Portability | GHC only |
---|---|
Stability | experimental |
Maintainer | ekmett@gmail.com |
Allows the choice of AD Mode
to be specified at the term level for
benchmarking or more complicated usage patterns.
- grad :: (Traversable f, Num a) => Direction -> FU f a -> f a -> f a
- grad' :: (Traversable f, Num a) => Direction -> FU f a -> f a -> (a, f a)
- jacobian :: (Traversable f, Traversable g, Num a) => Direction -> FF f g a -> f a -> g (f a)
- jacobian' :: (Traversable f, Traversable g, Num a) => Direction -> FF f g a -> f a -> g (a, f a)
- diff :: Num a => Direction -> UU a -> a -> a
- diff' :: Num a => Direction -> UU a -> a -> (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)
- data Direction
- class Lifted t => Mode t where
- newtype AD f a = AD {
- runAD :: f a
Gradients
Jacobians
jacobian :: (Traversable f, Traversable g, Num a) => Direction -> FF f g a -> f a -> g (f a)Source
jacobian' :: (Traversable f, Traversable g, Num a) => Direction -> FF f g a -> f a -> g (a, f a)Source
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
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
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) | |
(Lifted f, Show a) => Show (AD f a) | |
(Typeable1 f, Typeable a) => Typeable (AD f a) |