Numeric.AD.Reverse

Mixed-Mode Automatic Differentiation.

For reverse mode AD we use System.Mem.StableName.StableName to recover sharing information from the tape to avoid combinatorial explosion, and thus run asymptotically faster than it could without such sharing information, but the use of side-effects contained herein is benign.

Gradient

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

The grad function calculates the gradient of a non-scalar-to-scalar function with Reverse AD in a single pass.

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

The grad2 function calculates the result and gradient of a non-scalar-to-scalar function with Reverse AD in a single pass.

Jacobian

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

The jacobian function calculates the jacobian of a non-scalar-to-non-scalar function with reverse AD lazily in m passes for m outputs.

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

The jacobian2 function calculates both the result and the Jacobian of a nonscalar-to-nonscalar function, using m invocations of reverse AD, where m is the output dimensionality. Applying fmap snd to the result will recover the result of jacobian

Derivatives

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

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

The diff2UU function calculates the value and derivative, as a pair, of a scalar-to-scalar function.

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

diff2FU :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f a)

diffUF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f a

diff2UF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f (a, a)

Synonyms

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

The diff function is a synonym for diffUU.

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

The diff2 function is a synonym for diff2UU.

Exposed Types

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)

Iso (f a) (AD f a)

(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

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)