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

Stability | experimental |

Maintainer | ekmett@gmail.com |

Forward mode automatic differentiation

- grad :: (Traversable f, Num a) => FU f a -> f a -> f a
- grad' :: (Traversable f, Num a) => FU f a -> f a -> (a, f a)
- gradWith :: (Traversable f, Num a) => (a -> a -> b) -> FU f a -> f a -> f b
- gradWith' :: (Traversable f, Num a) => (a -> a -> b) -> FU f a -> f a -> (a, f b)
- jacobian :: (Traversable f, Traversable g, Num a) => FF f g a -> f a -> g (f a)
- jacobian' :: (Traversable f, Traversable g, Num a) => FF f g a -> f a -> g (a, f a)
- jacobianWith :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> FF f g a -> f a -> g (f b)
- jacobianWith' :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> FF f g a -> f a -> g (a, f b)
- jacobianT :: (Traversable f, Functor g, Num a) => FF f g a -> f a -> f (g a)
- jacobianWithT :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> FF f g a -> f a -> f (g b)
- hessianProduct :: (Traversable f, Num a) => FU f a -> f (a, a) -> f a
- hessianProduct' :: (Traversable f, Num a) => FU f a -> f (a, a) -> f (a, a)
- diff :: Num a => UU a -> a -> a
- diff' :: Num a => UU a -> a -> (a, a)
- diffF :: (Functor f, Num a) => UF f a -> a -> f a
- diffF' :: (Functor f, Num a) => UF f a -> a -> f (a, 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)
- 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)
- diffM :: (Monad m, Num a) => UF m a -> a -> m a
- diffM' :: (Monad m, Num a) => UF m a -> a -> m (a, 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)
- newtype AD f a = AD {
- runAD :: f a

- class Lifted t => Mode t where

# Gradient

grad :: (Traversable f, Num a) => FU f a -> f a -> f aSource

grad' :: (Traversable f, Num a) => FU f a -> f a -> (a, f a)Source

gradWith :: (Traversable f, Num a) => (a -> a -> b) -> FU f a -> f a -> f bSource

gradWith' :: (Traversable f, Num a) => (a -> a -> b) -> FU f a -> f a -> (a, f b)Source

# Jacobian

jacobian :: (Traversable f, Traversable g, Num a) => FF f g a -> f a -> g (f a)Source

jacobian' :: (Traversable f, Traversable g, Num a) => FF f g a -> f a -> g (a, f a)Source

jacobianWith :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> FF f g a -> f a -> g (f b)Source

jacobianWith' :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> FF f g a -> f a -> g (a, f b)Source

# Transposed Jacobian

jacobianT :: (Traversable f, Functor g, Num a) => FF f g a -> f a -> f (g a)Source

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

jacobianWithT :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> FF f g a -> f a -> f (g b)Source

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

# Hessian Product

hessianProduct :: (Traversable f, Num a) => FU f a -> f (a, a) -> f aSource

Compute the product of a vector with the Hessian using forward-on-forward-mode AD.

hessianProduct' :: (Traversable f, Num a) => FU f a -> f (a, a) -> f (a, a)Source

Compute the gradient and hessian product using forward-on-forward-mode AD.

# Derivatives

diff' :: Num a => UU a -> a -> (a, a)Source

The `d'UU`

function calculates the result and first derivative of scalar-to-scalar function by F`orward`

`AD`

d' sin == sin &&& cos d' f = f &&& d f

# Directional Derivatives

# Monadic Combinators

diffM :: (Monad m, Num a) => UF m a -> a -> m aSource

The `dUM`

function calculates the first derivative of scalar-to-scalar monadic function by F`orward`

`AD`

diffM' :: (Monad m, Num a) => UF m a -> a -> m (a, a)Source

The `d'UM`

function calculates the result and first derivative of a scalar-to-scalar monadic function by F`orward`

`AD`

# 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.

`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