Safe Haskell	Safe-Inferred
Language	Haskell2010

ConCat.GAD

Description

Generalized automatic differentiation

Synopsis

newtype GD k a b = D {
- unD :: a -> b :* (a `k` b)
}
mkD :: HasRep (a `k` b) => (a -> b :* Rep (a `k` b)) -> GD k a b
unMkD :: HasRep (a `k` b) => GD k a b -> a -> b :* Rep (a `k` b)
linearD :: (a -> b) -> (a `k` b) -> GD k a b
scalarD :: ScalarCat k s => (s -> s) -> (s -> s -> s) -> GD k s s
scalarR :: ScalarCat k s => (s -> s) -> (s -> s) -> GD k s s
scalarX :: ScalarCat k s => (s -> s) -> (s -> s) -> GD k s s
discreteD :: (ConstCat k b, Ok k a, Additive b) => (a -> b) -> GD k a b
notDef :: String -> a
andDeriv :: forall k a b. (a -> b) -> a -> b :* (a `k` b)
deriv :: forall k a b. (a -> b) -> a -> a `k` b

Documentation

newtype GD k a b Source #

Constructors

D
Fields unD :: a -> b :* (a `k` b)

Instances

Instances details

(Num s, Additive s, Atomic s) => NumCat Inc s Source #
Instance details Defined in ConCat.Incremental Methods negateC :: Inc s s Source # addC :: Inc (Prod Inc s s) s Source # subC :: Inc (Prod Inc s s) s Source # mulC :: Inc (Prod Inc s s) s Source # powIC :: Inc (Prod Inc s Int) s Source #
(CoerceCat (->) a b, CoerceCat k a b) => CoerceCat (GD k :: Type -> Type -> Type) (a :: Type) (b :: Type) Source #
Instance details Defined in ConCat.GAD Methods coerceC :: GD k a b Source #
(RepCat (->) a r, RepCat k a r) => RepCat (GD k :: Type -> Type -> Type) (a :: Type) (r :: Type) Source #
Instance details Defined in ConCat.GAD Methods reprC :: GD k a r Source # abstC :: GD k r a Source #
(OkCAR (GD k a b), IfCat (:>) (Rep (GD k a b))) => IfCat (:>) (GD k a b) Source #
Instance details Defined in ConCat.GAD Methods ifC :: IfT (:>) (GD k a b) Source #
AssociativePCat k => AssociativePCat (GD k) Source #
Instance details Defined in ConCat.GAD Methods lassocP :: Ok3 (GD k) a b c => GD k (Prod (GD k) a (Prod (GD k) b c)) (Prod (GD k) (Prod (GD k) a b) c) Source # rassocP :: Ok3 (GD k) a b c => GD k (Prod (GD k) (Prod (GD k) a b) c) (Prod (GD k) a (Prod (GD k) b c)) Source #
(ProductCat k, ConstCat k Bool, Ok k Bool) => BoolCat (GD k) Source #
Instance details Defined in ConCat.GAD Methods notC :: GD k (BoolOf (GD k)) (BoolOf (GD k)) Source # andC :: GD k (Prod (GD k) (BoolOf (GD k)) (BoolOf (GD k))) (BoolOf (GD k)) Source # orC :: GD k (Prod (GD k) (BoolOf (GD k)) (BoolOf (GD k))) (BoolOf (GD k)) Source # xorC :: GD k (Prod (GD k) (BoolOf (GD k)) (BoolOf (GD k))) (BoolOf (GD k)) Source #
BraidedPCat k => BraidedPCat (GD k) Source #
Instance details Defined in ConCat.GAD Methods swapP :: Ok2 (GD k) a b => GD k (Prod (GD k) a b) (Prod (GD k) b a) Source #
Category k => Category (GD k) Source #
Instance details Defined in ConCat.GAD Associated Types type Ok (GD k) :: Type -> Constraint Source # Methods id :: Ok (GD k) a => GD k a a Source # (.) :: forall b c a. Ok3 (GD k) a b c => GD k b c -> GD k a b -> GD k a c Source #
MonoidalPCat k => MonoidalPCat (GD k) Source #
Instance details Defined in ConCat.GAD Methods (***) :: Ok4 (GD k) a b c d => GD k a c -> GD k b d -> GD k (Prod (GD k) a b) (Prod (GD k) c d) Source # first :: forall a a' b. Ok3 (GD k) a b a' => GD k a a' -> GD k (Prod (GD k) a b) (Prod (GD k) a' b) Source # second :: Ok3 (GD k) a b b' => GD k b b' -> GD k (Prod (GD k) a b) (Prod (GD k) a b') Source #
OkAdd k => OkAdd (GD k) Source #
Instance details Defined in ConCat.GAD Methods okAdd :: Ok' (GD k) a \|- Sat Additive a Source #
ProductCat k => ProductCat (GD k) Source #
Instance details Defined in ConCat.GAD Methods exl :: Ok2 (GD k) a b => GD k (Prod (GD k) a b) a Source # exr :: Ok2 (GD k) a b => GD k (Prod (GD k) a b) b Source # dup :: Ok (GD k) a => GD k a (Prod (GD k) a a) Source #
UnitCat k => UnitCat (GD k) Source #
Instance details Defined in ConCat.GAD Methods lunit :: Ok (GD k) a => GD k a (Prod (GD k) (Unit (GD k)) a) Source # lcounit :: Ok (GD k) a => GD k (Prod (GD k) (Unit (GD k)) a) a Source # runit :: Ok (GD k) a => GD k a (Prod (GD k) a (Unit (GD k))) Source # rcounit :: Ok (GD k) a => GD k (Prod (GD k) a (Unit (GD k))) a Source #
(TerminalCat k, CoterminalCat k, ConstCat k b, Additive b) => ConstCat (GD k) b Source #
Instance details Defined in ConCat.GAD Methods const :: Ok (GD k) a => b -> GD k a (ConstObj (GD k) b) Source # unitArrow :: b -> GD k (Unit (GD k)) (ConstObj (GD k) b) Source #
(ProductCat k, ConstCat k Bool, Eq a, Ok2 k a Bool) => EqCat (GD k) a Source #
Instance details Defined in ConCat.GAD Methods equal :: GD k (Prod (GD k) a a) (BoolOf (GD k)) Source # notEqual :: GD k (Prod (GD k) a a) (BoolOf (GD k)) Source #
(ScalarCat k s, Ok k s, Floating s) => FloatingCat (GD k) s Source #
Instance details Defined in ConCat.GAD Methods expC :: GD k s s Source # logC :: GD k s s Source # cosC :: GD k s s Source # sinC :: GD k s s Source # sqrtC :: GD k s s Source # tanhC :: GD k s s Source #
(LinearCat k s, Additive s, Fractional s) => FractionalCat (GD k) s Source #
Instance details Defined in ConCat.GAD Methods recipC :: GD k s s Source # divideC :: GD k (Prod (GD k) s s) s Source #
(IxProductCat k h, Functor h, FunctorCat k h) => FunctorCat (GD k) h Source #
Instance details Defined in ConCat.GAD Methods fmapC :: Ok2 (GD k) a b => GD k a b -> GD k (h a) (h b) Source # unzipC :: Ok2 (GD k) a b => GD k (h (a :* b)) (h a :* h b) Source #
(ProductCat k, ConstCat k Bool, Ok2 k Bool a) => IfCat (GD k) a Source #
Instance details Defined in ConCat.GAD Methods ifC :: IfT (GD k) a Source #
(IxMonoidalPCat (->) h, IxMonoidalPCat k h, Zip h) => IxMonoidalPCat (GD k) h Source #
Instance details Defined in ConCat.GAD Methods crossF :: Ok2 (GD k) a b => h (GD k a b) -> GD k (h a) (h b) Source #
(IxProductCat (->) h, IxProductCat k h, Zip h) => IxProductCat (GD k) h Source #
Instance details Defined in ConCat.GAD Methods exF :: Ok (GD k) a => h (GD k (h a) a) Source # forkF :: Ok2 (GD k) a b => h (GD k a b) -> GD k a (h b) Source # replF :: Ok (GD k) a => GD k a (h a) Source #
(ProductCat k, Ok k a, Ord a) => MinMaxCat (GD k) a Source #
Instance details Defined in ConCat.GAD Methods minC :: GD k (Prod (GD k) a a) a Source # maxC :: GD k (Prod (GD k) a a) a Source #
(LinearCat k s, Additive s, Num s) => NumCat (GD k) s Source #
Instance details Defined in ConCat.GAD Methods negateC :: GD k s s Source # addC :: GD k (Prod (GD k) s s) s Source # subC :: GD k (Prod (GD k) s s) s Source # mulC :: GD k (Prod (GD k) s s) s Source # powIC :: GD k (Prod (GD k) s Int) s Source #
OkFunctor k h => OkFunctor (GD k) h Source #
Instance details Defined in ConCat.GAD Methods okFunctor :: Ok' (GD k) a \|- Ok' (GD k) (h a) Source #
OkIxProd k h => OkIxProd (GD k) h Source #
Instance details Defined in ConCat.GAD Methods okIxProd :: Ok' (GD k) a \|- Ok' (GD k) (h a) Source #
(ProductCat k, ConstCat k Bool, Ord a, Ok2 k a Bool) => OrdCat (GD k) a Source #
Instance details Defined in ConCat.GAD Methods lessThan :: GD k (Prod (GD k) a a) (BoolOf (GD k)) Source # greaterThan :: GD k (Prod (GD k) a a) (BoolOf (GD k)) Source # lessThanOrEqual :: GD k (Prod (GD k) a a) (BoolOf (GD k)) Source # greaterThanOrEqual :: GD k (Prod (GD k) a a) (BoolOf (GD k)) Source #
(RepresentableCat (->) g, RepresentableCat k g) => RepresentableCat (GD k) g Source #
Instance details Defined in ConCat.GAD Methods tabulateC :: Ok (GD k) a => GD k (Rep g -> a) (g a) Source # indexC :: Ok (GD k) a => GD k (g a) (Rep g -> a) Source #
(ZapCat k h, OkFunctor k h, Zip h) => ZapCat (GD k) h Source #
Instance details Defined in ConCat.GAD Methods zapC :: Ok2 (GD k) a b => h (GD k a b) -> GD k (h a) (h b) Source #
(ZipCat k h, OkFunctor (GD k) h) => ZipCat (GD k) h Source #
Instance details Defined in ConCat.GAD Methods zipC :: Ok2 (GD k) a b => GD k (h a :* h b) (h (a :* b)) Source #
(AddCat (->) h a, AddCat k h a, OkFunctor (GD k) h) => AddCat (GD k) h a Source #
Instance details Defined in ConCat.GAD Methods sumAC :: GD k (h a) a Source #
(DistributiveCat (->) g f, DistributiveCat k g f) => DistributiveCat (GD k) g f Source #
Instance details Defined in ConCat.GAD Methods distributeC :: Ok (GD k) a => GD k (f (g a)) (g (f a)) Source #
(ProductCat k, MinMaxFFunctorCat k h a, Ord a) => MinMaxFunctorCat (GD k) h a Source #
Instance details Defined in ConCat.GAD Methods minimumC :: GD k (h a) a Source # maximumC :: GD k (h a) a Source #
(OkFunctor (GD k) h, Pointed h, PointedCat k h a) => PointedCat (GD k) h a Source #
Instance details Defined in ConCat.GAD Methods pointC :: GD k a (h a) Source #
(TraversableCat (->) t f, TraversableCat k t f) => TraversableCat (GD k) t f Source #
Instance details Defined in ConCat.GAD Methods sequenceAC :: Ok (GD k) a => GD k (t (f a)) (f (t a)) Source #
HasRep (GD k a b) Source #
Instance details Defined in ConCat.GAD Associated Types type Rep (GD k a b) Source # Methods repr :: GD k a b -> Rep (GD k a b) Source # abst :: Rep (GD k a b) -> GD k a b Source #
OkCAR (GD k a b) => GenBuses (GD k a b) Source #
Instance details Defined in ConCat.GAD Methods genBuses' :: Template u v -> [Source] -> BusesM (Buses (GD k a b)) Source # ty :: Ty Source # unflattenB' :: State [Source] (Buses (GD k a b)) Source #
type Ok (GD k) Source #
Instance details Defined in ConCat.GAD type Ok (GD k) = Ok k
type Rep (GD k a b) Source #
Instance details Defined in ConCat.GAD type Rep (GD k a b) = a -> b :* k a b

mkD :: HasRep (a `k` b) => (a -> b :* Rep (a `k` b)) -> GD k a b Source #

unMkD :: HasRep (a `k` b) => GD k a b -> a -> b :* Rep (a `k` b) Source #

linearD :: (a -> b) -> (a `k` b) -> GD k a b Source #

scalarD :: ScalarCat k s => (s -> s) -> (s -> s -> s) -> GD k s s Source #

scalarR :: ScalarCat k s => (s -> s) -> (s -> s) -> GD k s s Source #

scalarX :: ScalarCat k s => (s -> s) -> (s -> s) -> GD k s s Source #

discreteD :: (ConstCat k b, Ok k a, Additive b) => (a -> b) -> GD k a b Source #

notDef :: String -> a Source #

andDeriv :: forall k a b. (a -> b) -> a -> b :* (a `k` b) Source #

A function combined with its derivative

deriv :: forall k a b. (a -> b) -> a -> a `k` b Source #

The derivative of a given function