ad-4.5.6: Automatic Differentiation
Copyright(c) Edward Kmett 2010-2021
LicenseBSD3
Maintainerekmett@gmail.com
Stabilityexperimental
PortabilityGHC only
Safe HaskellSafe-Inferred
LanguageHaskell2010

Numeric.AD.Rank1.Dense

Description

 
Synopsis

Documentation

data Dense f a Source #

Instances

Instances details
(Traversable f, Num a) => Jacobian (Dense f a) Source # 
Instance details

Defined in Numeric.AD.Internal.Dense

Associated Types

type D (Dense f a) Source #

Methods

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

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

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 Source #

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 Source #

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 Source #

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 Source #

(Num a, Traversable f) => Mode (Dense f a) Source # 
Instance details

Defined in Numeric.AD.Internal.Dense

Associated Types

type Scalar (Dense f a) Source #

Methods

isKnownConstant :: Dense f a -> Bool Source #

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

isKnownZero :: Dense f a -> Bool Source #

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

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

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

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

zero :: Dense f a Source #

(Traversable f, Num a, Bounded a) => Bounded (Dense f a) Source # 
Instance details

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) Source # 
Instance details

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, Floating a) => Floating (Dense f a) Source # 
Instance details

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, RealFloat a) => RealFloat (Dense f a) Source # 
Instance details

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, Num a) => Num (Dense f a) Source # 
Instance details

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, Fractional a) => Fractional (Dense f a) Source # 
Instance details

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, Real a) => Real (Dense f a) Source # 
Instance details

Defined in Numeric.AD.Internal.Dense

Methods

toRational :: Dense f a -> Rational #

(Traversable f, RealFrac a) => RealFrac (Dense f a) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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 #

(Traversable f, Num a, Eq a) => Eq (Dense f a) Source # 
Instance details

Defined in Numeric.AD.Internal.Dense

Methods

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

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

(Traversable f, Num a, Ord a) => Ord (Dense f a) Source # 
Instance details

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 #

type D (Dense f a) Source # 
Instance details

Defined in Numeric.AD.Internal.Dense

type D (Dense f a) = Id a
type Scalar (Dense f a) Source # 
Instance details

Defined in Numeric.AD.Internal.Dense

type Scalar (Dense f a) = a

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

Embed a constant

Sparse Gradients

grad :: (Traversable f, Num a) => (f (Dense f a) -> Dense f a) -> f a -> f a Source #

grad' :: (Traversable f, Num a) => (f (Dense f a) -> Dense f a) -> f a -> (a, f a) Source #

gradWith :: (Traversable f, Num a) => (a -> a -> b) -> (f (Dense f a) -> Dense f a) -> f a -> f b Source #

gradWith' :: (Traversable f, Num a) => (a -> a -> b) -> (f (Dense f a) -> Dense f a) -> f a -> (a, f b) Source #

Sparse Jacobians (synonyms)

jacobian :: (Traversable f, Functor g, Num a) => (f (Dense f a) -> g (Dense f a)) -> f a -> g (f a) Source #

jacobian' :: (Traversable f, Functor g, Num a) => (f (Dense f a) -> g (Dense f a)) -> f a -> g (a, f a) Source #

jacobianWith :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (f (Dense f a) -> g (Dense f a)) -> f a -> g (f b) Source #

jacobianWith' :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (f (Dense f a) -> g (Dense f a)) -> f a -> g (a, f b) Source #