module Numeric.AD.Forward
(
grad
, grad2
, gradWith
, gradWith2
, jacobian
, jacobian2
, jacobianT
, jacobianWith
, jacobianWith2
, jacobianWithT
, diffUU
, diff2UU
, diffUF
, diff2UF
, diffMU
, diff2MU
, diff
, diff2
, AD(..)
, Mode(..)
) where
import Data.Traversable (Traversable)
import Control.Applicative
import Numeric.AD.Classes
import Numeric.AD.Internal
import Numeric.AD.Internal.Forward
diffMU :: (Functor f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> a
diffMU f = tangent . f . fmap (uncurry bundle)
diff2MU :: (Functor f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f (a, a) -> (a, a)
diff2MU f = unbundle . f . fmap (uncurry bundle)
diff :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> a
diff = diffUU
diff2 :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)
diff2 = diff2UU
diffUU :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> a
diffUU f a = tangent $ apply f a
diff2UU :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)
diff2UU f a = unbundle $ apply f a
diffUF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f a
diffUF f a = tangent <$> apply f a
diff2UF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f (a, a)
diff2UF f a = unbundle <$> apply f a
jacobianT :: (Traversable f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> f (g a)
jacobianT f = bind (fmap tangent . f)
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)
jacobianWithT g f = bindWith g' f
where g' a ga = g a . tangent <$> ga
jacobian :: (Traversable f, Traversable g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f a)
jacobian f as = transposeWith (const id) t p
where
(p, t) = bind2 (fmap tangent . f) as
jacobianWith :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f b)
jacobianWith g f as = transposeWith (const id) t p
where
(p, t) = bindWith2 g' f as
g' a ga = g a . tangent <$> ga
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)
jacobian2 f as = transposeWith row t p
where
(p, t) = bind2 f as
row x as' = (primal x, tangent <$> as')
jacobianWith2 :: (Traversable f, Traversable g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (a, f b)
jacobianWith2 g f as = transposeWith row t p
where
(p, t) = bindWith2 g' f as
row x as' = (primal x, as')
g' a ga = g a . tangent <$> ga
grad :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f a
grad f = bind (tangent . f)
grad2 :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f a)
grad2 f as = (primal b, tangent <$> bs)
where
(b, bs) = bind2 f as
gradWith :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f b
gradWith g f = bindWith g (tangent . f)
gradWith2 :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f b)
gradWith2 g f = bindWith2 g (tangent . f)