Safe Haskell	None
Language	Haskell2010

Numeric.AffineForm

Synopsis

type AFM t a = AFMT t Identity a
data AF s a
newEps :: Num a => AFM t (AF t a)
newFromInterval :: (Eq a, Fractional a, ExplicitRounding a) => Interval a -> AFM t (AF t a)
singleton :: Num a => a -> AF s a
evalAFM :: (forall t. AFM t b) -> b
radius :: (Num a, ExplicitRounding a) => AF s a -> a
midpoint :: AF s a -> a
inf :: (Num a, ExplicitRounding a) => AF s a -> a
sup :: (Num a, ExplicitRounding a) => AF s a -> a
interval :: (Num a, Ord a, ExplicitRounding a) => AF s a -> Interval a
afError :: AF s a -> a
member :: (Num a, Ord a, ExplicitRounding a) => a -> AF s a -> Bool
epscount_ :: AF s a -> Int
setMidpoint :: (Num a, ExplicitRounding a) => a -> AF s a -> AF s a
fix :: (Num a, Ord a, ExplicitRounding a) => AF s a -> [a] -> Interval a
addError :: (Num a, Ord a) => AF s a -> a -> AF s a
(.+) :: (Num a, ExplicitRounding a) => a -> AF s a -> AF s a
(.*) :: (Eq a, Num a, Ord a, ExplicitRounding a) => a -> AF s a -> AF s a

Documentation

type AFM t a = AFMT t Identity a Source #

data AF s a Source #

An affine form is defined by its midpoint, list of epsilon coefficients and an error coefficient

Instances

(Floating a, RealFrac a, ExplicitRounding a, Ord a) => Floating (AF s a) Source #
Instance details Defined in Numeric.AffineForm.Internal Methods pi :: AF s a # exp :: AF s a -> AF s a # log :: AF s a -> AF s a # sqrt :: AF s a -> AF s a # (**) :: AF s a -> AF s a -> AF s a # logBase :: AF s a -> AF s a -> AF s a # sin :: AF s a -> AF s a # cos :: AF s a -> AF s a # tan :: AF s a -> AF s a # asin :: AF s a -> AF s a # acos :: AF s a -> AF s a # atan :: AF s a -> AF s a # sinh :: AF s a -> AF s a # cosh :: AF s a -> AF s a # tanh :: AF s a -> AF s a # asinh :: AF s a -> AF s a # acosh :: AF s a -> AF s a # atanh :: AF s a -> AF s a # log1p :: AF s a -> AF s a # expm1 :: AF s a -> AF s a # log1pexp :: AF s a -> AF s a # log1mexp :: AF s a -> AF s a #
(Fractional a, ExplicitRounding a, Ord a) => Fractional (AF s a) Source #
Instance details Defined in Numeric.AffineForm.Internal Methods (/) :: AF s a -> AF s a -> AF s a # recip :: AF s a -> AF s a # fromRational :: Rational -> AF s a #
(Fractional a, ExplicitRounding a, Ord a) => Num (AF s a) Source #
Instance details Defined in Numeric.AffineForm.Internal Methods (+) :: AF s a -> AF s a -> AF s a # (-) :: AF s a -> AF s a -> AF s a # (*) :: AF s a -> AF s a -> AF s a # negate :: AF s a -> AF s a # abs :: AF s a -> AF s a # signum :: AF s a -> AF s a # fromInteger :: Integer -> AF s a #
Show a => Show (AF s a) Source #
Instance details Defined in Numeric.AffineForm.Internal Methods showsPrec :: Int -> AF s a -> ShowS # show :: AF s a -> String # showList :: [AF s a] -> ShowS #
(Ord a, Fractional a, ExplicitRounding a) => Subdivisible (AF s a) Source #
Instance details Defined in Numeric.AffineForm.Internal Methods subdivide :: AF s a -> Int -> [AF s a] Source # combine2 :: AF s a -> AF s a -> AF s a Source # combine :: [AF s a] -> AF s a Source #

newEps :: Num a => AFM t (AF t a) Source #

This gives an affine form with midpoint 0 and radius 1. This affine form does not share epsilons with any affine forms created before it. It can be used to instantiate new affine forms.

newFromInterval :: (Eq a, Fractional a, ExplicitRounding a) => Interval a -> AFM t (AF t a) Source #

Creates a new affine form that covers the interval. This affine form does not share epsilons with any affine forms created before it.

singleton :: Num a => a -> AF s a Source #

Creates a new affine form that represents some exact value

evalAFM :: (forall t. AFM t b) -> b Source #

Evaluates the AFM monad. It is not possible to get an AF out of an AFM monad.

radius :: (Num a, ExplicitRounding a) => AF s a -> a Source #

Gives the radius of the affine form

midpoint :: AF s a -> a Source #

Gives the midpoint of the affine form (the first term of the affine form).

inf :: (Num a, ExplicitRounding a) => AF s a -> a Source #

Gives the minimal possible value of the affine form