{-# LANGUAGE Rank2Types #-}
-----------------------------------------------------------------------------
-- |
-- Copyright   :  (c) Edward Kmett 2010-2021
-- License     :  BSD3
-- Maintainer  :  ekmett@gmail.com
-- Stability   :  experimental
-- Portability :  GHC only
--
-- Forward Mode AD specialized to `Double`. This enables the entire structure
-- to be unboxed.
--
-----------------------------------------------------------------------------

module Numeric.AD.Mode.Forward.Double
  ( AD
  , ForwardDouble
  -- * Gradient
  , grad
  , grad'
  , gradWith
  , gradWith'
  -- * Jacobian
  , jacobian
  , jacobian'
  , jacobianWith
  , jacobianWith'
  -- * Transposed Jacobian
  , jacobianT
  , jacobianWithT
  -- * Derivatives
  , diff
  , diff'
  , diffF
  , diffF'
  -- * Directional Derivatives
  , du
  , du'
  , duF
  , duF'
  ) where

import Numeric.AD.Internal.Type (AD(AD), runAD)
import Numeric.AD.Internal.Forward.Double (ForwardDouble)
import qualified Numeric.AD.Rank1.Forward.Double as Rank1

-- | Compute the directional derivative of a function given a zipped up 'Functor' of the input values and their derivatives
du :: Functor f => (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f (Double, Double) -> Double
du :: forall (f :: * -> *).
Functor f =>
(forall s. f (AD s ForwardDouble) -> AD s ForwardDouble)
-> f (Double, Double) -> Double
du forall s. f (AD s ForwardDouble) -> AD s ForwardDouble
f = (f ForwardDouble -> ForwardDouble) -> f (Double, Double) -> Double
forall (f :: * -> *).
Functor f =>
(f ForwardDouble -> ForwardDouble) -> f (Double, Double) -> Double
Rank1.du (AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD (AD Any ForwardDouble -> ForwardDouble)
-> (f ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble
-> ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
. f (AD Any ForwardDouble) -> AD Any ForwardDouble
forall s. f (AD s ForwardDouble) -> AD s ForwardDouble
f (f (AD Any ForwardDouble) -> AD Any ForwardDouble)
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> AD Any ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE du #-}

-- | Compute the answer and directional derivative of a function given a zipped up 'Functor' of the input values and their derivatives
du' :: Functor f => (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f (Double, Double) -> (Double, Double)
du' :: forall (f :: * -> *).
Functor f =>
(forall s. f (AD s ForwardDouble) -> AD s ForwardDouble)
-> f (Double, Double) -> (Double, Double)
du' forall s. f (AD s ForwardDouble) -> AD s ForwardDouble
f = (f ForwardDouble -> ForwardDouble)
-> f (Double, Double) -> (Double, Double)
forall (f :: * -> *).
Functor f =>
(f ForwardDouble -> ForwardDouble)
-> f (Double, Double) -> (Double, Double)
Rank1.du' (AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD (AD Any ForwardDouble -> ForwardDouble)
-> (f ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble
-> ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
. f (AD Any ForwardDouble) -> AD Any ForwardDouble
forall s. f (AD s ForwardDouble) -> AD s ForwardDouble
f (f (AD Any ForwardDouble) -> AD Any ForwardDouble)
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> AD Any ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE du' #-}

-- | Compute a vector of directional derivatives for a function given a zipped up 'Functor' of the input values and their derivatives.
duF :: (Functor f, Functor g) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f (Double, Double) -> g Double
duF :: forall (f :: * -> *) (g :: * -> *).
(Functor f, Functor g) =>
(forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble))
-> f (Double, Double) -> g Double
duF forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f = (f ForwardDouble -> g ForwardDouble)
-> f (Double, Double) -> g Double
forall (f :: * -> *) (g :: * -> *).
(Functor f, Functor g) =>
(f ForwardDouble -> g ForwardDouble)
-> f (Double, Double) -> g Double
Rank1.duF ((AD Any ForwardDouble -> ForwardDouble)
-> g (AD Any ForwardDouble) -> g ForwardDouble
forall a b. (a -> b) -> g a -> g b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD (g (AD Any ForwardDouble) -> g ForwardDouble)
-> (f ForwardDouble -> g (AD Any ForwardDouble))
-> f ForwardDouble
-> g ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
. f (AD Any ForwardDouble) -> g (AD Any ForwardDouble)
forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f (f (AD Any ForwardDouble) -> g (AD Any ForwardDouble))
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> g (AD Any ForwardDouble)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE duF #-}

-- | Compute a vector of answers and directional derivatives for a function given a zipped up 'Functor' of the input values and their derivatives.
duF' :: (Functor f, Functor g) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f (Double, Double) -> g (Double, Double)
duF' :: forall (f :: * -> *) (g :: * -> *).
(Functor f, Functor g) =>
(forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble))
-> f (Double, Double) -> g (Double, Double)
duF' forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f = (f ForwardDouble -> g ForwardDouble)
-> f (Double, Double) -> g (Double, Double)
forall (f :: * -> *) (g :: * -> *).
(Functor f, Functor g) =>
(f ForwardDouble -> g ForwardDouble)
-> f (Double, Double) -> g (Double, Double)
Rank1.duF' ((AD Any ForwardDouble -> ForwardDouble)
-> g (AD Any ForwardDouble) -> g ForwardDouble
forall a b. (a -> b) -> g a -> g b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD (g (AD Any ForwardDouble) -> g ForwardDouble)
-> (f ForwardDouble -> g (AD Any ForwardDouble))
-> f ForwardDouble
-> g ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
. f (AD Any ForwardDouble) -> g (AD Any ForwardDouble)
forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f (f (AD Any ForwardDouble) -> g (AD Any ForwardDouble))
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> g (AD Any ForwardDouble)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE duF' #-}

-- | 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
diff :: (forall s. AD s ForwardDouble -> AD s ForwardDouble)
-> Double -> Double
diff forall s. AD s ForwardDouble -> AD s ForwardDouble
f = (ForwardDouble -> ForwardDouble) -> Double -> Double
Rank1.diff (AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(AD Any ForwardDouble -> ForwardDouble)
-> (ForwardDouble -> AD Any ForwardDouble)
-> ForwardDouble
-> ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.AD Any ForwardDouble -> AD Any ForwardDouble
forall s. AD s ForwardDouble -> AD s ForwardDouble
f(AD Any ForwardDouble -> AD Any ForwardDouble)
-> (ForwardDouble -> AD Any ForwardDouble)
-> ForwardDouble
-> AD Any ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE diff #-}

-- | The 'diff'' function calculates the result and first derivative of scalar-to-scalar function by 'Forward' mode 'AD'
--
-- @
-- 'diff'' 'sin' == 'sin' 'Control.Arrow.&&&' 'cos'
-- 'diff'' f = f 'Control.Arrow.&&&' d f
-- @
--
-- >>> diff' sin 0
-- (0.0,1.0)
--
-- >>> diff' exp 0
-- (1.0,1.0)
diff' :: (forall s. AD s ForwardDouble -> AD s ForwardDouble) -> Double -> (Double, Double)
diff' :: (forall s. AD s ForwardDouble -> AD s ForwardDouble)
-> Double -> (Double, Double)
diff' forall s. AD s ForwardDouble -> AD s ForwardDouble
f = (ForwardDouble -> ForwardDouble) -> Double -> (Double, Double)
Rank1.diff' (AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(AD Any ForwardDouble -> ForwardDouble)
-> (ForwardDouble -> AD Any ForwardDouble)
-> ForwardDouble
-> ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.AD Any ForwardDouble -> AD Any ForwardDouble
forall s. AD s ForwardDouble -> AD s ForwardDouble
f(AD Any ForwardDouble -> AD Any ForwardDouble)
-> (ForwardDouble -> AD Any ForwardDouble)
-> ForwardDouble
-> AD Any ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE diff' #-}

-- | 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
diffF :: forall (f :: * -> *).
Functor f =>
(forall s. AD s ForwardDouble -> f (AD s ForwardDouble))
-> Double -> f Double
diffF forall s. AD s ForwardDouble -> f (AD s ForwardDouble)
f = (ForwardDouble -> f ForwardDouble) -> Double -> f Double
forall (f :: * -> *).
Functor f =>
(ForwardDouble -> f ForwardDouble) -> Double -> f Double
Rank1.diffF ((AD Any ForwardDouble -> ForwardDouble)
-> f (AD Any ForwardDouble) -> f ForwardDouble
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(f (AD Any ForwardDouble) -> f ForwardDouble)
-> (ForwardDouble -> f (AD Any ForwardDouble))
-> ForwardDouble
-> f ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.AD Any ForwardDouble -> f (AD Any ForwardDouble)
forall s. AD s ForwardDouble -> f (AD s ForwardDouble)
f(AD Any ForwardDouble -> f (AD Any ForwardDouble))
-> (ForwardDouble -> AD Any ForwardDouble)
-> ForwardDouble
-> f (AD Any ForwardDouble)
forall b c a. (b -> c) -> (a -> b) -> a -> c
.ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE diffF #-}

-- | 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)]
diffF' :: Functor f => (forall s. AD s ForwardDouble -> f (AD s ForwardDouble)) -> Double -> f (Double, Double)
diffF' :: forall (f :: * -> *).
Functor f =>
(forall s. AD s ForwardDouble -> f (AD s ForwardDouble))
-> Double -> f (Double, Double)
diffF' forall s. AD s ForwardDouble -> f (AD s ForwardDouble)
f = (ForwardDouble -> f ForwardDouble) -> Double -> f (Double, Double)
forall (f :: * -> *).
Functor f =>
(ForwardDouble -> f ForwardDouble) -> Double -> f (Double, Double)
Rank1.diffF' ((AD Any ForwardDouble -> ForwardDouble)
-> f (AD Any ForwardDouble) -> f ForwardDouble
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(f (AD Any ForwardDouble) -> f ForwardDouble)
-> (ForwardDouble -> f (AD Any ForwardDouble))
-> ForwardDouble
-> f ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.AD Any ForwardDouble -> f (AD Any ForwardDouble)
forall s. AD s ForwardDouble -> f (AD s ForwardDouble)
f(AD Any ForwardDouble -> f (AD Any ForwardDouble))
-> (ForwardDouble -> AD Any ForwardDouble)
-> ForwardDouble
-> f (AD Any ForwardDouble)
forall b c a. (b -> c) -> (a -> b) -> a -> c
.ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE diffF' #-}

-- | A fast, simple, transposed Jacobian computed with forward-mode AD.
jacobianT :: (Traversable f, Functor g) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> f (g Double)
jacobianT :: forall (f :: * -> *) (g :: * -> *).
(Traversable f, Functor g) =>
(forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble))
-> f Double -> f (g Double)
jacobianT forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f = (f ForwardDouble -> g ForwardDouble) -> f Double -> f (g Double)
forall (f :: * -> *) (g :: * -> *).
(Traversable f, Functor g) =>
(f ForwardDouble -> g ForwardDouble) -> f Double -> f (g Double)
Rank1.jacobianT ((AD Any ForwardDouble -> ForwardDouble)
-> g (AD Any ForwardDouble) -> g ForwardDouble
forall a b. (a -> b) -> g a -> g b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(g (AD Any ForwardDouble) -> g ForwardDouble)
-> (f ForwardDouble -> g (AD Any ForwardDouble))
-> f ForwardDouble
-> g ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.f (AD Any ForwardDouble) -> g (AD Any ForwardDouble)
forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f(f (AD Any ForwardDouble) -> g (AD Any ForwardDouble))
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> g (AD Any ForwardDouble)
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE jacobianT #-}

-- | A fast, simple, transposed Jacobian computed with 'Forward' mode 'AD' that combines the output with the input.
jacobianWithT :: (Traversable f, Functor g) => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> f (g b)
jacobianWithT :: forall (f :: * -> *) (g :: * -> *) b.
(Traversable f, Functor g) =>
(Double -> Double -> b)
-> (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble))
-> f Double
-> f (g b)
jacobianWithT Double -> Double -> b
g forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f = (Double -> Double -> b)
-> (f ForwardDouble -> g ForwardDouble) -> f Double -> f (g b)
forall (f :: * -> *) (g :: * -> *) b.
(Traversable f, Functor g) =>
(Double -> Double -> b)
-> (f ForwardDouble -> g ForwardDouble) -> f Double -> f (g b)
Rank1.jacobianWithT Double -> Double -> b
g ((AD Any ForwardDouble -> ForwardDouble)
-> g (AD Any ForwardDouble) -> g ForwardDouble
forall a b. (a -> b) -> g a -> g b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(g (AD Any ForwardDouble) -> g ForwardDouble)
-> (f ForwardDouble -> g (AD Any ForwardDouble))
-> f ForwardDouble
-> g ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.f (AD Any ForwardDouble) -> g (AD Any ForwardDouble)
forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f(f (AD Any ForwardDouble) -> g (AD Any ForwardDouble))
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> g (AD Any ForwardDouble)
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE jacobianWithT #-}

-- | Compute the Jacobian using 'Forward' mode 'AD'. This must transpose the result, so 'jacobianT' is faster and allows more result types.
--
--
-- >>> jacobian (\[x,y] -> [y,x,x+y,x*y,exp x * sin y]) [pi,1]
-- [[0.0,1.0],[1.0,0.0],[1.0,1.0],[1.0,3.141592653589793],[19.472221418841606,12.502969588876512]]
jacobian :: (Traversable f, Traversable g) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> g (f Double)
jacobian :: forall (f :: * -> *) (g :: * -> *).
(Traversable f, Traversable g) =>
(forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble))
-> f Double -> g (f Double)
jacobian forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f = (f ForwardDouble -> g ForwardDouble) -> f Double -> g (f Double)
forall (f :: * -> *) (g :: * -> *).
(Traversable f, Traversable g) =>
(f ForwardDouble -> g ForwardDouble) -> f Double -> g (f Double)
Rank1.jacobian ((AD Any ForwardDouble -> ForwardDouble)
-> g (AD Any ForwardDouble) -> g ForwardDouble
forall a b. (a -> b) -> g a -> g b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(g (AD Any ForwardDouble) -> g ForwardDouble)
-> (f ForwardDouble -> g (AD Any ForwardDouble))
-> f ForwardDouble
-> g ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.f (AD Any ForwardDouble) -> g (AD Any ForwardDouble)
forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f(f (AD Any ForwardDouble) -> g (AD Any ForwardDouble))
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> g (AD Any ForwardDouble)
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE jacobian #-}

-- | Compute the Jacobian using 'Forward' mode 'AD' and combine the output with the input. This must transpose the result, so 'jacobianWithT' is faster, and allows more result types.
jacobianWith :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> g (f b)
jacobianWith :: forall (f :: * -> *) (g :: * -> *) b.
(Traversable f, Traversable g) =>
(Double -> Double -> b)
-> (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble))
-> f Double
-> g (f b)
jacobianWith Double -> Double -> b
g forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f = (Double -> Double -> b)
-> (f ForwardDouble -> g ForwardDouble) -> f Double -> g (f b)
forall (f :: * -> *) (g :: * -> *) b.
(Traversable f, Traversable g) =>
(Double -> Double -> b)
-> (f ForwardDouble -> g ForwardDouble) -> f Double -> g (f b)
Rank1.jacobianWith Double -> Double -> b
g ((AD Any ForwardDouble -> ForwardDouble)
-> g (AD Any ForwardDouble) -> g ForwardDouble
forall a b. (a -> b) -> g a -> g b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(g (AD Any ForwardDouble) -> g ForwardDouble)
-> (f ForwardDouble -> g (AD Any ForwardDouble))
-> f ForwardDouble
-> g ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.f (AD Any ForwardDouble) -> g (AD Any ForwardDouble)
forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f(f (AD Any ForwardDouble) -> g (AD Any ForwardDouble))
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> g (AD Any ForwardDouble)
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE jacobianWith #-}

-- | Compute the Jacobian using 'Forward' mode 'AD' along with the actual answer.
jacobian' :: (Traversable f, Traversable g) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> g (Double, f Double)
jacobian' :: forall (f :: * -> *) (g :: * -> *).
(Traversable f, Traversable g) =>
(forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble))
-> f Double -> g (Double, f Double)
jacobian' forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f = (f ForwardDouble -> g ForwardDouble)
-> f Double -> g (Double, f Double)
forall (f :: * -> *) (g :: * -> *).
(Traversable f, Traversable g) =>
(f ForwardDouble -> g ForwardDouble)
-> f Double -> g (Double, f Double)
Rank1.jacobian' ((AD Any ForwardDouble -> ForwardDouble)
-> g (AD Any ForwardDouble) -> g ForwardDouble
forall a b. (a -> b) -> g a -> g b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(g (AD Any ForwardDouble) -> g ForwardDouble)
-> (f ForwardDouble -> g (AD Any ForwardDouble))
-> f ForwardDouble
-> g ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.f (AD Any ForwardDouble) -> g (AD Any ForwardDouble)
forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f(f (AD Any ForwardDouble) -> g (AD Any ForwardDouble))
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> g (AD Any ForwardDouble)
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE jacobian' #-}

-- | Compute the Jacobian using 'Forward' mode 'AD' combined with the input using a user specified function, along with the actual answer.
jacobianWith' :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> g (Double, f b)
jacobianWith' :: forall (f :: * -> *) (g :: * -> *) b.
(Traversable f, Traversable g) =>
(Double -> Double -> b)
-> (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble))
-> f Double
-> g (Double, f b)
jacobianWith' Double -> Double -> b
g forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f = (Double -> Double -> b)
-> (f ForwardDouble -> g ForwardDouble)
-> f Double
-> g (Double, f b)
forall (f :: * -> *) (g :: * -> *) b.
(Traversable f, Traversable g) =>
(Double -> Double -> b)
-> (f ForwardDouble -> g ForwardDouble)
-> f Double
-> g (Double, f b)
Rank1.jacobianWith' Double -> Double -> b
g ((AD Any ForwardDouble -> ForwardDouble)
-> g (AD Any ForwardDouble) -> g ForwardDouble
forall a b. (a -> b) -> g a -> g b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(g (AD Any ForwardDouble) -> g ForwardDouble)
-> (f ForwardDouble -> g (AD Any ForwardDouble))
-> f ForwardDouble
-> g ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.f (AD Any ForwardDouble) -> g (AD Any ForwardDouble)
forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)
f(f (AD Any ForwardDouble) -> g (AD Any ForwardDouble))
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> g (AD Any ForwardDouble)
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE jacobianWith' #-}

-- | Compute the gradient of a function using forward mode AD.
--
-- Note, this performs /O(n)/ worse than 'Numeric.AD.Mode.Reverse.grad' for @n@ inputs, in exchange for better space utilization.
grad :: Traversable f => (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f Double -> f Double
grad :: forall (f :: * -> *).
Traversable f =>
(forall s. f (AD s ForwardDouble) -> AD s ForwardDouble)
-> f Double -> f Double
grad forall s. f (AD s ForwardDouble) -> AD s ForwardDouble
f = (f ForwardDouble -> ForwardDouble) -> f Double -> f Double
forall (f :: * -> *).
Traversable f =>
(f ForwardDouble -> ForwardDouble) -> f Double -> f Double
Rank1.grad (AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(AD Any ForwardDouble -> ForwardDouble)
-> (f ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble
-> ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.f (AD Any ForwardDouble) -> AD Any ForwardDouble
forall s. f (AD s ForwardDouble) -> AD s ForwardDouble
f(f (AD Any ForwardDouble) -> AD Any ForwardDouble)
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> AD Any ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE grad #-}

-- | Compute the gradient and answer to a function using forward mode AD.
--
-- Note, this performs /O(n)/ worse than 'Numeric.AD.Mode.Reverse.grad'' for @n@ inputs, in exchange for better space utilization.
grad' :: Traversable f => (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f Double -> (Double, f Double)
grad' :: forall (f :: * -> *).
Traversable f =>
(forall s. f (AD s ForwardDouble) -> AD s ForwardDouble)
-> f Double -> (Double, f Double)
grad' forall s. f (AD s ForwardDouble) -> AD s ForwardDouble
f = (f ForwardDouble -> ForwardDouble)
-> f Double -> (Double, f Double)
forall (f :: * -> *).
Traversable f =>
(f ForwardDouble -> ForwardDouble)
-> f Double -> (Double, f Double)
Rank1.grad' (AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(AD Any ForwardDouble -> ForwardDouble)
-> (f ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble
-> ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.f (AD Any ForwardDouble) -> AD Any ForwardDouble
forall s. f (AD s ForwardDouble) -> AD s ForwardDouble
f(f (AD Any ForwardDouble) -> AD Any ForwardDouble)
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> AD Any ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE grad' #-}

-- | Compute the gradient of a function using forward mode AD and combine the result with the input using a user-specified function.
--
-- Note, this performs /O(n)/ worse than 'Numeric.AD.Mode.Reverse.gradWith' for @n@ inputs, in exchange for better space utilization.
gradWith :: Traversable f => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f Double -> f b
gradWith :: forall (f :: * -> *) b.
Traversable f =>
(Double -> Double -> b)
-> (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble)
-> f Double
-> f b
gradWith Double -> Double -> b
g forall s. f (AD s ForwardDouble) -> AD s ForwardDouble
f = (Double -> Double -> b)
-> (f ForwardDouble -> ForwardDouble) -> f Double -> f b
forall (f :: * -> *) b.
Traversable f =>
(Double -> Double -> b)
-> (f ForwardDouble -> ForwardDouble) -> f Double -> f b
Rank1.gradWith Double -> Double -> b
g (AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(AD Any ForwardDouble -> ForwardDouble)
-> (f ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble
-> ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.f (AD Any ForwardDouble) -> AD Any ForwardDouble
forall s. f (AD s ForwardDouble) -> AD s ForwardDouble
f(f (AD Any ForwardDouble) -> AD Any ForwardDouble)
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> AD Any ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE gradWith #-}

-- | Compute the gradient of a function using forward mode AD and the answer, and combine the result with the input using a
-- user-specified function.
--
-- Note, this performs /O(n)/ worse than 'Numeric.AD.Mode.Reverse.gradWith'' for @n@ inputs, in exchange for better space utilization.
--
-- >>> gradWith' (,) sum [0..4]
-- (10.0,[(0.0,1.0),(1.0,1.0),(2.0,1.0),(3.0,1.0),(4.0,1.0)])
gradWith' :: Traversable f => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f Double -> (Double, f b)
gradWith' :: forall (f :: * -> *) b.
Traversable f =>
(Double -> Double -> b)
-> (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble)
-> f Double
-> (Double, f b)
gradWith' Double -> Double -> b
g forall s. f (AD s ForwardDouble) -> AD s ForwardDouble
f = (Double -> Double -> b)
-> (f ForwardDouble -> ForwardDouble) -> f Double -> (Double, f b)
forall (f :: * -> *) b.
Traversable f =>
(Double -> Double -> b)
-> (f ForwardDouble -> ForwardDouble) -> f Double -> (Double, f b)
Rank1.gradWith' Double -> Double -> b
g (AD Any ForwardDouble -> ForwardDouble
forall s a. AD s a -> a
runAD(AD Any ForwardDouble -> ForwardDouble)
-> (f ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble
-> ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.f (AD Any ForwardDouble) -> AD Any ForwardDouble
forall s. f (AD s ForwardDouble) -> AD s ForwardDouble
f(f (AD Any ForwardDouble) -> AD Any ForwardDouble)
-> (f ForwardDouble -> f (AD Any ForwardDouble))
-> f ForwardDouble
-> AD Any ForwardDouble
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(ForwardDouble -> AD Any ForwardDouble)
-> f ForwardDouble -> f (AD Any ForwardDouble)
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ForwardDouble -> AD Any ForwardDouble
forall s a. a -> AD s a
AD)
{-# INLINE gradWith' #-}