ad-4.3.2.1: Automatic Differentiation

Copyright(c) Edward Kmett 2010-2015
LicenseBSD3
Maintainerekmett@gmail.com
Stabilityexperimental
PortabilityGHC only
Safe HaskellNone
LanguageHaskell2010

Numeric.AD.Internal.Identity

Description

 

Documentation

newtype Id a Source #

Constructors

Id 

Fields

Instances

Bounded a => Bounded (Id a) Source # 

Methods

minBound :: Id a #

maxBound :: Id a #

Enum a => Enum (Id a) Source # 

Methods

succ :: Id a -> Id a #

pred :: Id a -> Id a #

toEnum :: Int -> Id a #

fromEnum :: Id a -> Int #

enumFrom :: Id a -> [Id a] #

enumFromThen :: Id a -> Id a -> [Id a] #

enumFromTo :: Id a -> Id a -> [Id a] #

enumFromThenTo :: Id a -> Id a -> Id a -> [Id a] #

Eq a => Eq (Id a) Source # 

Methods

(==) :: Id a -> Id a -> Bool #

(/=) :: Id a -> Id a -> Bool #

Floating a => Floating (Id a) Source # 

Methods

pi :: Id a #

exp :: Id a -> Id a #

log :: Id a -> Id a #

sqrt :: Id a -> Id a #

(**) :: Id a -> Id a -> Id a #

logBase :: Id a -> Id a -> Id a #

sin :: Id a -> Id a #

cos :: Id a -> Id a #

tan :: Id a -> Id a #

asin :: Id a -> Id a #

acos :: Id a -> Id a #

atan :: Id a -> Id a #

sinh :: Id a -> Id a #

cosh :: Id a -> Id a #

tanh :: Id a -> Id a #

asinh :: Id a -> Id a #

acosh :: Id a -> Id a #

atanh :: Id a -> Id a #

log1p :: Id a -> Id a #

expm1 :: Id a -> Id a #

log1pexp :: Id a -> Id a #

log1mexp :: Id a -> Id a #

Fractional a => Fractional (Id a) Source # 

Methods

(/) :: Id a -> Id a -> Id a #

recip :: Id a -> Id a #

fromRational :: Rational -> Id a #

Data a => Data (Id a) Source # 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Id a -> c (Id a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Id a) #

toConstr :: Id a -> Constr #

dataTypeOf :: Id a -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Id a)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Id a)) #

gmapT :: (forall b. Data b => b -> b) -> Id a -> Id a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Id a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Id a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Id a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Id a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Id a -> m (Id a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Id a -> m (Id a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Id a -> m (Id a) #

Num a => Num (Id a) Source # 

Methods

(+) :: Id a -> Id a -> Id a #

(-) :: Id a -> Id a -> Id a #

(*) :: Id a -> Id a -> Id a #

negate :: Id a -> Id a #

abs :: Id a -> Id a #

signum :: Id a -> Id a #

fromInteger :: Integer -> Id a #

Ord a => Ord (Id a) Source # 

Methods

compare :: Id a -> Id a -> Ordering #

(<) :: Id a -> Id a -> Bool #

(<=) :: Id a -> Id a -> Bool #

(>) :: Id a -> Id a -> Bool #

(>=) :: Id a -> Id a -> Bool #

max :: Id a -> Id a -> Id a #

min :: Id a -> Id a -> Id a #

Real a => Real (Id a) Source # 

Methods

toRational :: Id a -> Rational #

RealFloat a => RealFloat (Id a) Source # 

Methods

floatRadix :: Id a -> Integer #

floatDigits :: Id a -> Int #

floatRange :: Id a -> (Int, Int) #

decodeFloat :: Id a -> (Integer, Int) #

encodeFloat :: Integer -> Int -> Id a #

exponent :: Id a -> Int #

significand :: Id a -> Id a #

scaleFloat :: Int -> Id a -> Id a #

isNaN :: Id a -> Bool #

isInfinite :: Id a -> Bool #

isDenormalized :: Id a -> Bool #

isNegativeZero :: Id a -> Bool #

isIEEE :: Id a -> Bool #

atan2 :: Id a -> Id a -> Id a #

RealFrac a => RealFrac (Id a) Source # 

Methods

properFraction :: Integral b => Id a -> (b, Id a) #

truncate :: Integral b => Id a -> b #

round :: Integral b => Id a -> b #

ceiling :: Integral b => Id a -> b #

floor :: Integral b => Id a -> b #

Show a => Show (Id a) Source # 

Methods

showsPrec :: Int -> Id a -> ShowS #

show :: Id a -> String #

showList :: [Id a] -> ShowS #

Monoid a => Monoid (Id a) Source # 

Methods

mempty :: Id a #

mappend :: Id a -> Id a -> Id a #

mconcat :: [Id a] -> Id a #

Erf a => Erf (Id a) Source # 

Methods

erf :: Id a -> Id a #

erfc :: Id a -> Id a #

erfcx :: Id a -> Id a #

normcdf :: Id a -> Id a #

InvErf a => InvErf (Id a) Source # 

Methods

inverf :: Id a -> Id a #

inverfc :: Id a -> Id a #

invnormcdf :: Id a -> Id a #

Num a => Mode (Id a) Source # 

Associated Types

type Scalar (Id a) :: * Source #

Methods

isKnownConstant :: Id a -> Bool Source #

isKnownZero :: Id a -> Bool Source #

auto :: Scalar (Id a) -> Id a Source #

(*^) :: Scalar (Id a) -> Id a -> Id a Source #

(^*) :: Id a -> Scalar (Id a) -> Id a Source #

(^/) :: Id a -> Scalar (Id a) -> Id a Source #

zero :: Id a Source #

type Scalar (Id a) Source # 
type Scalar (Id a) = a

probe :: a -> Id a Source #

unprobe :: Id a -> a Source #

probed :: Functor f => f a -> f (Id a) Source #

unprobed :: Functor f => f (Id a) -> f a Source #