polynomials-bernstein-1.1.2: A solver for systems of polynomial equations in bernstein form

Safe HaskellNone
LanguageHaskell98

Algebra.Polynomials.Numerical

Contents

Description

This module contains the definition of the main arithmetic tools used in Metafont'.

Synopsis

Raw operations

fromIntegral# :: Integral x => x -> (#Double, Double#) #

Converts an Integral value into an interval.

plus :: Double -> Double -> Double -> Double -> (#Double, Double#) #

Interval addition

minus :: Double -> Double -> Double -> Double -> (#Double, Double#) #

Interval substraction

over :: Double -> Double -> Double -> Double -> (#Double, Double#) #

Interval division

times :: Double -> Double -> Double -> Double -> (#Double, Double#) #

Interval multiplication

sqrt# :: Double -> Double -> (#Double, Double#) #

cos# :: Double -> Double -> (#Double, Double#) #

Interval cosine

sin# :: Double -> Double -> (#Double, Double#) #

Interval sine

acos# :: Double -> Double -> (#Double, Double#) #

asin# :: Double -> Double -> (#Double, Double#) #

The Interval type

data Interval #

The interval type (most of its operations are calls to the raw functions)

Constructors

Interval 

Fields

Instances
Eq Interval # 
Instance details

Defined in Algebra.Polynomials.Numerical

Methods

(==) :: Interval -> Interval -> Bool #

(/=) :: Interval -> Interval -> Bool #

Floating Interval # 
Instance details

Defined in Algebra.Polynomials.Numerical

Methods

pi :: Interval #

exp :: Interval -> Interval #

log :: Interval -> Interval #

sqrt :: Interval -> Interval #

(**) :: Interval -> Interval -> Interval #

logBase :: Interval -> Interval -> Interval #

sin :: Interval -> Interval #

cos :: Interval -> Interval #

tan :: Interval -> Interval #

asin :: Interval -> Interval #

acos :: Interval -> Interval #

atan :: Interval -> Interval #

sinh :: Interval -> Interval #

cosh :: Interval -> Interval #

tanh :: Interval -> Interval #

asinh :: Interval -> Interval #

acosh :: Interval -> Interval #

atanh :: Interval -> Interval #

log1p :: Interval -> Interval #

expm1 :: Interval -> Interval #

log1pexp :: Interval -> Interval #

log1mexp :: Interval -> Interval #

Fractional Interval # 
Instance details

Defined in Algebra.Polynomials.Numerical

Methods

(/) :: Interval -> Interval -> Interval #

recip :: Interval -> Interval #

fromRational :: Rational -> Interval #

Num Interval # 
Instance details

Defined in Algebra.Polynomials.Numerical

Methods

(+) :: Interval -> Interval -> Interval #

(-) :: Interval -> Interval -> Interval #

(*) :: Interval -> Interval -> Interval #

negate :: Interval -> Interval #

abs :: Interval -> Interval #

signum :: Interval -> Interval #

fromInteger :: Integer -> Interval #

Show Interval # 
Instance details

Defined in Algebra.Polynomials.Numerical

Methods

showsPrec :: Int -> Interval -> ShowS #

show :: Interval -> String #

showList :: [Interval] -> ShowS #

Unbox Interval # 
Instance details

Defined in Algebra.Polynomials.Numerical

Vector Vector Interval # 
Instance details

Defined in Algebra.Polynomials.Numerical

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) Interval -> m (Vector Interval) #

basicUnsafeThaw :: PrimMonad m => Vector Interval -> m (Mutable Vector (PrimState m) Interval) #

basicLength :: Vector Interval -> Int #

basicUnsafeSlice :: Int -> Int -> Vector Interval -> Vector Interval #

basicUnsafeIndexM :: Monad m => Vector Interval -> Int -> m Interval #

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) Interval -> Vector Interval -> m () #

elemseq :: Vector Interval -> Interval -> b -> b #

MVector MVector Interval # 
Instance details

Defined in Algebra.Polynomials.Numerical

Methods

basicLength :: MVector s Interval -> Int #

basicUnsafeSlice :: Int -> Int -> MVector s Interval -> MVector s Interval #

basicOverlaps :: MVector s Interval -> MVector s Interval -> Bool #

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) Interval) #

basicInitialize :: PrimMonad m => MVector (PrimState m) Interval -> m () #

basicUnsafeReplicate :: PrimMonad m => Int -> Interval -> m (MVector (PrimState m) Interval) #

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) Interval -> Int -> m Interval #

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) Interval -> Int -> Interval -> m () #

basicClear :: PrimMonad m => MVector (PrimState m) Interval -> m () #

basicSet :: PrimMonad m => MVector (PrimState m) Interval -> Interval -> m () #

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) Interval -> MVector (PrimState m) Interval -> m () #

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) Interval -> MVector (PrimState m) Interval -> m () #

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) Interval -> Int -> m (MVector (PrimState m) Interval) #

newtype Vector Interval # 
Instance details

Defined in Algebra.Polynomials.Numerical

newtype Vector Interval = V_Interval (Vector (Double, Double))
newtype MVector s Interval # 
Instance details

Defined in Algebra.Polynomials.Numerical

newtype MVector s Interval = MV_Interval (MVector s (Double, Double))

class Intervalize a where #

Two common operations on types defined with intervals.

Methods

intervalize :: a Double -> a Interval #

intersects :: a Interval -> a Interval -> Bool #

Instances
Num (Bernsteinp a Interval) => Intervalize (Bernsteinp a) # 
Instance details

Defined in Algebra.Polynomials.Bernstein

Methods

intervalize :: Bernsteinp a Double -> Bernsteinp a Interval #

intersects :: Bernsteinp a Interval -> Bernsteinp a Interval -> Bool #

interval :: Double -> Interval #

Converts an optimal IEEE-754 representation of a number into an optimal interval containing this number.

intersectsd :: Interval -> Interval -> Bool #

Intersection of two Intervals.

union :: Interval -> Interval -> Interval #

Union of two intersecting intervals (undefined behaviour if they do not intersect).

fpred :: Double -> Double #

fsucc :: Double -> Double #