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

Stability | experimental |

Maintainer | ekmett@gmail.com |

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.

- 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)
- jacobian :: (Traversable f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f a)
- 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)
- 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)
- diffFU :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f a
- diff2FU :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f 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)
- 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

# 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

# Derivatives

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.

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

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) | |

Var (AD Reverse a) 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