Numeric.AD.Mode.Dense

First order dense forward mode using Traversable functors

Documentation

data AD s a

Instances

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]

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

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

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

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

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

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]

Real a => Real (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

toRational :: AD s a -> Rational

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

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

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

type Scalar (AD s a)

Defined in Numeric.AD.Internal.Type

type Scalar (AD s a) = Scalar a

data Dense f a

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)

Methods

isKnownConstant :: Dense f a -> Bool

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

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)

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

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

Embed a constant

Dense Gradients

grad :: (Traversable f, Num a) => (forall s. f (AD s (Dense f a)) -> AD s (Dense 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 (\[x,y,z] -> x*y+z) [1,2,3]
[2,1,1]

grad' :: (Traversable f, Num a) => (forall s. f (AD s (Dense f a)) -> AD s (Dense f a)) -> f a -> (a, f a)

gradWith :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. f (AD s (Dense f a)) -> AD s (Dense f a)) -> f a -> f b

gradWith' :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. f (AD s (Dense f a)) -> AD s (Dense f a)) -> f a -> (a, f b)

Dense Jacobians (synonyms)

jacobian :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Dense f a)) -> g (AD s (Dense f a))) -> f a -> g (f a)

jacobian' :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Dense f a)) -> g (AD s (Dense f a))) -> f a -> g (a, f a)

jacobianWith :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. f (AD s (Dense f a)) -> g (AD s (Dense f a))) -> f a -> g (f b)

jacobianWith' :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. f (AD s (Dense f a)) -> g (AD s (Dense f a))) -> f a -> g (a, f b)