Portability GHC only experimental ekmett@gmail.com

Contents

Description

Mixed-Mode Automatic Differentiation.

For reverse mode AD we use `System.Mem.StableName.StableName` to recover sharing information from the tape to avoid combinatorial explosion, and thus run asymptotically faster than it could without such sharing information, but the use of side-effects contained herein is benign.

Synopsis

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

The `grad` function calculates the gradient of a non-scalar-to-scalar function with `Reverse` AD in a single pass.

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

The `grad2` function calculates the result and gradient of a non-scalar-to-scalar function with `Reverse` AD in a single pass.

# Jacobian

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

The `jacobian` function calculates the jacobian of a non-scalar-to-non-scalar function with reverse AD lazily in `m` passes for `m` outputs.

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

The `jacobian2` function calculates both the result and the Jacobian of a nonscalar-to-nonscalar function, using `m` invocations of reverse AD, where `m` is the output dimensionality. Applying `fmap snd` to the result will recover the result of `jacobian`

# Derivatives

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

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

The `diff2UU` function calculates the value and derivative, as a pair, of a scalar-to-scalar function.

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

diff2FU :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f a)Source

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

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

# Synonyms

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

The `diff` function is a synonym for `diffUU`.

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

The `diff2` function is a synonym for `diff2UU`.

# 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)