Numeric.AD.Types

Documentation

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

Typeable1 f => Typeable1 (AD f)

Primal f => Primal (AD f)

Mode f => Mode (AD f)

Lifted f => Lifted (AD f)

Var (AD Reverse)

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)

(Typeable1 f, Typeable a, Data (f a), Data a) => Data (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)

(Typeable1 f, Typeable a) => Typeable (AD f a)

Num a => Grad (AD Reverse a) [a] (a, [a]) a

Num a => Grad (AD Sparse a) [a] (a, [a]) a

Grads i o a => Grads (AD Sparse a -> i) (a -> o) a

Num a => Grads (AD Sparse a) (Stream [] a) a

Grad i o o' a => Grad (AD Reverse a -> i) (a -> o) (a -> o') a

Grad i o o' a => Grad (AD Sparse a -> i) (a -> o) (a -> o') a

Differentiable Functions

type UU a = forall s. Mode s => AD s a -> AD s a

A scalar-to-scalar automatically-differentiable function.

type UF f a = forall s. Mode s => AD s a -> f (AD s a)

A scalar-to-non-scalar automatically-differentiable function.

type FU f a = forall s. Mode s => f (AD s a) -> AD s a

A non-scalar-to-scalar automatically-differentiable function.

type FF f g a = forall s. Mode s => f (AD s a) -> g (AD s a)

A non-scalar-to-non-scalar automatically-differentiable function.

Tensors

data Tensors f a

Constructors

a :- (Tensors f (f a))

Instances

Functor f => Functor (Tensors f)

Typeable1 f => Typeable1 (Tensors f)

Foldable f => Foldable (Tensors f)

Traversable f => Traversable (Tensors 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.

(Typeable1 f, Typeable a) => Typeable (Tensors f a)

headT :: Tensors f a -> a

tailT :: Tensors f a -> Tensors f (f a)

tensors :: Functor f => Stream f a -> Tensors f a

f-Branching Streams

data Stream f a

Constructors

a :< (f (Stream f a))

Instances

Functor f => Functor (Stream f)

Typeable1 f => Typeable1 (Stream f)

Foldable f => Foldable (Stream f)

Traversable f => Traversable (Stream f)

Functor f => Comonad (Stream f)

Functor f => Copointed (Stream f)

(Typeable1 f, Data (f (Stream f a)), Data a) => Data (Stream f a)

(Show a, Show (f (Stream f a))) => Show (Stream f a)

(Typeable1 f, Typeable a) => Typeable (Stream f a)

Num a => Grads (AD Sparse a) (Stream [] a) a

headS :: Stream f a -> a

tailS :: Stream f a -> f (Stream f a)

unfoldS :: Functor f => (a -> (b, f a)) -> a -> Stream f b

An Identity Mode.

newtype Id a

Constructors

Id a

Instances

Monad Id

Functor Id

Typeable1 Id

Applicative Id

Foldable Id

Traversable Id

Primal Id

Mode Id

Lifted Id

Iso a (Id a)

Bounded a => Bounded (Id a)

Enum a => Enum (Id a)

Eq a => Eq (Id a)

Floating a => Floating (Id a)

Fractional a => Fractional (Id a)

Data a => Data (Id a)

Num a => Num (Id a)

Ord a => Ord (Id a)

Real a => Real (Id a)

RealFloat a => RealFloat (Id a)

RealFrac a => RealFrac (Id a)

Show a => Show (Id a)

Monoid a => Monoid (Id a)

probe :: a -> AD Id a

unprobe :: AD Id a -> a

probed :: f a -> f (AD Id a)

unprobed :: f (AD Id a) -> f a

Apply functions that use lift

lowerUU :: UU a -> a -> a

lowerUF :: UF f a -> a -> f a

lowerFU :: FU f a -> f a -> a

lowerFF :: FF f g a -> f a -> g a