Numeric.AD.Mode.Forward

Forward mode automatic differentiation

Gradient

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

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)

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)

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)

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 a

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)

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

The diff function calculates the first derivative of a scalar-to-scalar function by forward-mode AD

 diff sin == cos

diff' :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)

The d' function calculates the result and first derivative of scalar-to-scalar function by Forward AD

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

diffF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f a

The diffF function calculates the first derivative of scalar-to-nonscalar function by Forward AD

diffF' :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f (a, a)

The diffF' function calculates the result and first derivative of a scalar-to-non-scalar function by Forward AD

Directional Derivatives

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)