module Numeric.AD.Tower
(
taylor
, taylor0
, maclaurin
, maclaurin0
, diff
, diff'
, diffs
, diffs0
, diffsF
, diffs0F
, diffsM
, diffs0M
, Mode(..)
, AD(..)
) where
import Control.Monad (liftM)
import Control.Applicative ((<$>))
import Numeric.AD.Classes
import Numeric.AD.Internal
import Numeric.AD.Internal.Tower
diffs :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
diffs f a = getADTower $ apply f a
diffs0 :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
diffs0 f a = zeroPad (diffs f a)
diffsF :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f [a]
diffsF f a = getADTower <$> apply f a
diffs0F :: (Functor f, Num a) => (forall s. Mode s => AD s a -> f (AD s a)) -> a -> f [a]
diffs0F f a = (zeroPad . getADTower) <$> apply f a
diffsM :: (Monad m, Num a) => (forall s. Mode s => AD s a -> m (AD s a)) -> a -> m [a]
diffsM f a = getADTower `liftM` apply f a
diffs0M :: (Monad m, Num a) => (forall s. Mode s => AD s a -> m (AD s a)) -> a -> m [a]
diffs0M f a = (zeroPad . getADTower) `liftM` apply f a
taylor :: Fractional a => (forall s. Mode s => AD s a -> AD s a) -> a -> a -> [a]
taylor f x dx = go 1 1 (diffs f x)
where
go !n !acc (a:as) = a * acc : go (n + 1) (acc * dx / n) as
go _ _ [] = []
taylor0 :: Fractional a => (forall s. Mode s => AD s a -> AD s a) -> a -> a -> [a]
taylor0 f x dx = zeroPad (taylor f x dx)
maclaurin :: Fractional a => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
maclaurin f = taylor f 0
maclaurin0 :: Fractional a => (forall s. Mode s => AD s a -> AD s a) -> a -> [a]
maclaurin0 f = taylor0 f 0
diff :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> a
diff f a = d $ diffs f a
diff' :: Num a => (forall s. Mode s => AD s a -> AD s a) -> a -> (a, a)
diff' f a = d' $ diffs f a