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)
- 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)
- 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
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.
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) | |
(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) | |
Var (AD Reverse a) 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