Portability | GHC only |
---|---|
Stability | experimental |
Maintainer | ekmett@gmail.com |
Forward mode automatic differentiation
- grad :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f a
- grad' :: (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
- gradWith' :: (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)
- jacobian' :: (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)
- 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 (a, f b)
- jacobianT :: (Traversable f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> f (g a)
- jacobianWithT :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> f (g b)
- hessianProduct :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> f a
- hessianProduct' :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> f (a, a)
- diff :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> a
- diff' :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)
- diffF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f a
- diffF' :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f (a, a)
- du :: (Functor f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> a
- du' :: (Functor f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> (a, a)
- duF :: (Functor f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f (a, a) -> g a
- duF' :: (Functor f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f (a, a) -> g (a, a)
- diffM :: (Monad m, Num a) => (forall s. Mode s => AD s a -> m (AD s a)) -> a -> m a
- diffM' :: (Monad m, Num a) => (forall s. Mode s => AD s a -> m (AD s a)) -> a -> m (a, a)
- newtype AD f a = AD {
- runAD :: f a
- class Lifted t => Mode t where
Gradient
grad' :: (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
gradWith' :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f b)Source
Jacobian
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
jacobian' :: (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
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
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 (a, f b)Source
Transposed Jacobian
jacobianT :: (Traversable f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s 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) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> f (g b)Source
A fast, simple transposed Jacobian computed with forward-mode AD.
Hessian Product
hessianProduct :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s 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) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> f (a, a)Source
Compute the gradient and hessian product using forward-on-forward-mode AD.
Derivatives
diff' :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)Source
The d'UU
function calculates the result and first derivative of scalar-to-scalar function by Forward
AD
d' sin == sin &&& cos d' f = f &&& d f
Directional Derivatives
duF :: (Functor f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f (a, a) -> g aSource
duF' :: (Functor f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f (a, a) -> g (a, a)Source
Monadic Combinators
diffM :: (Monad m, Num a) => (forall s. Mode s => AD s a -> m (AD s a)) -> a -> m aSource
The dUM
function calculates the first derivative of scalar-to-scalar monadic function by Forward
AD
diffM' :: (Monad m, Num a) => (forall s. Mode s => AD s a -> m (AD s a)) -> a -> m (a, a)Source
The d'UM
function calculates the result and first derivative of a scalar-to-scalar monadic function by Forward
AD
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