Numeric.AD.Directed

Allows the choice of AD Mode to be specified at the term level for benchmarking or more complicated usage patterns.

Derivatives

diffUU :: Num a => Direction -> (forall s. Mode s => AD s a -> AD s a) -> a -> a

diff2UU :: Num a => Direction -> (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)

Common access patterns

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

diff2 :: Num a => Direction -> (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)

Jacobians

jacobian :: (Traversable f, Traversable g, Num a) => Direction -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f a)

jacobian2 :: (Traversable f, Traversable g, Num a) => Direction -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (a, f a)

Gradients

grad :: (Traversable f, Num a) => Direction -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f a

grad2 :: (Traversable f, Num a) => Direction -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f a)

Exposed Types

data Direction

Constructors

Forward

Reverse

Tower

Mixed

Instances

Bounded Direction

Enum Direction

Eq Direction

Ord Direction

Read Direction

Show Direction

Ix Direction

class Lifted t => Mode t where

Methods

lift :: Num a => a -> t a

Embed a constant

(<+>) :: Num a => t a -> t a -> t a

Vector sum

(*^) :: Num a => a -> t a -> t a

Scalar-vector multiplication

(^*) :: Num a => t a -> a -> t a

Vector-scalar multiplication

(^/) :: Fractional a => t a -> a -> t a

Scalar division

zero :: Num a => t a

 'zero' = 'lift' 0

Instances

Mode Id

Lifted Forward => Mode Forward

Lifted Reverse => Mode Reverse

Lifted Tower => Mode Tower

Mode f => Mode (AD f)

newtype AD f a

AD serves as a common wrapper for different Mode instances, exposing a traditional numerical tower. Universal quantification is used to limit the actions in user code to machinery that will return the same answers under all AD modes, allowing us to use modes interchangeably as both the type level "brand" and dictionary, providing a common API.

Constructors

AD

Fields

runAD :: f a

Instances

Primal f => Primal (AD f)

Mode f => Mode (AD f)

Lifted f => Lifted (AD f)

(Num a, Lifted f, Bounded a) => Bounded (AD f a)

(Num a, Lifted f, Enum a) => Enum (AD f a)

(Num a, Lifted f, Eq a) => Eq (AD f a)

(Lifted f, Floating a) => Floating (AD f a)

(Lifted f, Fractional a) => Fractional (AD f a)

(Lifted f, Num a) => Num (AD f a)

(Num a, Lifted f, Ord a) => Ord (AD f a)

(Lifted f, Real a) => Real (AD f a)

(Lifted f, RealFloat a) => RealFloat (AD f a)

(Lifted f, RealFrac a) => RealFrac (AD f a)

(Lifted f, Show a) => Show (AD f a)

Var (AD Reverse a) a