```-----------------------------------------------------------------------------
-- |
-- Copyright   : (c) Edward Kmett 2010-2021
-- Maintainer  : ekmett@gmail.com
-- Stability   : experimental
-- Portability : GHC only
--
-----------------------------------------------------------------------------

( Dense
, auto

-- * Sparse Jacobians (synonyms)
, jacobian
, jacobian'
, jacobianWith
, jacobianWith'

) where

second :: (a -> b) -> (c, a) -> (c, b)
second :: forall a b c. (a -> b) -> (c, a) -> (c, b)
second a -> b
g (c
a,a
b) = (c
a, a -> b
g a
b)
{-# INLINE second #-}

:: (Traversable f, Num a)
=> (f (Dense f a) -> Dense f a)
-> f a
-> f a
grad :: forall (f :: * -> *) a.
(Traversable f, Num a) =>
(f (Dense f a) -> Dense f a) -> f a -> f a
grad f (Dense f a) -> Dense f a
f f a
as = forall (f :: * -> *) a. f a -> Dense f a -> f a
ds (a
0 forall (f :: * -> *) a b. Functor f => a -> f b -> f a
<\$ f a
as) forall a b. (a -> b) -> a -> b
\$ forall (f :: * -> *) a b.
(Traversable f, Num a) =>
(f (Dense f a) -> b) -> f a -> b
apply f (Dense f a) -> Dense f a
f f a
as

:: (Traversable f, Num a)
=> (f (Dense f a) -> Dense f a)
-> f a
-> (a, f a)
grad' :: forall (f :: * -> *) a.
(Traversable f, Num a) =>
(f (Dense f a) -> Dense f a) -> f a -> (a, f a)
grad' f (Dense f a) -> Dense f a
f f a
as = forall a (f :: * -> *). Num a => f a -> Dense f a -> (a, f a)
ds' (a
0 forall (f :: * -> *) a b. Functor f => a -> f b -> f a
<\$ f a
as) forall a b. (a -> b) -> a -> b
\$ forall (f :: * -> *) a b.
(Traversable f, Num a) =>
(f (Dense f a) -> b) -> f a -> b
apply f (Dense f a) -> Dense f a
f f a
as

:: (Traversable f, Num a)
=> (a -> a -> b)
-> (f (Dense f a) -> Dense f a)
-> f a
-> f b
gradWith :: forall (f :: * -> *) a b.
(Traversable f, Num a) =>
(a -> a -> b) -> (f (Dense f a) -> Dense f a) -> f a -> f b
gradWith a -> a -> b
g f (Dense f a) -> Dense f a
f f a
as = forall (f :: * -> *) (g :: * -> *) a b c.
(Foldable f, Traversable g) =>
(a -> b -> c) -> f a -> g b -> g c
zipWithT a -> a -> b
g f a
as forall a b. (a -> b) -> a -> b
\$ forall (f :: * -> *) a.
(Traversable f, Num a) =>
(f (Dense f a) -> Dense f a) -> f a -> f a
grad f (Dense f a) -> Dense f a
f f a
as

:: (Traversable f, Num a)
=> (a -> a -> b)
-> (f (Dense f a) -> Dense f a)
-> f a
-> (a, f b)
gradWith' :: forall (f :: * -> *) a b.
(Traversable f, Num a) =>
(a -> a -> b) -> (f (Dense f a) -> Dense f a) -> f a -> (a, f b)
gradWith' a -> a -> b
g f (Dense f a) -> Dense f a
f f a
as = forall a b c. (a -> b) -> (c, a) -> (c, b)
second (forall (f :: * -> *) (g :: * -> *) a b c.
(Foldable f, Traversable g) =>
(a -> b -> c) -> f a -> g b -> g c
zipWithT a -> a -> b
g f a
as) forall a b. (a -> b) -> a -> b
\$ forall (f :: * -> *) a.
(Traversable f, Num a) =>
(f (Dense f a) -> Dense f a) -> f a -> (a, f a)
grad' f (Dense f a) -> Dense f a
f f a
as

jacobian
:: (Traversable f, Functor g, Num a)
=> (f (Dense f a) -> g (Dense f a))
-> f a
-> g (f a)
jacobian :: forall (f :: * -> *) (g :: * -> *) a.
(Traversable f, Functor g, Num a) =>
(f (Dense f a) -> g (Dense f a)) -> f a -> g (f a)
jacobian f (Dense f a) -> g (Dense f a)
f f a
as = forall (f :: * -> *) a. f a -> Dense f a -> f a
ds (a
0 forall (f :: * -> *) a b. Functor f => a -> f b -> f a
<\$ f a
as) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<\$> forall (f :: * -> *) a b.
(Traversable f, Num a) =>
(f (Dense f a) -> b) -> f a -> b
apply f (Dense f a) -> g (Dense f a)
f f a
as
{-# INLINE jacobian #-}

jacobian'
:: (Traversable f, Functor g, Num a)
=> (f (Dense f a) -> g (Dense f a))
-> f a
-> g (a, f a)
jacobian' :: forall (f :: * -> *) (g :: * -> *) a.
(Traversable f, Functor g, Num a) =>
(f (Dense f a) -> g (Dense f a)) -> f a -> g (a, f a)
jacobian' f (Dense f a) -> g (Dense f a)
f f a
as = forall a (f :: * -> *). Num a => f a -> Dense f a -> (a, f a)
ds' (a
0 forall (f :: * -> *) a b. Functor f => a -> f b -> f a
<\$ f a
as) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<\$> forall (f :: * -> *) a b.
(Traversable f, Num a) =>
(f (Dense f a) -> b) -> f a -> b
apply f (Dense f a) -> g (Dense f a)
f f a
as
{-# INLINE jacobian' #-}

jacobianWith
:: (Traversable f, Functor g, Num a)
=> (a -> a -> b)
-> (f (Dense f a) -> g (Dense f a))
-> f a
-> g (f b)
jacobianWith :: forall (f :: * -> *) (g :: * -> *) a b.
(Traversable f, Functor g, Num a) =>
(a -> a -> b) -> (f (Dense f a) -> g (Dense f a)) -> f a -> g (f b)
jacobianWith a -> a -> b
g f (Dense f a) -> g (Dense f a)
f f a
as = forall (f :: * -> *) (g :: * -> *) a b c.
(Foldable f, Traversable g) =>
(a -> b -> c) -> f a -> g b -> g c
zipWithT a -> a -> b
g f a
as forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<\$> forall (f :: * -> *) (g :: * -> *) a.
(Traversable f, Functor g, Num a) =>
(f (Dense f a) -> g (Dense f a)) -> f a -> g (f a)
jacobian f (Dense f a) -> g (Dense f a)
f f a
as
{-# INLINE jacobianWith #-}

jacobianWith'
:: (Traversable f, Functor g, Num a)
=> (a -> a -> b)
-> (f (Dense f a) -> g (Dense f a))
-> f a
-> g (a, f b)
jacobianWith' :: forall (f :: * -> *) (g :: * -> *) a b.
(Traversable f, Functor g, Num a) =>
(a -> a -> b)
-> (f (Dense f a) -> g (Dense f a)) -> f a -> g (a, f b)
jacobianWith' a -> a -> b
g f (Dense f a) -> g (Dense f a)
f f a
as = forall a b c. (a -> b) -> (c, a) -> (c, b)
second (forall (f :: * -> *) (g :: * -> *) a b c.
(Foldable f, Traversable g) =>
(a -> b -> c) -> f a -> g b -> g c
zipWithT a -> a -> b
g f a
as) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<\$> forall (f :: * -> *) (g :: * -> *) a.
(Traversable f, Functor g, Num a) =>
(f (Dense f a) -> g (Dense f a)) -> f a -> g (a, f a)
jacobian' f (Dense f a) -> g (Dense f a)
f f a
as
{-# INLINE jacobianWith' #-}
```