Portability | GHC only |
---|---|

Stability | experimental |

Maintainer | ekmett@gmail.com |

Allows the choice of AD `Mode`

to be specified at the term level for
benchmarking or more complicated usage patterns.

- grad :: (Traversable f, Num a) => Direction -> FU f a -> f a -> f a
- grad' :: (Traversable f, Num a) => Direction -> FU f a -> f a -> (a, f a)
- jacobian :: (Traversable f, Traversable g, Num a) => Direction -> FF f g a -> f a -> g (f a)
- jacobian' :: (Traversable f, Traversable g, Num a) => Direction -> FF f g a -> f a -> g (a, f a)
- diff :: Num a => Direction -> UU a -> a -> a
- diff' :: Num a => Direction -> UU a -> a -> (a, a)
- type UU a = forall s. Mode s => AD s a -> AD s a
- type UF f a = forall s. Mode s => AD s a -> f (AD s a)
- type FU f a = forall s. Mode s => f (AD s a) -> AD s a
- type FF f g a = forall s. Mode s => f (AD s a) -> g (AD s a)
- data Direction
- class Lifted t => Mode t where
- newtype AD f a = AD {
- runAD :: f a

# Gradients

# 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

# 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.

class Lifted t => Mode t whereSource

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' = 'lift' 0

`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.

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) | |

(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) |