Numeric.AD.Classes

AD Modes

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 Tower => Mode Tower

Lifted Reverse => Mode Reverse

Lifted Sparse => Mode Sparse

Mode f => Mode (AD f)

(Traversable f, Lifted (Dense f)) => Mode (Dense f)

(Mode f, Mode g) => Mode (ComposeMode f g)

Comonads

class Functor f => Copointed f where

Methods

extract :: f a -> a

Instances

Functor f => Copointed (Stream f)

Functor f => Copointed (Tensors f)

While we can not be a Comonad without a fzip-like operation, you can use the comonad for Stream f a to manipulate a structure comonadically that you can turn into Tensors.

class Copointed f => Comonad f where

Methods

duplicate :: f a -> f (f a)

extend :: (f a -> b) -> f a -> f b

Instances

Functor f => Comonad (Stream f)