Numeric.AD.Mode.Tower

Contents

Description

Higher order derivatives via a "dual number tower".

Synopsis

Documentation

data AD s a Source

Instances

Bounded a => Bounded (AD s a) Source
Enum a => Enum (AD s a) Source
Eq a => Eq (AD s a) Source
Floating a => Floating (AD s a) Source
Fractional a => Fractional (AD s a) Source
Num a => Num (AD s a) Source
Ord a => Ord (AD s a) Source
Read a => Read (AD s a) Source
Real a => Real (AD s a) Source
RealFloat a => RealFloat (AD s a) Source
RealFrac a => RealFrac (AD s a) Source
Show a => Show (AD s a) Source
Erf a => Erf (AD s a) Source
InvErf a => InvErf (AD s a) Source
Mode a => Mode (AD s a) Source
type Scalar (AD s a) = Scalar a Source

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) Source
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) Source
Erf a => Erf (Tower a)
InvErf a => InvErf (Tower a)
Num a => Mode (Tower a) Source
Num a => Jacobian (Tower a) Source
type Scalar (Tower a) = a Source
type D (Tower a) = Tower a Source

Embed a constant

Taylor Series

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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) Source

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

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