source # Methods intersect :: Bool -> CN b -> IntersectionType Bool (CN b) Source #
CanIntersectAsymmetric (CN Kleenean) (CN b) => CanIntersectAsymmetric Kleenean (CN b) Source #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType Kleenean (CN b) Source # Methods intersect :: Kleenean -> CN b -> IntersectionType Kleenean (CN b) Source #
(CanIntersectAsymmetric MPBall b, CanBeErrors es) => CanIntersectAsymmetric MPBall (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type IntersectionType MPBall (CollectErrors es b) Source # Methods intersect :: MPBall -> CollectErrors es b -> IntersectionType MPBall (CollectErrors es b) Source #
CanIntersectAsymmetric (CN a) (CN Kleenean) => CanIntersectAsymmetric (CN a) Kleenean Source #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType (CN a) Kleenean Source # Methods intersect :: CN a -> Kleenean -> IntersectionType (CN a) Kleenean Source #
CanIntersectAsymmetric (CN a) (CN Bool) => CanIntersectAsymmetric (CN a) Bool Source #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType (CN a) Bool Source # Methods intersect :: CN a -> Bool -> IntersectionType (CN a) Bool Source #
(CanIntersectAsymmetric a b, IntersectionType a b ~ CN c) => CanIntersectAsymmetric (CN a) (CN b) Source #
Instance details Defined in AERN2.MP.Enclosure Associated Types type IntersectionType (CN a) (CN b) Source # Methods intersect :: CN a -> CN b -> IntersectionType (CN a) (CN b) Source #
(CanIntersectAsymmetric a MPBall, CanBeErrors es) => CanIntersectAsymmetric (CollectErrors es a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type IntersectionType (CollectErrors es a) MPBall Source # Methods intersect :: CollectErrors es a -> MPBall -> IntersectionType (CollectErrors es a) MPBall Source #

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

type CanIntersectBy e1 e2 = (CanIntersect e1 e2, IntersectionType e1 e2 ~ e1) Source #

type CanIntersectSameType e1 = CanIntersectBy e1 e1 Source #

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

type CanIntersectCNSameType e1 = CanIntersectCNBy e1 e1 Source #

class CanUnionAsymmetric e1 e2 where Source #

A set union (usually partial)

Associated Types

type UnionType e1 e2 Source #

type UnionType e1 e2 = CN e1

Methods

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

Instances

Instances details

CanUnionAsymmetric MPBall MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type UnionType MPBall MPBall Source # Methods union :: MPBall -> MPBall -> UnionType MPBall MPBall Source #
(CanUnionAsymmetric MPBall b, CanBeErrors es) => CanUnionAsymmetric MPBall (CollectErrors es b) Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type UnionType MPBall (CollectErrors es b) Source # Methods union :: MPBall -> CollectErrors es b -> UnionType MPBall (CollectErrors es b) Source #
(CanUnionAsymmetric a b, UnionType a b ~ CN c) => CanUnionAsymmetric (CN a) (CN b) Source #
Instance details Defined in AERN2.MP.Enclosure Associated Types type UnionType (CN a) (CN b) Source # Methods union :: CN a -> CN b -> UnionType (CN a) (CN b) Source #
(CanUnionAsymmetric a MPBall, CanBeErrors es) => CanUnionAsymmetric (CollectErrors es a) MPBall Source #
Instance details Defined in AERN2.MP.Ball.Comparisons Associated Types type UnionType (CollectErrors es a) MPBall Source # Methods union :: CollectErrors es a -> MPBall -> UnionType (CollectErrors es a) MPBall Source #

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

type CanUnionBy e1 e2 = (CanUnion e1 e2, UnionType e1 e2 ~ e1) Source #

type CanUnionSameType e1 = CanUnionBy e1 e1 Source #

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

type CanUnionCNSameType e1 = CanUnionCNBy e1 e1 Source #

Orphan instances

(CanUnionSameType t, CanTakeCNErrors t) => HasIfThenElse Kleenean t Source #
Instance details Associated Types type IfThenElseType Kleenean t # Methods ifThenElse :: Kleenean -> t -> t -> IfThenElseType Kleenean t #