Numeric.AD.Mode.Tower

Higher order derivatives via a "dual number tower".

Documentation

data AD s a

Instances

Typeable2 AD

Bounded a => Bounded (AD s a)

Enum a => Enum (AD s a)

Eq a => Eq (AD s a)

Floating a => Floating (AD s a)

Fractional a => Fractional (AD s a)

Num a => Num (AD s a)

Ord a => Ord (AD s a)

Read a => Read (AD s a)

Real a => Real (AD s a)

RealFloat a => RealFloat (AD s a)

RealFrac a => RealFrac (AD s a)

Show a => Show (AD s a)

Erf a => Erf (AD s a)

InvErf a => InvErf (AD s a)

Mode a => Mode (AD s a)

data Tower a

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

Instances

Typeable1 Tower

(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)

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

Embed a constant

Taylor Series

taylor :: Fractional a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> a -> [a]

taylor0 :: Fractional a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> a -> [a]

Maclaurin Series

maclaurin :: Fractional a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> [a]

maclaurin0 :: Fractional a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> [a]

Derivatives

diff :: Num a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> a

diff' :: Num a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> (a, a)

diffs :: Num a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> [a]

diffs0 :: Num a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> [a]

diffsF :: (Functor f, Num a) => (forall s. AD s (Tower a) -> f (AD s (Tower a))) -> a -> f [a]

diffs0F :: (Functor f, Num a) => (forall s. AD s (Tower a) -> f (AD s (Tower a))) -> a -> f [a]

Directional Derivatives

du :: (Functor f, Num a) => (forall s. f (AD s (Tower a)) -> AD s (Tower a)) -> f (a, a) -> a

du' :: (Functor f, Num a) => (forall s. f (AD s (Tower a)) -> AD s (Tower a)) -> f (a, a) -> (a, a)

dus :: (Functor f, Num a) => (forall s. f (AD s (Tower a)) -> AD s (Tower a)) -> f [a] -> [a]

dus0 :: (Functor f, Num a) => (forall s. f (AD s (Tower a)) -> AD s (Tower a)) -> f [a] -> [a]

duF :: (Functor f, Functor g, Num a) => (forall s. f (AD s (Tower a)) -> g (AD s (Tower a))) -> f (a, a) -> g a

duF' :: (Functor f, Functor g, Num a) => (forall s. f (AD s (Tower a)) -> g (AD s (Tower a))) -> f (a, a) -> g (a, a)

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

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