Portability GHC only experimental ekmett@gmail.com

Contents

Description

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

Synopsis

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

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

# 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)Source

jacobian' :: (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)Source

# Derivatives

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

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

# Exposed Types

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 Reverse => Mode Reverse Lifted Tower => Mode Tower Mode f => Mode (AD f)

`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.