Portability GHC only experimental ekmett@gmail.com

Contents

Description

Forward mode automatic differentiation

Synopsis

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

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

# Jacobian

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

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

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

# Derivatives

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

The `diffUU` function calculates the first derivative of a scalar-to-scalar function by `Forward` `AD`

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

The `diff2UU` function calculates the result and first derivative of scalar-to-scalar function by `Forward` `AD`

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

The `diffUF` function calculates the first derivative of scalar-to-nonscalar function by `Forward` `AD`

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

The `diff2UF` function calculates the result and first derivative of a scalar-to-non-scalar function by `Forward` `AD`

# Synonyms

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

The `diff2` function calculates the first derivative of scalar-to-scalar function by `Forward` `AD`

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

The `diff2` function calculates the result and first derivative of scalar-to-scalar function by `Forward` `AD`

# Exposed Types

`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

Instances

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)