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

Stability | experimental |

Maintainer | ekmett@gmail.com |

Higher order derivatives via a "dual number tower".

- taylor :: Fractional a => (forall s. Mode s => AD s a -> AD s a) -> a -> a -> [a]
- taylor0 :: Fractional a => (forall s. Mode s => AD s a -> AD s a) -> a -> a -> [a]
- maclaurin :: Fractional a => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
- maclaurin0 :: Fractional a => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
- diff :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> a
- diff' :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)
- diffs :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
- diffs0 :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
- diffsF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f [a]
- diffs0F :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f [a]
- du :: (Functor f, Num a) => (forall s. f (AD s a) -> AD s a) -> f (a, a) -> a
- du' :: (Functor f, Num a) => (forall s. f (AD s a) -> AD s a) -> f (a, a) -> (a, a)
- dus :: (Functor f, Num a) => (forall s. f (AD s a) -> AD s a) -> f [a] -> [a]
- dus0 :: (Functor f, Num a) => (forall s. f (AD s a) -> AD s a) -> f [a] -> [a]
- duF :: (Functor f, Functor g, Num a) => (forall s. f (AD s a) -> g (AD s a)) -> f (a, a) -> g a
- duF' :: (Functor f, Functor g, Num a) => (forall s. f (AD s a) -> g (AD s a)) -> f (a, a) -> g (a, a)
- dusF :: (Functor f, Functor g, Num a) => (forall s. f (AD s a) -> g (AD s a)) -> f [a] -> g [a]
- dus0F :: (Functor f, Functor g, Num a) => (forall s. f (AD s a) -> g (AD s a)) -> f [a] -> g [a]
- diffsM :: (Monad m, Num a) => (forall s. Mode s => AD s a -> m (AD s a)) -> a -> m [a]
- diffs0M :: (Monad m, Num a) => (forall s. Mode s => AD s a -> m (AD s a)) -> a -> m [a]
- class Lifted t => Mode t where
- newtype AD f a = AD {
- runAD :: f a

# Taylor Series

# Maclaurin Series

maclaurin0 :: Fractional a => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]Source

# Derivatives

# Directional Derivatives

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

duF' :: (Functor f, Functor g, Num a) => (forall s. f (AD s a) -> g (AD s a)) -> f (a, a) -> g (a, a)Source

dusF :: (Functor f, Functor g, Num a) => (forall s. f (AD s a) -> g (AD s a)) -> f [a] -> g [a]Source

dus0F :: (Functor f, Functor g, Num a) => (forall s. f (AD s a) -> g (AD s a)) -> f [a] -> g [a]Source

# Monadic Combinators

# 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) | |

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) |