Copyright	(c) Edward Kmett 2010-2021
License	BSD3
Maintainer	ekmett@gmail.com
Stability	experimental
Portability	GHC only
Safe Haskell	Safe-Inferred
Language	Haskell2010

Numeric.AD.Rank1.Tower.Double

Contents

Taylor Series
Maclaurin Series
Derivatives
Directional Derivatives

Description

Higher order derivatives via a "dual number tower".

Synopsis

data TowerDouble
auto :: Mode t => Scalar t -> t
taylor :: (TowerDouble -> TowerDouble) -> Double -> Double -> [Double]
taylor0 :: (TowerDouble -> TowerDouble) -> Double -> Double -> [Double]
maclaurin :: (TowerDouble -> TowerDouble) -> Double -> [Double]
maclaurin0 :: (TowerDouble -> TowerDouble) -> Double -> [Double]
diff :: (TowerDouble -> TowerDouble) -> Double -> Double
diff' :: (TowerDouble -> TowerDouble) -> Double -> (Double, Double)
diffs :: (TowerDouble -> TowerDouble) -> Double -> [Double]
diffs0 :: (TowerDouble -> TowerDouble) -> Double -> [Double]
diffsF :: Functor f => (TowerDouble -> f TowerDouble) -> Double -> f [Double]
diffs0F :: Functor f => (TowerDouble -> f TowerDouble) -> Double -> f [Double]
du :: Functor f => (f TowerDouble -> TowerDouble) -> f (Double, Double) -> Double
du' :: Functor f => (f TowerDouble -> TowerDouble) -> f (Double, Double) -> (Double, Double)
dus :: Functor f => (f TowerDouble -> TowerDouble) -> f [Double] -> [Double]
dus0 :: Functor f => (f TowerDouble -> TowerDouble) -> f [Double] -> [Double]
duF :: (Functor f, Functor g) => (f TowerDouble -> g TowerDouble) -> f (Double, Double) -> g Double
duF' :: (Functor f, Functor g) => (f TowerDouble -> g TowerDouble) -> f (Double, Double) -> g (Double, Double)
dusF :: (Functor f, Functor g) => (f TowerDouble -> g TowerDouble) -> f [Double] -> g [Double]
dus0F :: (Functor f, Functor g) => (f TowerDouble -> g TowerDouble) -> f [Double] -> g [Double]

Documentation

data TowerDouble Source #

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

Instances

Instances details

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 #
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 #
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 #
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] #
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 #
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 #
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 #
Fractional TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods (/) :: TowerDouble -> TowerDouble -> TowerDouble # recip :: TowerDouble -> TowerDouble # fromRational :: Rational -> TowerDouble #
Real TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods toRational :: TowerDouble -> Rational #
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 #
Eq TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double Methods (==) :: TowerDouble -> TowerDouble -> Bool # (/=) :: TowerDouble -> TowerDouble -> Bool #
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 #
type D TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double type D TowerDouble = TowerDouble
type Scalar TowerDouble Source #
Instance details Defined in Numeric.AD.Internal.Tower.Double type Scalar TowerDouble = Double

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

Embed a constant

Taylor Series

taylor :: (TowerDouble -> TowerDouble) -> Double -> Double -> [Double] Source #

taylor f x compute the Taylor series of f around x.

taylor0 :: (TowerDouble -> TowerDouble) -> Double -> Double -> [Double] Source #

taylor0 f x compute the Taylor series of f around x, zero-padded.

Maclaurin Series

maclaurin :: (TowerDouble -> TowerDouble) -> Double -> [Double] Source #

maclaurin f compute the Maclaurin series of f

maclaurin0 :: (TowerDouble -> TowerDouble) -> Double -> [Double] Source #

maclaurin f compute the Maclaurin series of f, zero-padded

Derivatives

diff :: (TowerDouble -> TowerDouble) -> Double -> Double Source #

Compute the first derivative of a function (a -> a)

diff' :: (TowerDouble -> TowerDouble) -> Double -> (Double, Double) Source #

Compute the answer and first derivative of a function (a -> a)

diffs :: (TowerDouble -> TowerDouble) -> Double -> [Double] Source #

Compute the answer and all derivatives of a function (a -> a)

diffs0 :: (TowerDouble -> TowerDouble) -> Double -> [Double] Source #

Compute the zero-padded derivatives of a function (a -> a)

diffsF :: Functor f => (TowerDouble -> f TowerDouble) -> Double -> f [Double] Source #

Compute the answer and all derivatives of a function (a -> f a)

diffs0F :: Functor f => (TowerDouble -> f TowerDouble) -> Double -> f [Double] Source #

Compute the zero-padded derivatives of a function (a -> f a)

Directional Derivatives

du :: Functor f => (f TowerDouble -> TowerDouble) -> f (Double, Double) -> Double Source #

Compute a directional derivative of a function (f a -> a)

du' :: Functor f => (f TowerDouble -> TowerDouble) -> f (Double, Double) -> (Double, Double) Source #

Compute the answer and a directional derivative of a function (f a -> a)

dus :: Functor f => (f TowerDouble -> TowerDouble) -> f [Double] -> [Double] Source #

Given a function (f a -> a), and a tower of derivatives, compute the corresponding directional derivatives.

dus0 :: Functor f => (f TowerDouble -> TowerDouble) -> f [Double] -> [Double] Source #

Given a function (f a -> a), and a tower of derivatives, compute the corresponding directional derivatives, zero-padded

duF :: (Functor f, Functor g) => (f TowerDouble -> g TowerDouble) -> f (Double, Double) -> g Double Source #

Compute a directional derivative of a function (f a -> g a)

duF' :: (Functor f, Functor g) => (f TowerDouble -> g TowerDouble) -> f (Double, Double) -> g (Double, Double) Source #

Compute the answer and a directional derivative of a function (f a -> g a)

dusF :: (Functor f, Functor g) => (f TowerDouble -> g TowerDouble) -> f [Double] -> g [Double] Source #

Given a function (f a -> g a), and a tower of derivatives, compute the corresponding directional derivatives

dus0F :: (Functor f, Functor g) => (f TowerDouble -> g TowerDouble) -> f [Double] -> g [Double] Source #

Given a function (f a -> g a), and a tower of derivatives, compute the corresponding directional derivatives, zero-padded