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

Stability | experimental |

Maintainer | ekmett@gmail.com |

Safe Haskell | None |

- class Lifted t => Mode t where
- newtype AD f a = AD {
- runAD :: f a

- data Jet f a = a :- (Jet f (f a))
- headJet :: Jet f a -> a
- tailJet :: Jet f a -> Jet f (f a)
- jet :: Functor f => Cofree f a -> Jet f a
- lowerUU :: (forall s. Mode s => AD s a -> AD s a) -> a -> a
- lowerUF :: (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f a
- lowerFU :: (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> a
- lowerFF :: (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g a

# AD modes

class Lifted t => Mode t whereSource

isKnownConstant :: t a -> BoolSource

allowed to return False for items with a zero derivative, but we'll give more NaNs than strictly necessary

isKnownZero :: Num a => t a -> BoolSource

allowed to return False for zero, but we give more NaN's than strictly necessary then

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

(<**>) :: Floating a => t a -> t a -> t aSource

Exponentiation, this should be overloaded if you can figure out anything about what is constant!

'zero' = 'lift' 0

Lifted Tower => Mode Tower | |

Lifted Sparse => Mode Sparse | |

Mode Id | |

Lifted Forward => Mode Forward | |

Lifted Reverse => Mode Reverse | |

(Lifted (AD f), Mode f) => Mode (AD f) | |

(Reifies s Tape, Lifted (Chain s)) => Mode (Chain s) | |

(Traversable f, Lifted (Dense f)) => Mode (Dense f) | |

(Lifted (ComposeMode f g), Mode f, Mode g) => Mode (ComposeMode f g) |

# AD variables

`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.

Typeable1 f => Typeable1 (AD f) | |

Primal f => Primal (AD f) | |

(Lifted (AD f), Mode f) => Mode (AD f) | |

Lifted f => Lifted (AD f) | |

(Primal (AD f), Var f) => Var (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) | |

(Fractional (AD f a), Lifted f, Floating a) => Floating (AD f a) | |

(Num (AD f a), Lifted f, Fractional a) => Fractional (AD f a) | |

(Typeable (AD f a), Typeable1 f, Typeable a, Data (f a), Data a) => Data (AD f a) | |

(Lifted f, Num a) => Num (AD f a) | |

(Eq (AD f a), Num a, Lifted f, Ord a) => Ord (AD f a) | |

(Num (AD f a), Ord (AD f a), Lifted f, Real a) => Real (AD f a) | |

(RealFrac (AD f a), Floating (AD f a), Lifted f, RealFloat a) => RealFloat (AD f a) | |

(Real (AD f a), Fractional (AD f a), Lifted f, RealFrac a) => RealFrac (AD f a) | |

(Num a, Lifted f, Show a) => Show (AD f a) | |

Num a => Grad (AD Sparse a) [a] (a, [a]) a | |

Num a => Grad (AD Reverse a) [a] (a, [a]) a | |

(Num a, Grads i o a) => Grads (AD Sparse a -> i) (a -> o) a | |

Num a => Grads (AD Sparse a) (Cofree [] a) a | |

(Num a, Grad i o o' a) => Grad (AD Sparse a -> i) (a -> o) (a -> o') a | |

(Num a, Grad i o o' a) => Grad (AD Reverse a -> i) (a -> o) (a -> o') a |

# Jets

# Apply functions that use `lift`

lowerUU :: (forall s. Mode s => AD s a -> AD s a) -> a -> aSource

Evaluate a scalar-to-scalar function in the trivial identity AD mode.

lowerUF :: (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f aSource

Evaluate a scalar-to-nonscalar function in the trivial identity AD mode.