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

Stability | experimental |

Maintainer | ekmett@gmail.com |

Forward mode automatic differentiation

- grad :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f a
- grad2 :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f a)
- gradWith :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f b
- gradWith2 :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f b)
- jacobian :: (Traversable f, Traversable g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f a)
- 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)
- jacobianT :: (Traversable f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> f (g a)
- jacobianWith :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f b)
- jacobianWith2 :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (a, f b)
- jacobianWithT :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> f (g b)
- diffUU :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> a
- diff2UU :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)
- diffUF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f a
- diff2UF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f (a, a)
- diffMU :: (Functor f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> a
- diff2MU :: (Functor f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> (a, a)
- diff :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> a
- diff2 :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)
- newtype AD f a = AD {
- runAD :: f a

- class Lifted t => Mode t where

# Gradient

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

gradWith :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f bSource

gradWith2 :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f b)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

A fast, simple transposed Jacobian computed with forward-mode AD.

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

jacobianWith2 :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (a, f b)Source

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

A fast, simple transposed Jacobian computed with forward-mode AD.

# Derivatives

# Directional Derivatives

diff2MU :: (Functor f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> (a, a)Source

# Synonyms

# 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.

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) |

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