ad-4.5: src/Numeric/AD/Internal/Dense.hs
{-# LANGUAGE CPP #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE UndecidableInstances #-}
{-# OPTIONS_HADDOCK not-home #-}
-----------------------------------------------------------------------------
-- |
-- Copyright : (c) Edward Kmett 2010-2021
-- License : BSD3
-- Maintainer : ekmett@gmail.com
-- Stability : experimental
-- Portability : GHC only
--
-- Dense Forward AD. Useful when the result involves the majority of the input
-- elements. Do not use for 'Numeric.AD.Mode.Mixed.hessian' and beyond, since
-- they only contain a small number of unique @n@th derivatives --
-- @(n + k - 1) `choose` k@ for functions of @k@ inputs rather than the
-- @k^n@ that would be generated by using 'Dense', not to mention the redundant
-- intermediate derivatives that would be
-- calculated over and over during that process!
--
-- Assumes all instances of 'f' have the same number of elements.
--
-- NB: We don't need the full power of 'Traversable' here, we could get
-- by with a notion of zippable that can plug in 0's for the missing
-- entries. This might allow for gradients where @f@ has exponentials like @((->) a)@
-----------------------------------------------------------------------------
module Numeric.AD.Internal.Dense
( Dense(..)
, ds
, ds'
, vars
, apply
) where
import Control.Monad (join)
import Data.Typeable ()
import Data.Traversable (mapAccumL)
import Data.Data ()
import Data.Number.Erf
import Numeric.AD.Internal.Combinators
import Numeric.AD.Internal.Identity
import Numeric.AD.Jacobian
import Numeric.AD.Mode
data Dense f a
= Lift !a
| Dense !a (f a)
| Zero
instance Show a => Show (Dense f a) where
showsPrec d (Lift a) = showsPrec d a
showsPrec d (Dense a _) = showsPrec d a
showsPrec _ Zero = showString "0"
ds :: f a -> Dense f a -> f a
ds _ (Dense _ da) = da
ds z _ = z
{-# INLINE ds #-}
ds' :: Num a => f a -> Dense f a -> (a, f a)
ds' _ (Dense a da) = (a, da)
ds' z (Lift a) = (a, z)
ds' z Zero = (0, z)
{-# INLINE ds' #-}
-- Bind variables and count inputs
vars :: (Traversable f, Num a) => f a -> f (Dense f a)
vars as = snd $ mapAccumL outer (0 :: Int) as where
outer !i a = (i + 1, Dense a $ snd $ mapAccumL (inner i) 0 as)
inner !i !j _ = (j + 1, if i == j then 1 else 0)
{-# INLINE vars #-}
apply :: (Traversable f, Num a) => (f (Dense f a) -> b) -> f a -> b
apply f as = f (vars as)
{-# INLINE apply #-}
primal :: Num a => Dense f a -> a
primal Zero = 0
primal (Lift a) = a
primal (Dense a _) = a
instance (Num a, Traversable f) => Mode (Dense f a) where
type Scalar (Dense f a) = a
asKnownConstant (Lift a) = Just a
asKnownConstant Zero = Just 0
asKnownConstant _ = Nothing
isKnownConstant Dense{} = False
isKnownConstant _ = True
isKnownZero Zero = True
isKnownZero _ = False
auto = Lift
zero = Zero
_ *^ Zero = Zero
a *^ Lift b = Lift (a * b)
a *^ Dense b db = Dense (a * b) $ fmap (a*) db
Zero ^* _ = Zero
Lift a ^* b = Lift (a * b)
Dense a da ^* b = Dense (a * b) $ fmap (*b) da
Zero ^/ _ = Zero
Lift a ^/ b = Lift (a / b)
Dense a da ^/ b = Dense (a / b) $ fmap (/b) da
(<+>) :: (Traversable f, Num a) => Dense f a -> Dense f a -> Dense f a
Zero <+> a = a
a <+> Zero = a
Lift a <+> Lift b = Lift (a + b)
Lift a <+> Dense b db = Dense (a + b) db
Dense a da <+> Lift b = Dense (a + b) da
Dense a da <+> Dense b db = Dense (a + b) $ zipWithT (+) da db
instance (Traversable f, Num a) => Jacobian (Dense f a) where
type D (Dense f a) = Id a
unary f _ Zero = Lift (f 0)
unary f _ (Lift b) = Lift (f b)
unary f (Id dadb) (Dense b db) = Dense (f b) (fmap (dadb *) db)
lift1 f _ Zero = Lift (f 0)
lift1 f _ (Lift b) = Lift (f b)
lift1 f df (Dense b db) = Dense (f b) (fmap (dadb *) db) where
Id dadb = df (Id b)
lift1_ f _ Zero = Lift (f 0)
lift1_ f _ (Lift b) = Lift (f b)
lift1_ f df (Dense b db) = Dense a (fmap (dadb *) db) where
a = f b
Id dadb = df (Id a) (Id b)
binary f _ _ Zero Zero = Lift (f 0 0)
binary f _ _ Zero (Lift c) = Lift (f 0 c)
binary f _ _ (Lift b) Zero = Lift (f b 0)
binary f _ _ (Lift b) (Lift c) = Lift (f b c)
binary f _ (Id dadc) Zero (Dense c dc) = Dense (f 0 c) $ fmap (* dadc) dc
binary f _ (Id dadc) (Lift b) (Dense c dc) = Dense (f b c) $ fmap (* dadc) dc
binary f (Id dadb) _ (Dense b db) Zero = Dense (f b 0) $ fmap (dadb *) db
binary f (Id dadb) _ (Dense b db) (Lift c) = Dense (f b c) $ fmap (dadb *) db
binary f (Id dadb) (Id dadc) (Dense b db) (Dense c dc) = Dense (f b c) $ zipWithT productRule db dc where
productRule dbi dci = dadb * dbi + dci * dadc
lift2 f _ Zero Zero = Lift (f 0 0)
lift2 f _ Zero (Lift c) = Lift (f 0 c)
lift2 f _ (Lift b) Zero = Lift (f b 0)
lift2 f _ (Lift b) (Lift c) = Lift (f b c)
lift2 f df Zero (Dense c dc) = Dense (f 0 c) $ fmap (*dadc) dc where dadc = runId (snd (df (Id 0) (Id c)))
lift2 f df (Lift b) (Dense c dc) = Dense (f b c) $ fmap (*dadc) dc where dadc = runId (snd (df (Id b) (Id c)))
lift2 f df (Dense b db) Zero = Dense (f b 0) $ fmap (dadb*) db where dadb = runId (fst (df (Id b) (Id 0)))
lift2 f df (Dense b db) (Lift c) = Dense (f b c) $ fmap (dadb*) db where dadb = runId (fst (df (Id b) (Id c)))
lift2 f df (Dense b db) (Dense c dc) = Dense (f b c) da where
(Id dadb, Id dadc) = df (Id b) (Id c)
da = zipWithT productRule db dc
productRule dbi dci = dadb * dbi + dci * dadc
lift2_ f _ Zero Zero = Lift (f 0 0)
lift2_ f _ Zero (Lift c) = Lift (f 0 c)
lift2_ f _ (Lift b) Zero = Lift (f b 0)
lift2_ f _ (Lift b) (Lift c) = Lift (f b c)
lift2_ f df Zero (Dense c dc) = Dense a $ fmap (*dadc) dc where
a = f 0 c
(_, Id dadc) = df (Id a) (Id 0) (Id c)
lift2_ f df (Lift b) (Dense c dc) = Dense a $ fmap (*dadc) dc where
a = f b c
(_, Id dadc) = df (Id a) (Id b) (Id c)
lift2_ f df (Dense b db) Zero = Dense a $ fmap (dadb*) db where
a = f b 0
(Id dadb, _) = df (Id a) (Id b) (Id 0)
lift2_ f df (Dense b db) (Lift c) = Dense a $ fmap (dadb*) db where
a = f b c
(Id dadb, _) = df (Id a) (Id b) (Id c)
lift2_ f df (Dense b db) (Dense c dc) = Dense a $ zipWithT productRule db dc where
a = f b c
(Id dadb, Id dadc) = df (Id a) (Id b) (Id c)
productRule dbi dci = dadb * dbi + dci * dadc
mul :: (Traversable f, Num a) => Dense f a -> Dense f a -> Dense f a
mul = lift2 (*) (\x y -> (y, x))
#define BODY1(x) (Traversable f, x) =>
#define BODY2(x,y) (Traversable f, x, y) =>
#define HEAD (Dense f a)
#include "instances.h"