module Numeric.AD.Reverse
(
grad
, grad'
, gradWith
, gradWith'
, jacobian
, jacobian'
, jacobianWith
, jacobianWith'
, diff
, diff'
, diffF
, diffF'
, diffM
, diffM'
, gradM
, gradM'
, gradWithM
, gradWithM'
, gradF
, gradF'
, gradWithF
, gradWithF'
, AD(..)
, Mode(..)
) where
import Control.Monad (liftM)
import Control.Applicative (WrappedMonad(..),(<$>))
import Data.Traversable (Traversable)
import Numeric.AD.Classes
import Numeric.AD.Internal
import Numeric.AD.Internal.Reverse
grad :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> f a
grad f as = unbind vs (partialArray bds $ f vs)
where (vs,bds) = bind as
grad' :: (Traversable f, Num a) => (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f a)
grad' f as = (primal r, unbind vs $ partialArray bds r)
where (vs, bds) = bind as
r = f vs
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 as = unbindWith g vs (partialArray bds $ f vs)
where (vs,bds) = bind as
gradWith' :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> AD s a) -> f a -> (a, f b)
gradWith' g f as = (primal r, unbindWith g vs $ partialArray bds r)
where (vs, bds) = bind as
r = f vs
gradF :: (Traversable f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f a)
gradF = jacobian
jacobian :: (Traversable f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f a)
jacobian f as = unbind vs . partialArray bds <$> f vs where
(vs, bds) = bind as
gradF' :: (Traversable f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (a, f a)
gradF' = jacobian'
jacobian' :: (Traversable f, Functor g, Num a) => (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (a, f a)
jacobian' f as = row <$> f vs where
(vs, bds) = bind as
row a = (primal a, unbind vs (partialArray bds a))
gradWithF :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f b)
gradWithF g f as = unbindWith g vs . partialArray bds <$> f vs where
(vs, bds) = bind as
jacobianWith :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (f b)
jacobianWith = gradWithF
gradWithF' :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (a, f b)
gradWithF' g f as = row <$> f vs where
(vs, bds) = bind as
row a = (primal a, unbindWith g vs (partialArray bds a))
jacobianWith' :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> g (AD s a)) -> f a -> g (a, f b)
jacobianWith' = gradWithF'
diff :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> a
diff f a = derivative $ f (var a 0)
diff' :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)
diff' f a = derivative' $ f (var a 0)
diffF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f a
diffF f a = derivative <$> f (var a 0)
diffF' :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f (a, a)
diffF' f a = derivative' <$> f (var a 0)
diffM :: (Monad m, Num a) => (forall s. Mode s => AD s a -> m (AD s a)) -> a -> m a
diffM f a = liftM derivative $ f (var a 0)
diffM' :: (Monad m, Num a) => (forall s. Mode s => AD s a -> m (AD s a)) -> a -> m (a, a)
diffM' f a = liftM derivative' $ f (var a 0)
gradM :: (Traversable f, Monad m, Num a) => (forall s. Mode s => f (AD s a) -> m (AD s a)) -> f a -> m (f a)
gradM f = unwrapMonad . jacobian (WrapMonad . f)
gradM' :: (Traversable f, Monad m, Num a) => (forall s. Mode s => f (AD s a) -> m (AD s a)) -> f a -> m (a, f a)
gradM' f = unwrapMonad . jacobian' (WrapMonad . f)
gradWithM :: (Traversable f, Monad m, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> m (AD s a)) -> f a -> m (f b)
gradWithM g f = unwrapMonad . jacobianWith g (WrapMonad . f)
gradWithM' :: (Traversable f, Monad m, Num a) => (a -> a -> b) -> (forall s. Mode s => f (AD s a) -> m (AD s a)) -> f a -> m (a, f b)
gradWithM' g f = unwrapMonad . jacobianWith' g (WrapMonad . f)