ad-1.1.0: Automatic Differentiation

Portability GHC only experimental ekmett@gmail.com

Numeric.AD.Mode.Directed

Contents

Description

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

Synopsis

# Gradients

grad :: (Traversable f, Num a) => Direction -> FU f a -> f a -> f aSource

grad' :: (Traversable f, Num a) => Direction -> FU f a -> f a -> (a, f a)Source

# Jacobians

jacobian :: (Traversable f, Traversable g, Num a) => Direction -> FF f g a -> f a -> g (f a)Source

jacobian' :: (Traversable f, Traversable g, Num a) => Direction -> FF f g a -> f a -> g (a, f a)Source

# Derivatives

diff :: Num a => Direction -> UU a -> a -> aSource

diff' :: Num a => Direction -> UU a -> a -> (a, a)Source

# Exposed Types

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

A scalar-to-scalar automatically-differentiable function.

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

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

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

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)Source

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

data Direction Source

Constructors

 Forward Reverse Tower Mixed

class Lifted t => Mode t whereSource

Methods

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

Embed a constant

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

Vector sum

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

Scalar-vector multiplication

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

Vector-scalar multiplication

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

Scalar division

zero :: Num a => t aSource

``` '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)

newtype AD f a Source

`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 FieldsrunAD :: 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) (Num a, Lifted f, Show a) => Show (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) (Cofree [] 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