Numeric.AD.Rank1.Tower

Higher order derivatives via a "dual number tower".

Documentation

data Tower a

Tower is an AD Mode that calculates a tangent tower by forward AD, and provides fast diffsUU, diffsUF

Instances

(Num a, Bounded a) => Bounded (Tower a)

(Num a, Enum a) => Enum (Tower a)

(Num a, Eq a) => Eq (Tower a)

Floating a => Floating (Tower a)

Fractional a => Fractional (Tower a)

Data a => Data (Tower a)

Num a => Num (Tower a)

(Num a, Ord a) => Ord (Tower a)

Real a => Real (Tower a)

RealFloat a => RealFloat (Tower a)

RealFrac a => RealFrac (Tower a)

Show a => Show (Tower a)

Erf a => Erf (Tower a)

InvErf a => InvErf (Tower a)

Num a => Mode (Tower a)

Num a => Jacobian (Tower a)

Typeable (* -> *) Tower

type Scalar (Tower a) = a

type D (Tower a) = Tower a

auto :: Mode t => Scalar t -> t

Embed a constant

Taylor Series

taylor :: Fractional a => (Tower a -> Tower a) -> a -> a -> [a]

taylor0 :: Fractional a => (Tower a -> Tower a) -> a -> a -> [a]

Maclaurin Series

maclaurin :: Fractional a => (Tower a -> Tower a) -> a -> [a]

maclaurin0 :: Fractional a => (Tower a -> Tower a) -> a -> [a]

Derivatives

diff :: Num a => (Tower a -> Tower a) -> a -> a

diff' :: Num a => (Tower a -> Tower a) -> a -> (a, a)

diffs :: Num a => (Tower a -> Tower a) -> a -> [a]

diffs0 :: Num a => (Tower a -> Tower a) -> a -> [a]

diffsF :: (Functor f, Num a) => (Tower a -> f (Tower a)) -> a -> f [a]

diffs0F :: (Functor f, Num a) => (Tower a -> f (Tower a)) -> a -> f [a]

Directional Derivatives

du :: (Functor f, Num a) => (f (Tower a) -> Tower a) -> f (a, a) -> a

du' :: (Functor f, Num a) => (f (Tower a) -> Tower a) -> f (a, a) -> (a, a)

dus :: (Functor f, Num a) => (f (Tower a) -> Tower a) -> f [a] -> [a]

dus0 :: (Functor f, Num a) => (f (Tower a) -> Tower a) -> f [a] -> [a]

duF :: (Functor f, Functor g, Num a) => (f (Tower a) -> g (Tower a)) -> f (a, a) -> g a

duF' :: (Functor f, Functor g, Num a) => (f (Tower a) -> g (Tower a)) -> f (a, a) -> g (a, a)

dusF :: (Functor f, Functor g, Num a) => (f (Tower a) -> g (Tower a)) -> f [a] -> g [a]

dus0F :: (Functor f, Functor g, Num a) => (f (Tower a) -> g (Tower a)) -> f [a] -> g [a]