{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE ScopedTypeVariables #-}
module Numeric.AD.Mode.Reverse.Double
( ReverseDouble, auto
, grad
, grad'
, gradWith
, gradWith'
, jacobian
, jacobian'
, jacobianWith
, jacobianWith'
, hessian
, hessianF
, diff
, diff'
, diffF
, diffF'
) where
import Data.Typeable
import Data.Functor.Compose
import Data.Reflection (Reifies)
import Numeric.AD.Internal.On
import qualified Numeric.AD.Internal.Reverse as R
import qualified Numeric.AD.Mode.Reverse as M
import Numeric.AD.Internal.Reverse.Double
import Numeric.AD.Mode
grad
:: Traversable f
=> (forall s. (Reifies s Tape, Typeable s) => f (ReverseDouble s) -> ReverseDouble s)
-> f Double
-> f Double
grad :: forall (f :: * -> *).
Traversable f =>
(forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> ReverseDouble s)
-> f Double -> f Double
grad forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> ReverseDouble s
f f Double
as = forall r.
Int
-> (forall s. (Reifies s Tape, Typeable s) => Proxy s -> r) -> r
reifyTypeableTape (forall a b. (a, b) -> b
snd (Int, Int)
bds) forall a b. (a -> b) -> a -> b
$ \Proxy s
p -> forall (f :: * -> *) s.
Functor f =>
f (ReverseDouble s) -> Array Int Double -> f Double
unbind forall {s}. f (ReverseDouble s)
vs forall a b. (a -> b) -> a -> b
$! forall s.
Reifies s Tape =>
Proxy s -> (Int, Int) -> ReverseDouble s -> Array Int Double
partialArrayOf Proxy s
p (Int, Int)
bds forall a b. (a -> b) -> a -> b
$! forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> ReverseDouble s
f forall {s}. f (ReverseDouble s)
vs where
(f (ReverseDouble s)
vs, (Int, Int)
bds) = forall (f :: * -> *) s.
Traversable f =>
f Double -> (f (ReverseDouble s), (Int, Int))
bind f Double
as
{-# INLINE grad #-}
grad'
:: Traversable f
=> (forall s. (Reifies s Tape, Typeable s) => f (ReverseDouble s) -> ReverseDouble s)
-> f Double
-> (Double, f Double)
grad' :: forall (f :: * -> *).
Traversable f =>
(forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> ReverseDouble s)
-> f Double -> (Double, f Double)
grad' forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> ReverseDouble s
f f Double
as = forall r.
Int
-> (forall s. (Reifies s Tape, Typeable s) => Proxy s -> r) -> r
reifyTypeableTape (forall a b. (a, b) -> b
snd (Int, Int)
bds) forall a b. (a -> b) -> a -> b
$ \Proxy s
p -> case forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> ReverseDouble s
f forall {s}. f (ReverseDouble s)
vs of
ReverseDouble s
r -> (forall s. ReverseDouble s -> Double
primal ReverseDouble s
r, forall (f :: * -> *) s.
Functor f =>
f (ReverseDouble s) -> Array Int Double -> f Double
unbind forall {s}. f (ReverseDouble s)
vs forall a b. (a -> b) -> a -> b
$! forall s.
Reifies s Tape =>
Proxy s -> (Int, Int) -> ReverseDouble s -> Array Int Double
partialArrayOf Proxy s
p (Int, Int)
bds forall a b. (a -> b) -> a -> b
$! ReverseDouble s
r)
where (f (ReverseDouble s)
vs, (Int, Int)
bds) = forall (f :: * -> *) s.
Traversable f =>
f Double -> (f (ReverseDouble s), (Int, Int))
bind f Double
as
{-# INLINE grad' #-}
gradWith
:: Traversable f
=> (Double -> Double -> b)
-> (forall s. (Reifies s Tape, Typeable s) => f (ReverseDouble s) -> ReverseDouble s)
-> f Double
-> f b
gradWith :: forall (f :: * -> *) b.
Traversable f =>
(Double -> Double -> b)
-> (forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> ReverseDouble s)
-> f Double
-> f b
gradWith Double -> Double -> b
g forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> ReverseDouble s
f f Double
as = forall r.
Int
-> (forall s. (Reifies s Tape, Typeable s) => Proxy s -> r) -> r
reifyTypeableTape (forall a b. (a, b) -> b
snd (Int, Int)
bds) forall a b. (a -> b) -> a -> b
$ \Proxy s
p -> forall (f :: * -> *) b c s.
Functor f =>
(Double -> b -> c) -> f (ReverseDouble s) -> Array Int b -> f c
unbindWith Double -> Double -> b
g forall {s}. f (ReverseDouble s)
vs forall a b. (a -> b) -> a -> b
$! forall s.
Reifies s Tape =>
Proxy s -> (Int, Int) -> ReverseDouble s -> Array Int Double
partialArrayOf Proxy s
p (Int, Int)
bds forall a b. (a -> b) -> a -> b
$! forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> ReverseDouble s
f forall {s}. f (ReverseDouble s)
vs
where (f (ReverseDouble s)
vs,(Int, Int)
bds) = forall (f :: * -> *) s.
Traversable f =>
f Double -> (f (ReverseDouble s), (Int, Int))
bind f Double
as
{-# INLINE gradWith #-}
gradWith'
:: Traversable f
=> (Double -> Double -> b)
-> (forall s. (Reifies s Tape, Typeable s) => f (ReverseDouble s) -> ReverseDouble s)
-> f Double
-> (Double, f b)
gradWith' :: forall (f :: * -> *) b.
Traversable f =>
(Double -> Double -> b)
-> (forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> ReverseDouble s)
-> f Double
-> (Double, f b)
gradWith' Double -> Double -> b
g forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> ReverseDouble s
f f Double
as = forall r.
Int
-> (forall s. (Reifies s Tape, Typeable s) => Proxy s -> r) -> r
reifyTypeableTape (forall a b. (a, b) -> b
snd (Int, Int)
bds) forall a b. (a -> b) -> a -> b
$ \Proxy s
p -> case forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> ReverseDouble s
f forall {s}. f (ReverseDouble s)
vs of
ReverseDouble s
r -> (forall s. ReverseDouble s -> Double
primal ReverseDouble s
r, forall (f :: * -> *) b c s.
Functor f =>
(Double -> b -> c) -> f (ReverseDouble s) -> Array Int b -> f c
unbindWith Double -> Double -> b
g forall {s}. f (ReverseDouble s)
vs forall a b. (a -> b) -> a -> b
$! forall s.
Reifies s Tape =>
Proxy s -> (Int, Int) -> ReverseDouble s -> Array Int Double
partialArrayOf Proxy s
p (Int, Int)
bds forall a b. (a -> b) -> a -> b
$! ReverseDouble s
r)
where (f (ReverseDouble s)
vs, (Int, Int)
bds) = forall (f :: * -> *) s.
Traversable f =>
f Double -> (f (ReverseDouble s), (Int, Int))
bind f Double
as
{-# INLINE gradWith' #-}
jacobian
:: (Traversable f, Functor g)
=> (forall s. (Reifies s Tape, Typeable s) => f (ReverseDouble s) -> g (ReverseDouble s))
-> f Double
-> g (f Double)
jacobian :: forall (f :: * -> *) (g :: * -> *).
(Traversable f, Functor g) =>
(forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s))
-> f Double -> g (f Double)
jacobian forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s)
f f Double
as = forall r.
Int
-> (forall s. (Reifies s Tape, Typeable s) => Proxy s -> r) -> r
reifyTypeableTape (forall a b. (a, b) -> b
snd (Int, Int)
bds) forall a b. (a -> b) -> a -> b
$ \Proxy s
p -> forall (f :: * -> *) s.
Functor f =>
f (ReverseDouble s) -> Array Int Double -> f Double
unbind forall {s}. f (ReverseDouble s)
vs forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall s.
Reifies s Tape =>
Proxy s -> (Int, Int) -> ReverseDouble s -> Array Int Double
partialArrayOf Proxy s
p (Int, Int)
bds forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s)
f forall {s}. f (ReverseDouble s)
vs where
(f (ReverseDouble s)
vs, (Int, Int)
bds) = forall (f :: * -> *) s.
Traversable f =>
f Double -> (f (ReverseDouble s), (Int, Int))
bind f Double
as
{-# INLINE jacobian #-}
jacobian'
:: (Traversable f, Functor g)
=> (forall s. (Reifies s Tape, Typeable s) => f (ReverseDouble s) -> g (ReverseDouble s))
-> f Double
-> g (Double, f Double)
jacobian' :: forall (f :: * -> *) (g :: * -> *).
(Traversable f, Functor g) =>
(forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s))
-> f Double -> g (Double, f Double)
jacobian' forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s)
f f Double
as = forall r.
Int
-> (forall s. (Reifies s Tape, Typeable s) => Proxy s -> r) -> r
reifyTypeableTape (forall a b. (a, b) -> b
snd (Int, Int)
bds) forall a b. (a -> b) -> a -> b
$ \Proxy s
p ->
let row :: ReverseDouble s -> (Double, f Double)
row ReverseDouble s
a = (forall s. ReverseDouble s -> Double
primal ReverseDouble s
a, forall (f :: * -> *) s.
Functor f =>
f (ReverseDouble s) -> Array Int Double -> f Double
unbind forall {s}. f (ReverseDouble s)
vs forall a b. (a -> b) -> a -> b
$! forall s.
Reifies s Tape =>
Proxy s -> (Int, Int) -> ReverseDouble s -> Array Int Double
partialArrayOf Proxy s
p (Int, Int)
bds forall a b. (a -> b) -> a -> b
$! ReverseDouble s
a)
in ReverseDouble s -> (Double, f Double)
row forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s)
f forall {s}. f (ReverseDouble s)
vs
where (f (ReverseDouble s)
vs, (Int, Int)
bds) = forall (f :: * -> *) s.
Traversable f =>
f Double -> (f (ReverseDouble s), (Int, Int))
bind f Double
as
{-# INLINE jacobian' #-}
jacobianWith
:: (Traversable f, Functor g)
=> (Double -> Double -> b)
-> (forall s. (Reifies s Tape, Typeable s) => f (ReverseDouble s) -> g (ReverseDouble s))
-> f Double
-> g (f b)
jacobianWith :: forall (f :: * -> *) (g :: * -> *) b.
(Traversable f, Functor g) =>
(Double -> Double -> b)
-> (forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s))
-> f Double
-> g (f b)
jacobianWith Double -> Double -> b
g forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s)
f f Double
as = forall r.
Int
-> (forall s. (Reifies s Tape, Typeable s) => Proxy s -> r) -> r
reifyTypeableTape (forall a b. (a, b) -> b
snd (Int, Int)
bds) forall a b. (a -> b) -> a -> b
$ \Proxy s
p -> forall (f :: * -> *) b c s.
Functor f =>
(Double -> b -> c) -> f (ReverseDouble s) -> Array Int b -> f c
unbindWith Double -> Double -> b
g forall {s}. f (ReverseDouble s)
vs forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall s.
Reifies s Tape =>
Proxy s -> (Int, Int) -> ReverseDouble s -> Array Int Double
partialArrayOf Proxy s
p (Int, Int)
bds forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s)
f forall {s}. f (ReverseDouble s)
vs where
(f (ReverseDouble s)
vs, (Int, Int)
bds) = forall (f :: * -> *) s.
Traversable f =>
f Double -> (f (ReverseDouble s), (Int, Int))
bind f Double
as
{-# INLINE jacobianWith #-}
jacobianWith'
:: (Traversable f, Functor g)
=> (Double -> Double -> b)
-> (forall s. (Reifies s Tape, Typeable s) => f (ReverseDouble s) -> g (ReverseDouble s))
-> f Double
-> g (Double, f b)
jacobianWith' :: forall (f :: * -> *) (g :: * -> *) b.
(Traversable f, Functor g) =>
(Double -> Double -> b)
-> (forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s))
-> f Double
-> g (Double, f b)
jacobianWith' Double -> Double -> b
g forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s)
f f Double
as = forall r.
Int
-> (forall s. (Reifies s Tape, Typeable s) => Proxy s -> r) -> r
reifyTypeableTape (forall a b. (a, b) -> b
snd (Int, Int)
bds) forall a b. (a -> b) -> a -> b
$ \Proxy s
p ->
let row :: ReverseDouble s -> (Double, f b)
row ReverseDouble s
a = (forall s. ReverseDouble s -> Double
primal ReverseDouble s
a, forall (f :: * -> *) b c s.
Functor f =>
(Double -> b -> c) -> f (ReverseDouble s) -> Array Int b -> f c
unbindWith Double -> Double -> b
g forall {s}. f (ReverseDouble s)
vs forall a b. (a -> b) -> a -> b
$! forall s.
Reifies s Tape =>
Proxy s -> (Int, Int) -> ReverseDouble s -> Array Int Double
partialArrayOf Proxy s
p (Int, Int)
bds forall a b. (a -> b) -> a -> b
$! ReverseDouble s
a)
in ReverseDouble s -> (Double, f b)
row forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s)
f forall {s}. f (ReverseDouble s)
vs
where (f (ReverseDouble s)
vs, (Int, Int)
bds) = forall (f :: * -> *) s.
Traversable f =>
f Double -> (f (ReverseDouble s), (Int, Int))
bind f Double
as
{-# INLINE jacobianWith' #-}
diff
:: (forall s. (Reifies s Tape, Typeable s) => ReverseDouble s -> ReverseDouble s)
-> Double
-> Double
diff :: (forall s.
(Reifies s Tape, Typeable s) =>
ReverseDouble s -> ReverseDouble s)
-> Double -> Double
diff forall s.
(Reifies s Tape, Typeable s) =>
ReverseDouble s -> ReverseDouble s
f Double
a = forall r.
Int
-> (forall s. (Reifies s Tape, Typeable s) => Proxy s -> r) -> r
reifyTypeableTape Int
1 forall a b. (a -> b) -> a -> b
$ \Proxy s
p -> forall s. Reifies s Tape => Proxy s -> ReverseDouble s -> Double
derivativeOf Proxy s
p forall a b. (a -> b) -> a -> b
$! forall s.
(Reifies s Tape, Typeable s) =>
ReverseDouble s -> ReverseDouble s
f (forall s. Double -> Int -> ReverseDouble s
var Double
a Int
0)
{-# INLINE diff #-}
diff'
:: (forall s. (Reifies s Tape, Typeable s) => ReverseDouble s -> ReverseDouble s)
-> Double
-> (Double, Double)
diff' :: (forall s.
(Reifies s Tape, Typeable s) =>
ReverseDouble s -> ReverseDouble s)
-> Double -> (Double, Double)
diff' forall s.
(Reifies s Tape, Typeable s) =>
ReverseDouble s -> ReverseDouble s
f Double
a = forall r.
Int
-> (forall s. (Reifies s Tape, Typeable s) => Proxy s -> r) -> r
reifyTypeableTape Int
1 forall a b. (a -> b) -> a -> b
$ \Proxy s
p -> forall s.
Reifies s Tape =>
Proxy s -> ReverseDouble s -> (Double, Double)
derivativeOf' Proxy s
p forall a b. (a -> b) -> a -> b
$! forall s.
(Reifies s Tape, Typeable s) =>
ReverseDouble s -> ReverseDouble s
f (forall s. Double -> Int -> ReverseDouble s
var Double
a Int
0)
{-# INLINE diff' #-}
diffF
:: Functor f
=> (forall s. (Reifies s Tape, Typeable s) => ReverseDouble s -> f (ReverseDouble s))
-> Double
-> f Double
diffF :: forall (f :: * -> *).
Functor f =>
(forall s.
(Reifies s Tape, Typeable s) =>
ReverseDouble s -> f (ReverseDouble s))
-> Double -> f Double
diffF forall s.
(Reifies s Tape, Typeable s) =>
ReverseDouble s -> f (ReverseDouble s)
f Double
a = forall r.
Int
-> (forall s. (Reifies s Tape, Typeable s) => Proxy s -> r) -> r
reifyTypeableTape Int
1 forall a b. (a -> b) -> a -> b
$ \Proxy s
p -> forall s. Reifies s Tape => Proxy s -> ReverseDouble s -> Double
derivativeOf Proxy s
p forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall s.
(Reifies s Tape, Typeable s) =>
ReverseDouble s -> f (ReverseDouble s)
f (forall s. Double -> Int -> ReverseDouble s
var Double
a Int
0)
{-# INLINE diffF #-}
diffF'
:: Functor f
=> (forall s. (Reifies s Tape, Typeable s) => ReverseDouble s -> f (ReverseDouble s))
-> Double
-> f (Double, Double)
diffF' :: forall (f :: * -> *).
Functor f =>
(forall s.
(Reifies s Tape, Typeable s) =>
ReverseDouble s -> f (ReverseDouble s))
-> Double -> f (Double, Double)
diffF' forall s.
(Reifies s Tape, Typeable s) =>
ReverseDouble s -> f (ReverseDouble s)
f Double
a = forall r.
Int
-> (forall s. (Reifies s Tape, Typeable s) => Proxy s -> r) -> r
reifyTypeableTape Int
1 forall a b. (a -> b) -> a -> b
$ \Proxy s
p -> forall s.
Reifies s Tape =>
Proxy s -> ReverseDouble s -> (Double, Double)
derivativeOf' Proxy s
p forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall s.
(Reifies s Tape, Typeable s) =>
ReverseDouble s -> f (ReverseDouble s)
f (forall s. Double -> Int -> ReverseDouble s
var Double
a Int
0)
{-# INLINE diffF' #-}
hessian
:: Traversable f
=> (forall s s'.
(Reifies s R.Tape, Typeable s, Reifies s' Tape, Typeable s') =>
f (On (R.Reverse s (ReverseDouble s'))) -> On (R.Reverse s (ReverseDouble s')))
-> f Double
-> f (f Double)
hessian :: forall (f :: * -> *).
Traversable f =>
(forall s s'.
(Reifies s Tape, Typeable s, Reifies s' Tape, Typeable s') =>
f (On (Reverse s (ReverseDouble s')))
-> On (Reverse s (ReverseDouble s')))
-> f Double -> f (f Double)
hessian forall s s'.
(Reifies s Tape, Typeable s, Reifies s' Tape, Typeable s') =>
f (On (Reverse s (ReverseDouble s')))
-> On (Reverse s (ReverseDouble s'))
f = forall (f :: * -> *) (g :: * -> *).
(Traversable f, Functor g) =>
(forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s))
-> f Double -> g (f Double)
jacobian (forall (f :: * -> *) a.
(Traversable f, Num a) =>
(forall s.
(Reifies s Tape, Typeable s) =>
f (Reverse s a) -> Reverse s a)
-> f a -> f a
M.grad (forall t. On t -> t
off forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall s s'.
(Reifies s Tape, Typeable s, Reifies s' Tape, Typeable s') =>
f (On (Reverse s (ReverseDouble s')))
-> On (Reverse s (ReverseDouble s'))
f forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall t. t -> On t
On))
{-# INLINE hessian #-}
hessianF
:: (Traversable f, Functor g)
=> (forall s s'.
(Reifies s R.Tape, Typeable s, Reifies s' Tape, Typeable s') =>
f (On (R.Reverse s (ReverseDouble s'))) -> g (On (R.Reverse s (ReverseDouble s'))))
-> f Double
-> g (f (f Double))
hessianF :: forall (f :: * -> *) (g :: * -> *).
(Traversable f, Functor g) =>
(forall s s'.
(Reifies s Tape, Typeable s, Reifies s' Tape, Typeable s') =>
f (On (Reverse s (ReverseDouble s')))
-> g (On (Reverse s (ReverseDouble s'))))
-> f Double -> g (f (f Double))
hessianF forall s s'.
(Reifies s Tape, Typeable s, Reifies s' Tape, Typeable s') =>
f (On (Reverse s (ReverseDouble s')))
-> g (On (Reverse s (ReverseDouble s')))
f = forall {k1} {k2} (f :: k1 -> *) (g :: k2 -> k1) (a :: k2).
Compose f g a -> f (g a)
getCompose forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *) (g :: * -> *).
(Traversable f, Functor g) =>
(forall s.
(Reifies s Tape, Typeable s) =>
f (ReverseDouble s) -> g (ReverseDouble s))
-> f Double -> g (f Double)
jacobian (forall {k} {k1} (f :: k -> *) (g :: k1 -> k) (a :: k1).
f (g a) -> Compose f g a
Compose forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *) (g :: * -> *) a.
(Traversable f, Functor g, Num a) =>
(forall s.
(Reifies s Tape, Typeable s) =>
f (Reverse s a) -> g (Reverse s a))
-> f a -> g (f a)
M.jacobian (forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall t. On t -> t
off forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall s s'.
(Reifies s Tape, Typeable s, Reifies s' Tape, Typeable s') =>
f (On (Reverse s (ReverseDouble s')))
-> g (On (Reverse s (ReverseDouble s')))
f forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall t. t -> On t
On))
{-# INLINE hessianF #-}