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

Stability | experimental |

Maintainer | ekmett@gmail.com |

Mixed-Mode Automatic Differentiation.

Each combinator exported from this module chooses an appropriate AD mode.

- 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)
- 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)
- 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)
- 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]
- diffUU :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> a
- diffUF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f a
- diff2UU :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)
- diff2UF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f (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)
- diffsUU :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
- diffsUF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f [a]
- diffs0UU :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
- diffs0UF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f [a]
- 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]
- newtype AD f a = AD {
- runAD :: f a

- class Lifted t => Mode t where

# Gradients

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

function calculates the gradient of a non-scalar-to-scalar function `grad`

g f`f`

with reverse-mode AD in a single pass.
The gradient is combined element-wise with the argument using the function `g`

.

grad == gradWith (\_ dx -> dx) id == gradWith const

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

# Jacobians

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

Calculate the Jacobian of a non-scalar-to-non-scalar function, automatically choosing between forward and reverse mode AD based on the number of inputs and outputs

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

Calculate the answer and Jacobian of a non-scalar-to-non-scalar function, automatically choosing between forward- and reverse- mode AD based on the relative, number of inputs and outputs. If you need to support functions where the output is only a `Functor`

, consider using `jacobianT`

from Numeric.AD.Forward or `jacobian2`

from Numeric.AD.Reverse directly.

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

calculates the Jacobian of a non-scalar-to-non-scalar function, automatically choosing between forward and reverse mode AD based on the number of inputs and outputs.
`jacobianWith`

g f

The resulting Jacobian matrix is then recombined element-wise with the input using `g`

.

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

calculates the answer and Jacobian of a non-scalar-to-non-scalar function, automatically choosing between forward and reverse mode AD based on the number of inputs and outputs.
`jacobianWith2`

g f

The resulting Jacobian matrix is then recombined element-wise with the input using `g`

.

# Synonyms

# Derivatives (Forward)

# Derivatives (Reverse)

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

# Derivatives (Tower)

# Taylor Series (Tower)

# 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