Numeric.AD.Rank1.Tower.Double

Higher order derivatives via a "dual number tower".

Documentation

data TowerDouble

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

Instances

Jacobian TowerDouble

Defined in Numeric.AD.Internal.Tower.Double

Associated Types

type D TowerDouble

Methods

unary :: (Scalar TowerDouble -> Scalar TowerDouble) -> D TowerDouble -> TowerDouble -> TowerDouble

lift1 :: (Scalar TowerDouble -> Scalar TowerDouble) -> (D TowerDouble -> D TowerDouble) -> TowerDouble -> TowerDouble

lift1_ :: (Scalar TowerDouble -> Scalar TowerDouble) -> (D TowerDouble -> D TowerDouble -> D TowerDouble) -> TowerDouble -> TowerDouble

binary :: (Scalar TowerDouble -> Scalar TowerDouble -> Scalar TowerDouble) -> D TowerDouble -> D TowerDouble -> TowerDouble -> TowerDouble -> TowerDouble

lift2 :: (Scalar TowerDouble -> Scalar TowerDouble -> Scalar TowerDouble) -> (D TowerDouble -> D TowerDouble -> (D TowerDouble, D TowerDouble)) -> TowerDouble -> TowerDouble -> TowerDouble

lift2_ :: (Scalar TowerDouble -> Scalar TowerDouble -> Scalar TowerDouble) -> (D TowerDouble -> D TowerDouble -> D TowerDouble -> (D TowerDouble, D TowerDouble)) -> TowerDouble -> TowerDouble -> TowerDouble

Mode TowerDouble

Defined in Numeric.AD.Internal.Tower.Double

Associated Types

type Scalar TowerDouble

Methods

isKnownConstant :: TowerDouble -> Bool

asKnownConstant :: TowerDouble -> Maybe (Scalar TowerDouble)

isKnownZero :: TowerDouble -> Bool

auto :: Scalar TowerDouble -> TowerDouble

(*^) :: Scalar TowerDouble -> TowerDouble -> TowerDouble

(^*) :: TowerDouble -> Scalar TowerDouble -> TowerDouble

(^/) :: TowerDouble -> Scalar TowerDouble -> TowerDouble

zero :: TowerDouble

Data TowerDouble

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

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

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

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

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

Defined in Numeric.AD.Internal.Tower.Double

Methods

(/) :: TowerDouble -> TowerDouble -> TowerDouble

recip :: TowerDouble -> TowerDouble

fromRational :: Rational -> TowerDouble

Real TowerDouble

Defined in Numeric.AD.Internal.Tower.Double

Methods

toRational :: TowerDouble -> Rational

RealFrac TowerDouble

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

Defined in Numeric.AD.Internal.Tower.Double

Methods

showsPrec :: Int -> TowerDouble -> ShowS

show :: TowerDouble -> String

showList :: [TowerDouble] -> ShowS

Erf TowerDouble

Defined in Numeric.AD.Internal.Tower.Double

Methods

erf :: TowerDouble -> TowerDouble

erfc :: TowerDouble -> TowerDouble

erfcx :: TowerDouble -> TowerDouble

normcdf :: TowerDouble -> TowerDouble

InvErf TowerDouble

Defined in Numeric.AD.Internal.Tower.Double

Methods

inverf :: TowerDouble -> TowerDouble

inverfc :: TowerDouble -> TowerDouble

invnormcdf :: TowerDouble -> TowerDouble

Eq TowerDouble

Defined in Numeric.AD.Internal.Tower.Double

Methods

(==) :: TowerDouble -> TowerDouble -> Bool

(/=) :: TowerDouble -> TowerDouble -> Bool

Ord TowerDouble

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

Defined in Numeric.AD.Internal.Tower.Double

type D TowerDouble = TowerDouble

type Scalar TowerDouble

Defined in Numeric.AD.Internal.Tower.Double

type Scalar TowerDouble = Double

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

Embed a constant

Taylor Series

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

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

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

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

Maclaurin Series

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

maclaurin f compute the Maclaurin series of f

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

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

Derivatives

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

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

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

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

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

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

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

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

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

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

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

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

Directional Derivatives

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

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

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

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

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

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]

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

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)

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]

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]

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