Numeric.AD.Mode.Dense.Representable

First order dense forward mode using Representable functors

Documentation

data AD s a

Instances

Mode a => Mode (AD s a)

Defined in Numeric.AD.Internal.Type

Associated Types

type Scalar (AD s a)

Methods

isKnownConstant :: AD s a -> Bool

asKnownConstant :: AD s a -> Maybe (Scalar (AD s a))

isKnownZero :: AD s a -> Bool

auto :: Scalar (AD s a) -> AD s a

(*^) :: Scalar (AD s a) -> AD s a -> AD s a

(^*) :: AD s a -> Scalar (AD s a) -> AD s a

(^/) :: AD s a -> Scalar (AD s a) -> AD s a

zero :: AD s a

Bounded a => Bounded (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

minBound :: AD s a

maxBound :: AD s a

Enum a => Enum (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

succ :: AD s a -> AD s a

pred :: AD s a -> AD s a

toEnum :: Int -> AD s a

fromEnum :: AD s a -> Int

enumFrom :: AD s a -> [AD s a]

enumFromThen :: AD s a -> AD s a -> [AD s a]

enumFromTo :: AD s a -> AD s a -> [AD s a]

enumFromThenTo :: AD s a -> AD s a -> AD s a -> [AD s a]

Floating a => Floating (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

pi :: AD s a

exp :: AD s a -> AD s a

log :: AD s a -> AD s a

sqrt :: AD s a -> AD s a

(**) :: AD s a -> AD s a -> AD s a

logBase :: AD s a -> AD s a -> AD s a

sin :: AD s a -> AD s a

cos :: AD s a -> AD s a

tan :: AD s a -> AD s a

asin :: AD s a -> AD s a

acos :: AD s a -> AD s a

atan :: AD s a -> AD s a

sinh :: AD s a -> AD s a

cosh :: AD s a -> AD s a

tanh :: AD s a -> AD s a

asinh :: AD s a -> AD s a

acosh :: AD s a -> AD s a

atanh :: AD s a -> AD s a

log1p :: AD s a -> AD s a

expm1 :: AD s a -> AD s a

log1pexp :: AD s a -> AD s a

log1mexp :: AD s a -> AD s a

RealFloat a => RealFloat (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

floatRadix :: AD s a -> Integer

floatDigits :: AD s a -> Int

floatRange :: AD s a -> (Int, Int)

decodeFloat :: AD s a -> (Integer, Int)

encodeFloat :: Integer -> Int -> AD s a

exponent :: AD s a -> Int

significand :: AD s a -> AD s a

scaleFloat :: Int -> AD s a -> AD s a

isNaN :: AD s a -> Bool

isInfinite :: AD s a -> Bool

isDenormalized :: AD s a -> Bool

isNegativeZero :: AD s a -> Bool

isIEEE :: AD s a -> Bool

atan2 :: AD s a -> AD s a -> AD s a

Num a => Num (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

(+) :: AD s a -> AD s a -> AD s a

(-) :: AD s a -> AD s a -> AD s a

(*) :: AD s a -> AD s a -> AD s a

negate :: AD s a -> AD s a

abs :: AD s a -> AD s a

signum :: AD s a -> AD s a

fromInteger :: Integer -> AD s a

Read a => Read (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

readsPrec :: Int -> ReadS (AD s a)

readList :: ReadS [AD s a]

readPrec :: ReadPrec (AD s a)

readListPrec :: ReadPrec [AD s a]

Fractional a => Fractional (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

(/) :: AD s a -> AD s a -> AD s a

recip :: AD s a -> AD s a

fromRational :: Rational -> AD s a

Real a => Real (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

toRational :: AD s a -> Rational

RealFrac a => RealFrac (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

properFraction :: Integral b => AD s a -> (b, AD s a)

truncate :: Integral b => AD s a -> b

round :: Integral b => AD s a -> b

ceiling :: Integral b => AD s a -> b

floor :: Integral b => AD s a -> b

Show a => Show (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

showsPrec :: Int -> AD s a -> ShowS

show :: AD s a -> String

showList :: [AD s a] -> ShowS

Erf a => Erf (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

erf :: AD s a -> AD s a

erfc :: AD s a -> AD s a

erfcx :: AD s a -> AD s a

normcdf :: AD s a -> AD s a

InvErf a => InvErf (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

inverf :: AD s a -> AD s a

inverfc :: AD s a -> AD s a

invnormcdf :: AD s a -> AD s a

Eq a => Eq (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

(==) :: AD s a -> AD s a -> Bool

(/=) :: AD s a -> AD s a -> Bool

Ord a => Ord (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

compare :: AD s a -> AD s a -> Ordering

(<) :: AD s a -> AD s a -> Bool

(<=) :: AD s a -> AD s a -> Bool

(>) :: AD s a -> AD s a -> Bool

(>=) :: AD s a -> AD s a -> Bool

max :: AD s a -> AD s a -> AD s a

min :: AD s a -> AD s a -> AD s a

type Scalar (AD s a)

Defined in Numeric.AD.Internal.Type

type Scalar (AD s a) = Scalar a

data Repr f a

Instances

(Representable f, Num a) => Jacobian (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Associated Types

type D (Repr f a)

Methods

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

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

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

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

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

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

(Representable f, Num a) => Mode (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Associated Types

type Scalar (Repr f a)

Methods

isKnownConstant :: Repr f a -> Bool

asKnownConstant :: Repr f a -> Maybe (Scalar (Repr f a))

isKnownZero :: Repr f a -> Bool

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

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

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

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

zero :: Repr f a

(Representable f, Num a, Bounded a) => Bounded (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

minBound :: Repr f a

maxBound :: Repr f a

(Representable f, Num a, Enum a) => Enum (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

succ :: Repr f a -> Repr f a

pred :: Repr f a -> Repr f a

toEnum :: Int -> Repr f a

fromEnum :: Repr f a -> Int

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

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

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

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

(Representable f, Floating a) => Floating (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

pi :: Repr f a

exp :: Repr f a -> Repr f a

log :: Repr f a -> Repr f a

sqrt :: Repr f a -> Repr f a

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

logBase :: Repr f a -> Repr f a -> Repr f a

sin :: Repr f a -> Repr f a

cos :: Repr f a -> Repr f a

tan :: Repr f a -> Repr f a

asin :: Repr f a -> Repr f a

acos :: Repr f a -> Repr f a

atan :: Repr f a -> Repr f a

sinh :: Repr f a -> Repr f a

cosh :: Repr f a -> Repr f a

tanh :: Repr f a -> Repr f a

asinh :: Repr f a -> Repr f a

acosh :: Repr f a -> Repr f a

atanh :: Repr f a -> Repr f a

log1p :: Repr f a -> Repr f a

expm1 :: Repr f a -> Repr f a

log1pexp :: Repr f a -> Repr f a

log1mexp :: Repr f a -> Repr f a

(Representable f, RealFloat a) => RealFloat (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

floatRadix :: Repr f a -> Integer

floatDigits :: Repr f a -> Int

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

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

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

exponent :: Repr f a -> Int

significand :: Repr f a -> Repr f a

scaleFloat :: Int -> Repr f a -> Repr f a

isNaN :: Repr f a -> Bool

isInfinite :: Repr f a -> Bool

isDenormalized :: Repr f a -> Bool

isNegativeZero :: Repr f a -> Bool

isIEEE :: Repr f a -> Bool

atan2 :: Repr f a -> Repr f a -> Repr f a

(Representable f, Num a) => Num (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

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

(-) :: Repr f a -> Repr f a -> Repr f a

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

negate :: Repr f a -> Repr f a

abs :: Repr f a -> Repr f a

signum :: Repr f a -> Repr f a

fromInteger :: Integer -> Repr f a

(Representable f, Fractional a) => Fractional (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

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

recip :: Repr f a -> Repr f a

fromRational :: Rational -> Repr f a

(Representable f, Real a) => Real (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

toRational :: Repr f a -> Rational

(Representable f, RealFrac a) => RealFrac (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

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

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

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

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

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

Show a => Show (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

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

show :: Repr f a -> String

showList :: [Repr f a] -> ShowS

(Representable f, Erf a) => Erf (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

erf :: Repr f a -> Repr f a

erfc :: Repr f a -> Repr f a

erfcx :: Repr f a -> Repr f a

normcdf :: Repr f a -> Repr f a

(Representable f, InvErf a) => InvErf (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

inverf :: Repr f a -> Repr f a

inverfc :: Repr f a -> Repr f a

invnormcdf :: Repr f a -> Repr f a

(Representable f, Num a, Eq a) => Eq (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

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

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

(Representable f, Num a, Ord a) => Ord (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

Methods

compare :: Repr f a -> Repr f a -> Ordering

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

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

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

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

max :: Repr f a -> Repr f a -> Repr f a

min :: Repr f a -> Repr f a -> Repr f a

type D (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

type D (Repr f a) = Id a

type Scalar (Repr f a)

Defined in Numeric.AD.Internal.Dense.Representable

type Scalar (Repr f a) = a

auto :: Mode t => Scalar t -> t

Embed a constant

Dense Gradients

grad :: (Representable f, Eq (Rep f), Num a) => (forall s. f (AD s (Repr f a)) -> AD s (Repr f a)) -> f a -> f a

The grad function calculates the gradient of a non-scalar-to-scalar function with dense-mode AD in a single pass.

>>> grad (\(V3 x y z) -> x*y+z) (V3 1 2 3)
V3 2 1 1

grad' :: (Representable f, Eq (Rep f), Num a) => (forall s. f (AD s (Repr f a)) -> AD s (Repr f a)) -> f a -> (a, f a)

gradWith :: (Representable f, Eq (Rep f), Num a) => (a -> a -> b) -> (forall s. f (AD s (Repr f a)) -> AD s (Repr f a)) -> f a -> f b

gradWith' :: (Representable f, Eq (Rep f), Num a) => (a -> a -> b) -> (forall s. f (AD s (Repr f a)) -> AD s (Repr f a)) -> f a -> (a, f b)

Dense Jacobians (synonyms)

jacobian :: (Representable f, Eq (Rep f), Functor g, Num a) => (forall s. f (AD s (Repr f a)) -> g (AD s (Repr f a))) -> f a -> g (f a)

jacobian' :: (Representable f, Eq (Rep f), Functor g, Num a) => (forall s. f (AD s (Repr f a)) -> g (AD s (Repr f a))) -> f a -> g (a, f a)

jacobianWith :: (Representable f, Eq (Rep f), Functor g, Num a) => (a -> a -> b) -> (forall s. f (AD s (Repr f a)) -> g (AD s (Repr f a))) -> f a -> g (f b)

jacobianWith' :: (Representable f, Eq (Rep f), Functor g, Num a) => (a -> a -> b) -> (forall s. f (AD s (Repr f a)) -> g (AD s (Repr f a))) -> f a -> g (a, f b)