Numeric.AD.Mode.Tower

Higher order derivatives via a "dual number tower".

Documentation

data AD s a

Instances

Bounded a => Bounded (AD s a)

Methods

minBound :: AD s a

maxBound :: AD s a

Enum a => Enum (AD s a)

Methods

succ :: AD s a -> AD s a

pred :: AD s a -> AD s a

toEnum :: Int -> AD s a

fromEnum :: AD s a -> Int

enumFrom :: AD s a -> [AD s a]

enumFromThen :: AD s a -> AD s a -> [AD s a]

enumFromTo :: AD s a -> AD s a -> [AD s a]

enumFromThenTo :: AD s a -> AD s a -> AD s a -> [AD s a]

Eq a => Eq (AD s a)

Methods

(==) :: AD s a -> AD s a -> Bool

(/=) :: AD s a -> AD s a -> Bool

Floating a => Floating (AD s a)

Methods

pi :: AD s a

exp :: AD s a -> AD s a

log :: AD s a -> AD s a

sqrt :: AD s a -> AD s a

(**) :: AD s a -> AD s a -> AD s a

logBase :: AD s a -> AD s a -> AD s a

sin :: AD s a -> AD s a

cos :: AD s a -> AD s a

tan :: AD s a -> AD s a

asin :: AD s a -> AD s a

acos :: AD s a -> AD s a

atan :: AD s a -> AD s a

sinh :: AD s a -> AD s a

cosh :: AD s a -> AD s a

tanh :: AD s a -> AD s a

asinh :: AD s a -> AD s a

acosh :: AD s a -> AD s a

atanh :: AD s a -> AD s a

log1p :: AD s a -> AD s a

expm1 :: AD s a -> AD s a

log1pexp :: AD s a -> AD s a

log1mexp :: AD s a -> AD s a

Fractional a => Fractional (AD s a)

Methods

(/) :: AD s a -> AD s a -> AD s a

recip :: AD s a -> AD s a

fromRational :: Rational -> AD s a

Num a => Num (AD s a)

Methods

(+) :: AD s a -> AD s a -> AD s a

(-) :: AD s a -> AD s a -> AD s a

(*) :: AD s a -> AD s a -> AD s a

negate :: AD s a -> AD s a

abs :: AD s a -> AD s a

signum :: AD s a -> AD s a

fromInteger :: Integer -> AD s a

Ord a => Ord (AD s a)

Methods

compare :: AD s a -> AD s a -> Ordering

(<) :: AD s a -> AD s a -> Bool

(<=) :: AD s a -> AD s a -> Bool

(>) :: AD s a -> AD s a -> Bool

(>=) :: AD s a -> AD s a -> Bool

max :: AD s a -> AD s a -> AD s a

min :: AD s a -> AD s a -> AD s a

Read a => Read (AD s a)

Methods

readsPrec :: Int -> ReadS (AD s a)

readList :: ReadS [AD s a]

readPrec :: ReadPrec (AD s a)

readListPrec :: ReadPrec [AD s a]

Real a => Real (AD s a)

Methods

toRational :: AD s a -> Rational

RealFloat a => RealFloat (AD s a)

Methods

floatRadix :: AD s a -> Integer

floatDigits :: AD s a -> Int

floatRange :: AD s a -> (Int, Int)

decodeFloat :: AD s a -> (Integer, Int)

encodeFloat :: Integer -> Int -> AD s a

exponent :: AD s a -> Int

significand :: AD s a -> AD s a

scaleFloat :: Int -> AD s a -> AD s a

isNaN :: AD s a -> Bool

isInfinite :: AD s a -> Bool

isDenormalized :: AD s a -> Bool

isNegativeZero :: AD s a -> Bool

isIEEE :: AD s a -> Bool

atan2 :: AD s a -> AD s a -> AD s a

RealFrac a => RealFrac (AD s a)

Methods

properFraction :: Integral b => AD s a -> (b, AD s a)

truncate :: Integral b => AD s a -> b

round :: Integral b => AD s a -> b

ceiling :: Integral b => AD s a -> b

floor :: Integral b => AD s a -> b

Show a => Show (AD s a)

Methods

showsPrec :: Int -> AD s a -> ShowS

show :: AD s a -> String

showList :: [AD s a] -> ShowS

Erf a => Erf (AD s a)

Methods

erf :: AD s a -> AD s a

erfc :: AD s a -> AD s a

erfcx :: AD s a -> AD s a

normcdf :: AD s a -> AD s a

InvErf a => InvErf (AD s a)

Methods

inverf :: AD s a -> AD s a

inverfc :: AD s a -> AD s a

invnormcdf :: AD s a -> AD s a

Mode a => Mode (AD s a)

Associated Types

type Scalar (AD s a) :: *

Methods

isKnownConstant :: AD s a -> Bool

isKnownZero :: AD s a -> Bool

auto :: Scalar (AD s a) -> AD s a

(*^) :: Scalar (AD s a) -> AD s a -> AD s a

(^*) :: AD s a -> Scalar (AD s a) -> AD s a

(^/) :: AD s a -> Scalar (AD s a) -> AD s a

zero :: AD s a

type Scalar (AD s a)

type Scalar (AD s a) = Scalar a

data Tower a

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

Instances

(Num a, Bounded a) => Bounded (Tower a)

Methods

minBound :: Tower a

maxBound :: Tower a

(Num a, Enum a) => Enum (Tower a)

Methods

succ :: Tower a -> Tower a

pred :: Tower a -> Tower a

toEnum :: Int -> Tower a

fromEnum :: Tower a -> Int

enumFrom :: Tower a -> [Tower a]

enumFromThen :: Tower a -> Tower a -> [Tower a]

enumFromTo :: Tower a -> Tower a -> [Tower a]

enumFromThenTo :: Tower a -> Tower a -> Tower a -> [Tower a]

(Num a, Eq a) => Eq (Tower a)

Methods

(==) :: Tower a -> Tower a -> Bool

(/=) :: Tower a -> Tower a -> Bool

Floating a => Floating (Tower a)

Methods

pi :: Tower a

exp :: Tower a -> Tower a

log :: Tower a -> Tower a

sqrt :: Tower a -> Tower a

(**) :: Tower a -> Tower a -> Tower a

logBase :: Tower a -> Tower a -> Tower a

sin :: Tower a -> Tower a

cos :: Tower a -> Tower a

tan :: Tower a -> Tower a

asin :: Tower a -> Tower a

acos :: Tower a -> Tower a

atan :: Tower a -> Tower a

sinh :: Tower a -> Tower a

cosh :: Tower a -> Tower a

tanh :: Tower a -> Tower a

asinh :: Tower a -> Tower a

acosh :: Tower a -> Tower a

atanh :: Tower a -> Tower a

log1p :: Tower a -> Tower a

expm1 :: Tower a -> Tower a

log1pexp :: Tower a -> Tower a

log1mexp :: Tower a -> Tower a

Fractional a => Fractional (Tower a)

Methods

(/) :: Tower a -> Tower a -> Tower a

recip :: Tower a -> Tower a

fromRational :: Rational -> Tower a

Data a => Data (Tower a)

Methods

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

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

toConstr :: Tower a -> Constr

dataTypeOf :: Tower a -> DataType

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

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

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

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

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

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

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

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

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

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

Num a => Num (Tower a)

Methods

(+) :: Tower a -> Tower a -> Tower a

(-) :: Tower a -> Tower a -> Tower a

(*) :: Tower a -> Tower a -> Tower a

negate :: Tower a -> Tower a

abs :: Tower a -> Tower a

signum :: Tower a -> Tower a

fromInteger :: Integer -> Tower a

(Num a, Ord a) => Ord (Tower a)

Methods

compare :: Tower a -> Tower a -> Ordering

(<) :: Tower a -> Tower a -> Bool

(<=) :: Tower a -> Tower a -> Bool

(>) :: Tower a -> Tower a -> Bool

(>=) :: Tower a -> Tower a -> Bool

max :: Tower a -> Tower a -> Tower a

min :: Tower a -> Tower a -> Tower a

Real a => Real (Tower a)

Methods

toRational :: Tower a -> Rational

RealFloat a => RealFloat (Tower a)

Methods

floatRadix :: Tower a -> Integer

floatDigits :: Tower a -> Int

floatRange :: Tower a -> (Int, Int)

decodeFloat :: Tower a -> (Integer, Int)

encodeFloat :: Integer -> Int -> Tower a

exponent :: Tower a -> Int

significand :: Tower a -> Tower a

scaleFloat :: Int -> Tower a -> Tower a

isNaN :: Tower a -> Bool

isInfinite :: Tower a -> Bool

isDenormalized :: Tower a -> Bool

isNegativeZero :: Tower a -> Bool

isIEEE :: Tower a -> Bool

atan2 :: Tower a -> Tower a -> Tower a

RealFrac a => RealFrac (Tower a)

Methods

properFraction :: Integral b => Tower a -> (b, Tower a)

truncate :: Integral b => Tower a -> b

round :: Integral b => Tower a -> b

ceiling :: Integral b => Tower a -> b

floor :: Integral b => Tower a -> b

Show a => Show (Tower a)

Methods

showsPrec :: Int -> Tower a -> ShowS

show :: Tower a -> String

showList :: [Tower a] -> ShowS

Erf a => Erf (Tower a)

Methods

erf :: Tower a -> Tower a

erfc :: Tower a -> Tower a

erfcx :: Tower a -> Tower a

normcdf :: Tower a -> Tower a

InvErf a => InvErf (Tower a)

Methods

inverf :: Tower a -> Tower a

inverfc :: Tower a -> Tower a

invnormcdf :: Tower a -> Tower a

Num a => Mode (Tower a)

Associated Types

type Scalar (Tower a) :: *

Methods

isKnownConstant :: Tower a -> Bool

isKnownZero :: Tower a -> Bool

auto :: Scalar (Tower a) -> Tower a

(*^) :: Scalar (Tower a) -> Tower a -> Tower a

(^*) :: Tower a -> Scalar (Tower a) -> Tower a

(^/) :: Tower a -> Scalar (Tower a) -> Tower a

zero :: Tower a

Num a => Jacobian (Tower a)

Associated Types

type D (Tower a) :: *

Methods

unary :: (Scalar (Tower a) -> Scalar (Tower a)) -> D (Tower a) -> Tower a -> Tower a

lift1 :: (Scalar (Tower a) -> Scalar (Tower a)) -> (D (Tower a) -> D (Tower a)) -> Tower a -> Tower a

lift1_ :: (Scalar (Tower a) -> Scalar (Tower a)) -> (D (Tower a) -> D (Tower a) -> D (Tower a)) -> Tower a -> Tower a

binary :: (Scalar (Tower a) -> Scalar (Tower a) -> Scalar (Tower a)) -> D (Tower a) -> D (Tower a) -> Tower a -> Tower a -> Tower a

lift2 :: (Scalar (Tower a) -> Scalar (Tower a) -> Scalar (Tower a)) -> (D (Tower a) -> D (Tower a) -> (D (Tower a), D (Tower a))) -> Tower a -> Tower a -> Tower a

lift2_ :: (Scalar (Tower a) -> Scalar (Tower a) -> Scalar (Tower a)) -> (D (Tower a) -> D (Tower a) -> D (Tower a) -> (D (Tower a), D (Tower a))) -> Tower a -> Tower a -> Tower a

type Scalar (Tower a)

type Scalar (Tower a) = a

type D (Tower a)

type D (Tower a) = Tower a

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

Embed a constant

Taylor Series

taylor :: Fractional a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> a -> [a]

taylor0 :: Fractional a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> a -> [a]

Maclaurin Series

maclaurin :: Fractional a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> [a]

maclaurin0 :: Fractional a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> [a]

Derivatives

diff :: Num a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> a

diff' :: Num a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> (a, a)

diffs :: Num a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> [a]

diffs0 :: Num a => (forall s. AD s (Tower a) -> AD s (Tower a)) -> a -> [a]

diffsF :: (Functor f, Num a) => (forall s. AD s (Tower a) -> f (AD s (Tower a))) -> a -> f [a]

diffs0F :: (Functor f, Num a) => (forall s. AD s (Tower a) -> f (AD s (Tower a))) -> a -> f [a]

Directional Derivatives

du :: (Functor f, Num a) => (forall s. f (AD s (Tower a)) -> AD s (Tower a)) -> f (a, a) -> a

du' :: (Functor f, Num a) => (forall s. f (AD s (Tower a)) -> AD s (Tower a)) -> f (a, a) -> (a, a)

dus :: (Functor f, Num a) => (forall s. f (AD s (Tower a)) -> AD s (Tower a)) -> f [a] -> [a]

dus0 :: (Functor f, Num a) => (forall s. f (AD s (Tower a)) -> AD s (Tower a)) -> f [a] -> [a]

duF :: (Functor f, Functor g, Num a) => (forall s. f (AD s (Tower a)) -> g (AD s (Tower a))) -> f (a, a) -> g a

duF' :: (Functor f, Functor g, Num a) => (forall s. f (AD s (Tower a)) -> g (AD s (Tower a))) -> f (a, a) -> g (a, a)

dusF :: (Functor f, Functor g, Num a) => (forall s. f (AD s (Tower a)) -> g (AD s (Tower a))) -> f [a] -> g [a]

dus0F :: (Functor f, Functor g, Num a) => (forall s. f (AD s (Tower a)) -> g (AD s (Tower a))) -> f [a] -> g [a]