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

Stability | experimental |

Maintainer | ekmett@gmail.com |

Safe Haskell | Safe-Infered |

Higher order derivatives via a "dual number tower".

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

# Taylor Series

taylor :: Fractional a => UU a -> a -> a -> [a]Source

taylor0 :: Fractional a => UU a -> a -> a -> [a]Source

# Maclaurin Series

maclaurin :: Fractional a => UU a -> a -> [a]Source

maclaurin0 :: Fractional a => UU a -> a -> [a]Source

# Derivatives

# Directional Derivatives

# Exposed Types

type UU a = forall s. Mode s => AD s a -> AD s aSource

A scalar-to-scalar automatically-differentiable function.

type UF f a = forall s. Mode s => AD s a -> f (AD s a)Source

A scalar-to-non-scalar automatically-differentiable function.

type FU f a = forall s. Mode s => f (AD s a) -> AD s aSource

A non-scalar-to-scalar automatically-differentiable function.

type FF f g a = forall s. Mode s => f (AD s a) -> g (AD s a)Source

A non-scalar-to-non-scalar automatically-differentiable function.

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

`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) | |

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) | |

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

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

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

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

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

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

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

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