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.

- diffUU :: Num a => Direction -> (forall s. Mode s => AD s a -> AD s a) -> a -> a
- diff2UU :: Num a => Direction -> (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)
- diff :: Num a => Direction -> (forall s. Mode s => AD s a -> AD s a) -> a -> a
- diff2 :: Num a => Direction -> (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)
- 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)
- jacobian2 :: (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)
- grad :: (Traversable f, Num a) => Direction -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f a
- grad2 :: (Traversable f, Num a) => Direction -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f a)
- data Direction
- class Lifted t => Mode t where
- newtype AD f a = AD {
- runAD :: f a

# Derivatives

# Common access patterns

# 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

jacobian2 :: (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

# Gradients

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

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

# Exposed Types

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) | |

(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) | |

Var (AD Reverse a) a |