diff package:ad

diff :: Num a => (forall s . AD s (Forward a) -> AD s (Forward a)) -> a -> a
ad Numeric.AD Numeric.AD.Mode.Forward
The diff function calculates the first derivative of a scalar-to-scalar function by forward-mode AD 
>>> diff sin 0
1.0
diff :: (forall s . AD s ForwardDouble -> AD s ForwardDouble) -> Double -> Double
ad Numeric.AD.Double Numeric.AD.Mode.Forward.Double
The diff function calculates the first derivative of a scalar-to-scalar function by forward-mode AD 
>>> diff sin 0
1.0
diff :: Num a => (forall s . AD s (Kahn a) -> AD s (Kahn a)) -> a -> a
ad Numeric.AD.Mode.Kahn
Compute the derivative of a function. 
>>> diff sin 0
1.0

>>> cos 0
1.0
diff :: (forall s . AD s KahnDouble -> AD s KahnDouble) -> Double -> Double
ad Numeric.AD.Mode.Kahn.Double
Compute the derivative of a function. 
>>> diff sin 0
1.0

>>> cos 0
1.0
diff :: Num a => (forall s . (Reifies s Tape, Typeable s) => Reverse s a -> Reverse s a) -> a -> a
ad Numeric.AD.Mode.Reverse
Compute the derivative of a function. 
>>> diff sin 0
1.0
diff :: (forall s . (Reifies s Tape, Typeable s) => ReverseDouble s -> ReverseDouble s) -> Double -> Double
ad Numeric.AD.Mode.Reverse.Double
Compute the derivative of a function. 
>>> diff sin 0
1.0
diff :: Num a => (forall s . AD s (Tower a) -> AD s (Tower a)) -> a -> a
ad Numeric.AD.Mode.Tower
diff :: (forall s . AD s TowerDouble -> AD s TowerDouble) -> Double -> Double
ad Numeric.AD.Mode.Tower.Double
diff :: Num a => (Forward a -> Forward a) -> a -> a
ad Numeric.AD.Rank1.Forward
The diff function calculates the first derivative of a scalar-to-scalar function by forward-mode AD 
>>> diff sin 0
1.0
diff :: (ForwardDouble -> ForwardDouble) -> Double -> Double
ad Numeric.AD.Rank1.Forward.Double
The diff function calculates the first derivative of a scalar-to-scalar function by forward-mode AD 
>>> diff sin 0
1.0
diff :: Num a => (Kahn a -> Kahn a) -> a -> a
ad Numeric.AD.Rank1.Kahn
Compute the derivative of a function. 
>>> diff sin 0
1.0

>>> cos 0
1.0
diff :: (KahnDouble -> KahnDouble) -> Double -> Double
ad Numeric.AD.Rank1.Kahn.Double
Compute the derivative of a function. 
>>> diff sin 0
1.0

>>> cos 0
1.0
diff :: (KahnFloat -> KahnFloat) -> Float -> Float
ad Numeric.AD.Rank1.Kahn.Float
Compute the derivative of a function. 
>>> diff sin 0
1.0

>>> cos 0
1.0
diff :: Num a => (Tower a -> Tower a) -> a -> a
ad Numeric.AD.Rank1.Tower
Compute the first derivative of a function (a -> a)
diff :: (TowerDouble -> TowerDouble) -> Double -> Double
ad Numeric.AD.Rank1.Tower.Double
Compute the first derivative of a function (a -> a)
diff' :: Num a => (forall s . AD s (Forward a) -> AD s (Forward a)) -> a -> (a, a)
ad Numeric.AD
The diff' function calculates the result and first derivative of scalar-to-scalar function by Forward mode AD 
diff' sin == sin &&& cos
diff' f = f &&& d f

>>> diff' sin 0
(0.0,1.0)

>>> diff' exp 0
(1.0,1.0)
diffF :: (Functor f, Num a) => (forall s . AD s (Forward a) -> f (AD s (Forward a))) -> a -> f a
ad Numeric.AD
The diffF function calculates the first derivatives of scalar-to-nonscalar function by Forward mode AD 
>>> diffF (\a -> [sin a, cos a]) 0
[1.0,-0.0]
diffF' :: (Functor f, Num a) => (forall s . AD s (Forward a) -> f (AD s (Forward a))) -> a -> f (a, a)
ad Numeric.AD
The diffF' function calculates the result and first derivatives of a scalar-to-non-scalar function by Forward mode AD 
>>> diffF' (\a -> [sin a, cos a]) 0
[(0.0,1.0),(1.0,-0.0)]
diffs :: Num a => (forall s . AD s (Tower a) -> AD s (Tower a)) -> a -> [a]
ad Numeric.AD
diffs0 :: Num a => (forall s . AD s (Tower a) -> AD s (Tower a)) -> a -> [a]
ad Numeric.AD
diffs0F :: (Functor f, Num a) => (forall s . AD s (Tower a) -> f (AD s (Tower a))) -> a -> f [a]
ad Numeric.AD
diffsF :: (Functor f, Num a) => (forall s . AD s (Tower a) -> f (AD s (Tower a))) -> a -> f [a]
ad Numeric.AD
diff' :: (forall s . AD s ForwardDouble -> AD s ForwardDouble) -> Double -> (Double, Double)
ad Numeric.AD.Double
The diff' function calculates the result and first derivative of scalar-to-scalar function by Forward mode AD 
diff' sin == sin &&& cos
diff' f = f &&& d f

>>> diff' sin 0
(0.0,1.0)

>>> diff' exp 0
(1.0,1.0)
diffF :: Functor f => (forall s . AD s ForwardDouble -> f (AD s ForwardDouble)) -> Double -> f Double
ad Numeric.AD.Double
The diffF function calculates the first derivatives of scalar-to-nonscalar function by Forward mode AD 
>>> diffF (\a -> [sin a, cos a]) 0
[1.0,-0.0]
diffF' :: Functor f => (forall s . AD s ForwardDouble -> f (AD s ForwardDouble)) -> Double -> f (Double, Double)
ad Numeric.AD.Double
The diffF' function calculates the result and first derivatives of a scalar-to-non-scalar function by Forward mode AD 
>>> diffF' (\a -> [sin a, cos a]) 0
[(0.0,1.0),(1.0,-0.0)]