Copyright	(c) Edward Kmett 2010-2021
License	BSD3
Maintainer	ekmett@gmail.com
Stability	experimental
Portability	GHC only
Safe Haskell	None
Language	Haskell2010

Numeric.AD.Internal.Tower.Double

Description

Synopsis

newtype TowerDouble = Tower {
- getTower :: List
}
data List
- = Nil
- | !Double :! List
zeroPad :: Num a => [a] -> [a]
zeroPadF :: (Functor f, Num a) => [f a] -> [f a]
transposePadF :: (Foldable f, Functor f) => Double -> f List -> [f Double]
d :: Num a => [a] -> a
dl :: List -> Double
d' :: Num a => [a] -> (a, a)
dl' :: List -> (Double, Double)
withD :: (Double, Double) -> TowerDouble
tangents :: TowerDouble -> TowerDouble
bundle :: Double -> TowerDouble -> TowerDouble
apply :: (TowerDouble -> b) -> Double -> b
getADTower :: TowerDouble -> [Double]
tower :: [Double] -> TowerDouble

Documentation

newtype TowerDouble Source #

Tower is an AD Mode that calculates a tangent tower by forward AD, and provides fast diffsUU, diffsUF

Constructors

Tower
Fields getTower :: List

Instances

Instances details

Enum TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods succ :: TowerDouble -> TowerDouble # pred :: TowerDouble -> TowerDouble # toEnum :: Int -> TowerDouble # fromEnum :: TowerDouble -> Int # enumFrom :: TowerDouble -> [TowerDouble] # enumFromThen :: TowerDouble -> TowerDouble -> [TowerDouble] # enumFromTo :: TowerDouble -> TowerDouble -> [TowerDouble] # enumFromThenTo :: TowerDouble -> TowerDouble -> TowerDouble -> [TowerDouble] #
Eq TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods (==) :: TowerDouble -> TowerDouble -> Bool # (/=) :: TowerDouble -> TowerDouble -> Bool #
Floating TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods pi :: TowerDouble # exp :: TowerDouble -> TowerDouble # log :: TowerDouble -> TowerDouble # sqrt :: TowerDouble -> TowerDouble # (**) :: TowerDouble -> TowerDouble -> TowerDouble # logBase :: TowerDouble -> TowerDouble -> TowerDouble # sin :: TowerDouble -> TowerDouble # cos :: TowerDouble -> TowerDouble # tan :: TowerDouble -> TowerDouble # asin :: TowerDouble -> TowerDouble # acos :: TowerDouble -> TowerDouble # atan :: TowerDouble -> TowerDouble # sinh :: TowerDouble -> TowerDouble # cosh :: TowerDouble -> TowerDouble # tanh :: TowerDouble -> TowerDouble # asinh :: TowerDouble -> TowerDouble # acosh :: TowerDouble -> TowerDouble # atanh :: TowerDouble -> TowerDouble # log1p :: TowerDouble -> TowerDouble # expm1 :: TowerDouble -> TowerDouble # log1pexp :: TowerDouble -> TowerDouble # log1mexp :: TowerDouble -> TowerDouble #
Fractional TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods (/) :: TowerDouble -> TowerDouble -> TowerDouble # recip :: TowerDouble -> TowerDouble # fromRational :: Rational -> TowerDouble #
Data TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TowerDouble -> c TowerDouble # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TowerDouble # toConstr :: TowerDouble -> Constr # dataTypeOf :: TowerDouble -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c TowerDouble) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TowerDouble) # gmapT :: (forall b. Data b => b -> b) -> TowerDouble -> TowerDouble # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TowerDouble -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TowerDouble -> r # gmapQ :: (forall d. Data d => d -> u) -> TowerDouble -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> TowerDouble -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> TowerDouble -> m TowerDouble # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> TowerDouble -> m TowerDouble # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> TowerDouble -> m TowerDouble #
Num TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods (+) :: TowerDouble -> TowerDouble -> TowerDouble # (-) :: TowerDouble -> TowerDouble -> TowerDouble # (*) :: TowerDouble -> TowerDouble -> TowerDouble # negate :: TowerDouble -> TowerDouble # abs :: TowerDouble -> TowerDouble # signum :: TowerDouble -> TowerDouble # fromInteger :: Integer -> TowerDouble #
Ord TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods compare :: TowerDouble -> TowerDouble -> Ordering # (<) :: TowerDouble -> TowerDouble -> Bool # (<=) :: TowerDouble -> TowerDouble -> Bool # (>) :: TowerDouble -> TowerDouble -> Bool # (>=) :: TowerDouble -> TowerDouble -> Bool # max :: TowerDouble -> TowerDouble -> TowerDouble # min :: TowerDouble -> TowerDouble -> TowerDouble #
Real TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods toRational :: TowerDouble -> Rational #
RealFloat TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods floatRadix :: TowerDouble -> Integer # floatDigits :: TowerDouble -> Int # floatRange :: TowerDouble -> (Int, Int) # decodeFloat :: TowerDouble -> (Integer, Int) # encodeFloat :: Integer -> Int -> TowerDouble # exponent :: TowerDouble -> Int # significand :: TowerDouble -> TowerDouble # scaleFloat :: Int -> TowerDouble -> TowerDouble # isNaN :: TowerDouble -> Bool # isInfinite :: TowerDouble -> Bool # isDenormalized :: TowerDouble -> Bool # isNegativeZero :: TowerDouble -> Bool # isIEEE :: TowerDouble -> Bool # atan2 :: TowerDouble -> TowerDouble -> TowerDouble #
RealFrac TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods properFraction :: Integral b => TowerDouble -> (b, TowerDouble) # truncate :: Integral b => TowerDouble -> b # round :: Integral b => TowerDouble -> b # ceiling :: Integral b => TowerDouble -> b # floor :: Integral b => TowerDouble -> b #
Show TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods showsPrec :: Int -> TowerDouble -> ShowS # show :: TowerDouble -> String # showList :: [TowerDouble] -> ShowS #
Erf TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods erf :: TowerDouble -> TowerDouble # erfc :: TowerDouble -> TowerDouble # erfcx :: TowerDouble -> TowerDouble # normcdf :: TowerDouble -> TowerDouble #
InvErf TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods inverf :: TowerDouble -> TowerDouble # inverfc :: TowerDouble -> TowerDouble # invnormcdf :: TowerDouble -> TowerDouble #
Mode TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Associated Types type Scalar TowerDouble Source # Methods isKnownConstant :: TowerDouble -> Bool Source # asKnownConstant :: TowerDouble -> Maybe (Scalar TowerDouble) Source # isKnownZero :: TowerDouble -> Bool Source # auto :: Scalar TowerDouble -> TowerDouble Source # (^) :: Scalar TowerDouble -> TowerDouble -> TowerDouble Source # (^) :: TowerDouble -> Scalar TowerDouble -> TowerDouble Source # (^/) :: TowerDouble -> Scalar TowerDouble -> TowerDouble Source # zero :: TowerDouble Source #
Jacobian TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Associated Types type D TowerDouble Source # Methods unary :: (Scalar TowerDouble -> Scalar TowerDouble) -> D TowerDouble -> TowerDouble -> TowerDouble Source # lift1 :: (Scalar TowerDouble -> Scalar TowerDouble) -> (D TowerDouble -> D TowerDouble) -> TowerDouble -> TowerDouble Source # lift1_ :: (Scalar TowerDouble -> Scalar TowerDouble) -> (D TowerDouble -> D TowerDouble -> D TowerDouble) -> TowerDouble -> TowerDouble Source # binary :: (Scalar TowerDouble -> Scalar TowerDouble -> Scalar TowerDouble) -> D TowerDouble -> D TowerDouble -> TowerDouble -> TowerDouble -> TowerDouble Source # lift2 :: (Scalar TowerDouble -> Scalar TowerDouble -> Scalar TowerDouble) -> (D TowerDouble -> D TowerDouble -> (D TowerDouble, D TowerDouble)) -> TowerDouble -> TowerDouble -> TowerDouble Source # lift2_ :: (Scalar TowerDouble -> Scalar TowerDouble -> Scalar TowerDouble) -> (D TowerDouble -> D TowerDouble -> D TowerDouble -> (D TowerDouble, D TowerDouble)) -> TowerDouble -> TowerDouble -> TowerDouble Source #
type Scalar TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double type Scalar TowerDouble = Double
type D TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double type D TowerDouble = TowerDouble

data List Source #

Constructors

Nil
!Double :! List infixr 5

Instances

Instances details

IsList List Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Associated Types type Item List # Methods fromList :: [Item List] -> List # fromListN :: Int -> [Item List] -> List # toList :: List -> [Item List] #
Eq List Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods (==) :: List -> List -> Bool # (/=) :: List -> List -> Bool #
Data List Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> List -> c List # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c List # toConstr :: List -> Constr # dataTypeOf :: List -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c List) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c List) # gmapT :: (forall b. Data b => b -> b) -> List -> List # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> List -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> List -> r # gmapQ :: (forall d. Data d => d -> u) -> List -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> List -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> List -> m List # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> List -> m List # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> List -> m List #
Ord List Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods compare :: List -> List -> Ordering # (<) :: List -> List -> Bool # (<=) :: List -> List -> Bool # (>) :: List -> List -> Bool # (>=) :: List -> List -> Bool # max :: List -> List -> List # min :: List -> List -> List #
Read List Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods readsPrec :: Int -> ReadS List # readList :: ReadS [List] # readPrec :: ReadPrec List # readListPrec :: ReadPrec [List] #
Show List Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods showsPrec :: Int -> List -> ShowS # show :: List -> String # showList :: [List] -> ShowS #
Semigroup List Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods (<>) :: List -> List -> List # sconcat :: NonEmpty List -> List # stimes :: Integral b => b -> List -> List #
Monoid List Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods mempty :: List # mappend :: List -> List -> List # mconcat :: [List] -> List #
type Item List Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double type Item List = Double

zeroPad :: Num a => [a] -> [a] Source #

zeroPadF :: (Functor f, Num a) => [f a] -> [f a] Source #

transposePadF :: (Foldable f, Functor f) => Double -> f List -> [f Double] Source #

d :: Num a => [a] -> a Source #

dl :: List -> Double Source #

d' :: Num a => [a] -> (a, a) Source #

dl' :: List -> (Double, Double) Source #

withD :: (Double, Double) -> TowerDouble Source #

tangents :: TowerDouble -> TowerDouble Source #

bundle :: Double -> TowerDouble -> TowerDouble Source #

apply :: (TowerDouble -> b) -> Double -> b Source #

getADTower :: TowerDouble -> [Double] Source #

tower :: [Double] -> TowerDouble Source #