Numeric.AD.Internal.Dense

Dense Forward AD. Useful when the result involves the majority of the input elements. Do not use for hessian and beyond, since they only contain a small number of unique nth 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)

Documentation

data Dense f a

Constructors

Lift !a

Dense !a (f a)

Zero

Instances

(Traversable f, Num a, Bounded a) => Bounded (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

minBound :: Dense f a

maxBound :: Dense f a

(Traversable f, Num a, Enum a) => Enum (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

succ :: Dense f a -> Dense f a

pred :: Dense f a -> Dense f a

toEnum :: Int -> Dense f a

fromEnum :: Dense f a -> Int

enumFrom :: Dense f a -> [Dense f a]

enumFromThen :: Dense f a -> Dense f a -> [Dense f a]

enumFromTo :: Dense f a -> Dense f a -> [Dense f a]

enumFromThenTo :: Dense f a -> Dense f a -> Dense f a -> [Dense f a]

(Traversable f, Num a, Eq a) => Eq (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

(==) :: Dense f a -> Dense f a -> Bool

(/=) :: Dense f a -> Dense f a -> Bool

(Traversable f, Floating a) => Floating (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

pi :: Dense f a

exp :: Dense f a -> Dense f a

log :: Dense f a -> Dense f a

sqrt :: Dense f a -> Dense f a

(**) :: Dense f a -> Dense f a -> Dense f a

logBase :: Dense f a -> Dense f a -> Dense f a

sin :: Dense f a -> Dense f a

cos :: Dense f a -> Dense f a

tan :: Dense f a -> Dense f a

asin :: Dense f a -> Dense f a

acos :: Dense f a -> Dense f a

atan :: Dense f a -> Dense f a

sinh :: Dense f a -> Dense f a

cosh :: Dense f a -> Dense f a

tanh :: Dense f a -> Dense f a

asinh :: Dense f a -> Dense f a

acosh :: Dense f a -> Dense f a

atanh :: Dense f a -> Dense f a

log1p :: Dense f a -> Dense f a

expm1 :: Dense f a -> Dense f a

log1pexp :: Dense f a -> Dense f a

log1mexp :: Dense f a -> Dense f a

(Traversable f, Fractional a) => Fractional (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

(/) :: Dense f a -> Dense f a -> Dense f a

recip :: Dense f a -> Dense f a

fromRational :: Rational -> Dense f a

(Traversable f, Num a) => Num (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

(+) :: Dense f a -> Dense f a -> Dense f a

(-) :: Dense f a -> Dense f a -> Dense f a

(*) :: Dense f a -> Dense f a -> Dense f a

negate :: Dense f a -> Dense f a

abs :: Dense f a -> Dense f a

signum :: Dense f a -> Dense f a

fromInteger :: Integer -> Dense f a

(Traversable f, Num a, Ord a) => Ord (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

compare :: Dense f a -> Dense f a -> Ordering

(<) :: Dense f a -> Dense f a -> Bool

(<=) :: Dense f a -> Dense f a -> Bool

(>) :: Dense f a -> Dense f a -> Bool

(>=) :: Dense f a -> Dense f a -> Bool

max :: Dense f a -> Dense f a -> Dense f a

min :: Dense f a -> Dense f a -> Dense f a

(Traversable f, Real a) => Real (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

toRational :: Dense f a -> Rational

(Traversable f, RealFloat a) => RealFloat (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

floatRadix :: Dense f a -> Integer

floatDigits :: Dense f a -> Int

floatRange :: Dense f a -> (Int, Int)

decodeFloat :: Dense f a -> (Integer, Int)

encodeFloat :: Integer -> Int -> Dense f a

exponent :: Dense f a -> Int

significand :: Dense f a -> Dense f a

scaleFloat :: Int -> Dense f a -> Dense f a

isNaN :: Dense f a -> Bool

isInfinite :: Dense f a -> Bool

isDenormalized :: Dense f a -> Bool

isNegativeZero :: Dense f a -> Bool

isIEEE :: Dense f a -> Bool

atan2 :: Dense f a -> Dense f a -> Dense f a

(Traversable f, RealFrac a) => RealFrac (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

properFraction :: Integral b => Dense f a -> (b, Dense f a)

truncate :: Integral b => Dense f a -> b

round :: Integral b => Dense f a -> b

ceiling :: Integral b => Dense f a -> b

floor :: Integral b => Dense f a -> b

Show a => Show (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

showsPrec :: Int -> Dense f a -> ShowS

show :: Dense f a -> String

showList :: [Dense f a] -> ShowS

(Traversable f, Erf a) => Erf (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

erf :: Dense f a -> Dense f a

erfc :: Dense f a -> Dense f a

erfcx :: Dense f a -> Dense f a

normcdf :: Dense f a -> Dense f a

(Traversable f, InvErf a) => InvErf (Dense f a)

Defined in Numeric.AD.Internal.Dense

Methods

inverf :: Dense f a -> Dense f a

inverfc :: Dense f a -> Dense f a

invnormcdf :: Dense f a -> Dense f a

(Num a, Traversable f) => Mode (Dense f a)

Defined in Numeric.AD.Internal.Dense

Associated Types

type Scalar (Dense f a) :: Type

Methods

isKnownConstant :: Dense f a -> Bool

isKnownZero :: Dense f a -> Bool

auto :: Scalar (Dense f a) -> Dense f a

(*^) :: Scalar (Dense f a) -> Dense f a -> Dense f a

(^*) :: Dense f a -> Scalar (Dense f a) -> Dense f a

(^/) :: Dense f a -> Scalar (Dense f a) -> Dense f a

zero :: Dense f a

(Traversable f, Num a) => Jacobian (Dense f a)

Defined in Numeric.AD.Internal.Dense

Associated Types

type D (Dense f a) :: Type

Methods

unary :: (Scalar (Dense f a) -> Scalar (Dense f a)) -> D (Dense f a) -> Dense f a -> Dense f a

lift1 :: (Scalar (Dense f a) -> Scalar (Dense f a)) -> (D (Dense f a) -> D (Dense f a)) -> Dense f a -> Dense f a

lift1_ :: (Scalar (Dense f a) -> Scalar (Dense f a)) -> (D (Dense f a) -> D (Dense f a) -> D (Dense f a)) -> Dense f a -> Dense f a

binary :: (Scalar (Dense f a) -> Scalar (Dense f a) -> Scalar (Dense f a)) -> D (Dense f a) -> D (Dense f a) -> Dense f a -> Dense f a -> Dense f a

lift2 :: (Scalar (Dense f a) -> Scalar (Dense f a) -> Scalar (Dense f a)) -> (D (Dense f a) -> D (Dense f a) -> (D (Dense f a), D (Dense f a))) -> Dense f a -> Dense f a -> Dense f a

lift2_ :: (Scalar (Dense f a) -> Scalar (Dense f a) -> Scalar (Dense f a)) -> (D (Dense f a) -> D (Dense f a) -> D (Dense f a) -> (D (Dense f a), D (Dense f a))) -> Dense f a -> Dense f a -> Dense f a

type Scalar (Dense f a)

Defined in Numeric.AD.Internal.Dense

type Scalar (Dense f a) = a

type D (Dense f a)

Defined in Numeric.AD.Internal.Dense

type D (Dense f a) = Id a

ds :: f a -> Dense f a -> f a

ds' :: Num a => f a -> Dense f a -> (a, f a)

vars :: (Traversable f, Num a) => f a -> f (Dense f a)

apply :: (Traversable f, Num a) => (f (Dense f a) -> b) -> f a -> b