Downhill.BVar.Num

Documentation

Automatic differentiation for Num hierarchy.

Polymorphic functions of type such as Num a => a -> a can't be differentiated directly, because backprop needs some additional instances. AsNum wrapper provides those instances.

derivative :: (forall b. Floating b => b -> b) -> (forall a. Floating a => a -> a)
derivative fun x0 = backpropNum (fun (var (AsNum x0)))

newtype AsNum a

AsNum a implements many instances in terms of Num a instance.

Constructors

AsNum

Fields

• unAsNum :: a

Instances

Floating a => Floating (AsNum a)

Defined in Downhill.BVar.Num

Methods

pi :: AsNum a

exp :: AsNum a -> AsNum a

log :: AsNum a -> AsNum a

sqrt :: AsNum a -> AsNum a

(**) :: AsNum a -> AsNum a -> AsNum a

logBase :: AsNum a -> AsNum a -> AsNum a

sin :: AsNum a -> AsNum a

cos :: AsNum a -> AsNum a

tan :: AsNum a -> AsNum a

asin :: AsNum a -> AsNum a

acos :: AsNum a -> AsNum a

atan :: AsNum a -> AsNum a

sinh :: AsNum a -> AsNum a

cosh :: AsNum a -> AsNum a

tanh :: AsNum a -> AsNum a

asinh :: AsNum a -> AsNum a

acosh :: AsNum a -> AsNum a

atanh :: AsNum a -> AsNum a

log1p :: AsNum a -> AsNum a

expm1 :: AsNum a -> AsNum a

log1pexp :: AsNum a -> AsNum a

log1mexp :: AsNum a -> AsNum a

Fractional a => Fractional (AsNum a)

Defined in Downhill.BVar.Num

Methods

(/) :: AsNum a -> AsNum a -> AsNum a

recip :: AsNum a -> AsNum a

fromRational :: Rational -> AsNum a

Num a => Num (AsNum a)

Defined in Downhill.BVar.Num

Methods

(+) :: AsNum a -> AsNum a -> AsNum a

(-) :: AsNum a -> AsNum a -> AsNum a

(*) :: AsNum a -> AsNum a -> AsNum a

negate :: AsNum a -> AsNum a

abs :: AsNum a -> AsNum a

signum :: AsNum a -> AsNum a

fromInteger :: Integer -> AsNum a

Show a => Show (AsNum a)

Defined in Downhill.BVar.Num

Methods

showsPrec :: Int -> AsNum a -> ShowS

show :: AsNum a -> String

showList :: [AsNum a] -> ShowS

Num a => AffineSpace (AsNum a)

Defined in Downhill.BVar.Num

Associated Types

type Diff (AsNum a)

Methods

(.-.) :: AsNum a -> AsNum a -> Diff (AsNum a)

(.+^) :: AsNum a -> Diff (AsNum a) -> AsNum a

Num a => VectorSpace (AsNum a)

Defined in Downhill.BVar.Num

Associated Types

type Scalar (AsNum a)

Methods

(*^) :: Scalar (AsNum a) -> AsNum a -> AsNum a

Num a => AdditiveGroup (AsNum a)

Defined in Downhill.BVar.Num

Methods

zeroV :: AsNum a

(^+^) :: AsNum a -> AsNum a -> AsNum a

negateV :: AsNum a -> AsNum a

(^-^) :: AsNum a -> AsNum a -> AsNum a

Num a => FullVector (AsNum a)

Defined in Downhill.BVar.Num

Methods

identityBuilder :: AsNum a -> VecBuilder (AsNum a)

negateBuilder :: AsNum a -> VecBuilder (AsNum a)

scaleBuilder :: Scalar (AsNum a) -> AsNum a -> VecBuilder (AsNum a)

Num a => BasicVector (AsNum a)

Defined in Downhill.BVar.Num

Associated Types

type VecBuilder (AsNum a)

Methods

sumBuilder :: VecBuilder (AsNum a) -> AsNum a

Num a => HasGrad (AsNum a)

Defined in Downhill.BVar.Num

Associated Types

type MScalar (AsNum a)

type Tang (AsNum a)

type Grad (AsNum a)

type Metric (AsNum a)

Num a => MetricTensor (AsNum a)

Defined in Downhill.BVar.Num

Associated Types

type MtVector (AsNum a)

type MtCovector (AsNum a)

Methods

evalMetric :: AsNum a -> MtCovector (AsNum a) -> MtVector (AsNum a)

innerProduct :: AsNum a -> MtCovector (AsNum a) -> MtCovector (AsNum a) -> Scalar (AsNum a)

sqrNorm :: AsNum a -> MtCovector (AsNum a) -> Scalar (AsNum a)

Num a => Dual (AsNum a) (AsNum a) (AsNum a)

Defined in Downhill.BVar.Num

Methods

evalGrad :: AsNum a -> AsNum a -> AsNum a

type Diff (AsNum a)

Defined in Downhill.BVar.Num

type Diff (AsNum a) = AsNum a

type Scalar (AsNum a)

Defined in Downhill.BVar.Num

type Scalar (AsNum a) = AsNum a

type VecBuilder (AsNum a)

Defined in Downhill.BVar.Num

type VecBuilder (AsNum a) = Sum a

type MScalar (AsNum a)

Defined in Downhill.BVar.Num

type MScalar (AsNum a) = AsNum a

type Tang (AsNum a)

Defined in Downhill.BVar.Num

type Tang (AsNum a) = AsNum a

type Grad (AsNum a)

Defined in Downhill.BVar.Num

type Grad (AsNum a) = AsNum a

type Metric (AsNum a)

Defined in Downhill.BVar.Num

type Metric (AsNum a) = AsNum a

type MtVector (AsNum a)

Defined in Downhill.BVar.Num

type MtVector (AsNum a) = AsNum a

type MtCovector (AsNum a)

Defined in Downhill.BVar.Num

type MtCovector (AsNum a) = AsNum a

type NumBVar a = BVar (AsNum a) (AsNum a)

numbvarValue :: NumBVar a -> a

var :: Num a => a -> NumBVar a

constant :: forall a. Num a => a -> NumBVar a

backpropNum :: forall a. Num a => NumBVar a -> a