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1. data SProduct (a1 :: Product a)

   singletons-base	Data.Semigroup.Singletons

   No documentation available.

2. SProduct :: forall a (n :: a) . Sing n -> SProduct ('Product n)

   singletons-base	Data.Semigroup.Singletons

   No documentation available.

3. sGetProduct :: forall a (t :: Product a) . Sing t -> Sing (Apply (GetProductSym0 :: TyFun (Product a) a -> Type) t)

   singletons-base	Data.Semigroup.Singletons

   No documentation available.

4. sProduct :: forall a (t1 :: t a) . (SFoldable t, SNum a) => Sing t1 -> Sing (Apply (ProductSym0 :: TyFun (t a) a -> Type) t1)

   singletons-base	Data.Singletons.Base.TH

   No documentation available.

5. sProduct :: forall a (t1 :: t a) . (SFoldable t, SNum a) => Sing t1 -> Sing (Apply (ProductSym0 :: TyFun (t a) a -> Type) t1)

   singletons-base	Prelude.Singletons

   No documentation available.

6. hessianProduct :: (Traversable f, Num a) => (forall s . (Reifies s Tape, Typeable s) => f (On (Reverse s (Forward a))) -> On (Reverse s (Forward a))) -> f (a, a) -> f a

   ad	Numeric.AD

   hessianProduct f wv computes the product of the hessian H of a non-scalar-to-scalar function f at w = fst <$> wv with a vector v = snd <$> wv using "Pearlmutter's method" from http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.6143, which states:

   H v = (d/dr) grad_w (w + r v) | r = 0
   

   Or in other words, we take the directional derivative of the gradient. The gradient is calculated in reverse mode, then the directional derivative is calculated in forward mode.

7. hessianProduct' :: (Traversable f, Num a) => (forall s . (Reifies s Tape, Typeable s) => f (On (Reverse s (Forward a))) -> On (Reverse s (Forward a))) -> f (a, a) -> f (a, a)

   ad	Numeric.AD

   hessianProduct' f wv computes both the gradient of a non-scalar-to-scalar f at w = fst <$> wv and the product of the hessian H at w with a vector v = snd <$> wv using "Pearlmutter's method". The outputs are returned wrapped in the same functor.

   H v = (d/dr) grad_w (w + r v) | r = 0
   

   Or in other words, we return the gradient and the directional derivative of the gradient. The gradient is calculated in reverse mode, then the directional derivative is calculated in forward mode.

8. hessianProduct :: Traversable f => (forall s . (Reifies s Tape, Typeable s) => f (On (Reverse s ForwardDouble)) -> On (Reverse s ForwardDouble)) -> f (Double, Double) -> f Double

   ad	Numeric.AD.Double

   hessianProduct f wv computes the product of the hessian H of a non-scalar-to-scalar function f at w = fst <$> wv with a vector v = snd <$> wv using "Pearlmutter's method" from http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.6143, which states:

   H v = (d/dr) grad_w (w + r v) | r = 0
   

   Or in other words, we take the directional derivative of the gradient. The gradient is calculated in reverse mode, then the directional derivative is calculated in forward mode.

9. hessianProduct' :: Traversable f => (forall s . (Reifies s Tape, Typeable s) => f (On (Reverse s ForwardDouble)) -> On (Reverse s ForwardDouble)) -> f (Double, Double) -> f (Double, Double)

   ad	Numeric.AD.Double

   hessianProduct' f wv computes both the gradient of a non-scalar-to-scalar f at w = fst <$> wv and the product of the hessian H at w with a vector v = snd <$> wv using "Pearlmutter's method". The outputs are returned wrapped in the same functor.

   H v = (d/dr) grad_w (w + r v) | r = 0
   

   Or in other words, we return the gradient and the directional derivative of the gradient. The gradient is calculated in reverse mode, then the directional derivative is calculated in forward mode.

10. hessianProduct :: (Traversable f, Num a) => (forall s . () => f (AD s (On (Forward (Forward a)))) -> AD s (On (Forward (Forward a)))) -> f (a, a) -> f a

    ad	Numeric.AD.Mode.Forward

    Compute the product of a vector with the Hessian using forward-on-forward-mode AD.

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