Numeric.AD.Mode.Forward.Double

Forward Mode AD specialized to Double. This enables the entire structure to be unboxed.

Documentation

data AD s a

Instances

Mode a => Mode (AD s a)

Defined in Numeric.AD.Internal.Type

Associated Types

type Scalar (AD s a)

Methods

isKnownConstant :: AD s a -> Bool

asKnownConstant :: AD s a -> Maybe (Scalar (AD s a))

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

Bounded a => Bounded (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

minBound :: AD s a

maxBound :: AD s a

Enum a => Enum (AD s a)

Defined in Numeric.AD.Internal.Type

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]

Floating a => Floating (AD s a)

Defined in Numeric.AD.Internal.Type

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

RealFloat a => RealFloat (AD s a)

Defined in Numeric.AD.Internal.Type

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

Num a => Num (AD s a)

Defined in Numeric.AD.Internal.Type

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

Read a => Read (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

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

readList :: ReadS [AD s a]

readPrec :: ReadPrec (AD s a)

readListPrec :: ReadPrec [AD s a]

Fractional a => Fractional (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

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

recip :: AD s a -> AD s a

fromRational :: Rational -> AD s a

Real a => Real (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

toRational :: AD s a -> Rational

RealFrac a => RealFrac (AD s a)

Defined in Numeric.AD.Internal.Type

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)

Defined in Numeric.AD.Internal.Type

Methods

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

show :: AD s a -> String

showList :: [AD s a] -> ShowS

Erf a => Erf (AD s a)

Defined in Numeric.AD.Internal.Type

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)

Defined in Numeric.AD.Internal.Type

Methods

inverf :: AD s a -> AD s a

inverfc :: AD s a -> AD s a

invnormcdf :: AD s a -> AD s a

Eq a => Eq (AD s a)

Defined in Numeric.AD.Internal.Type

Methods

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

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

Ord a => Ord (AD s a)

Defined in Numeric.AD.Internal.Type

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

type Scalar (AD s a)

Defined in Numeric.AD.Internal.Type

type Scalar (AD s a) = Scalar a

data ForwardDouble

Instances

Jacobian ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Associated Types

type D ForwardDouble

Methods

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

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

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

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

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

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

Mode ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Associated Types

type Scalar ForwardDouble

Methods

isKnownConstant :: ForwardDouble -> Bool

asKnownConstant :: ForwardDouble -> Maybe (Scalar ForwardDouble)

isKnownZero :: ForwardDouble -> Bool

auto :: Scalar ForwardDouble -> ForwardDouble

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

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

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

zero :: ForwardDouble

Enum ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

succ :: ForwardDouble -> ForwardDouble

pred :: ForwardDouble -> ForwardDouble

toEnum :: Int -> ForwardDouble

fromEnum :: ForwardDouble -> Int

enumFrom :: ForwardDouble -> [ForwardDouble]

enumFromThen :: ForwardDouble -> ForwardDouble -> [ForwardDouble]

enumFromTo :: ForwardDouble -> ForwardDouble -> [ForwardDouble]

enumFromThenTo :: ForwardDouble -> ForwardDouble -> ForwardDouble -> [ForwardDouble]

Floating ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

pi :: ForwardDouble

exp :: ForwardDouble -> ForwardDouble

log :: ForwardDouble -> ForwardDouble

sqrt :: ForwardDouble -> ForwardDouble

(**) :: ForwardDouble -> ForwardDouble -> ForwardDouble

logBase :: ForwardDouble -> ForwardDouble -> ForwardDouble

sin :: ForwardDouble -> ForwardDouble

cos :: ForwardDouble -> ForwardDouble

tan :: ForwardDouble -> ForwardDouble

asin :: ForwardDouble -> ForwardDouble

acos :: ForwardDouble -> ForwardDouble

atan :: ForwardDouble -> ForwardDouble

sinh :: ForwardDouble -> ForwardDouble

cosh :: ForwardDouble -> ForwardDouble

tanh :: ForwardDouble -> ForwardDouble

asinh :: ForwardDouble -> ForwardDouble

acosh :: ForwardDouble -> ForwardDouble

atanh :: ForwardDouble -> ForwardDouble

log1p :: ForwardDouble -> ForwardDouble

expm1 :: ForwardDouble -> ForwardDouble

log1pexp :: ForwardDouble -> ForwardDouble

log1mexp :: ForwardDouble -> ForwardDouble

RealFloat ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

floatRadix :: ForwardDouble -> Integer

floatDigits :: ForwardDouble -> Int

floatRange :: ForwardDouble -> (Int, Int)

decodeFloat :: ForwardDouble -> (Integer, Int)

encodeFloat :: Integer -> Int -> ForwardDouble

exponent :: ForwardDouble -> Int

significand :: ForwardDouble -> ForwardDouble

scaleFloat :: Int -> ForwardDouble -> ForwardDouble

isNaN :: ForwardDouble -> Bool

isInfinite :: ForwardDouble -> Bool

isDenormalized :: ForwardDouble -> Bool

isNegativeZero :: ForwardDouble -> Bool

isIEEE :: ForwardDouble -> Bool

atan2 :: ForwardDouble -> ForwardDouble -> ForwardDouble

Num ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

(+) :: ForwardDouble -> ForwardDouble -> ForwardDouble

(-) :: ForwardDouble -> ForwardDouble -> ForwardDouble

(*) :: ForwardDouble -> ForwardDouble -> ForwardDouble

negate :: ForwardDouble -> ForwardDouble

abs :: ForwardDouble -> ForwardDouble

signum :: ForwardDouble -> ForwardDouble

fromInteger :: Integer -> ForwardDouble

Read ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

readsPrec :: Int -> ReadS ForwardDouble

readList :: ReadS [ForwardDouble]

readPrec :: ReadPrec ForwardDouble

readListPrec :: ReadPrec [ForwardDouble]

Fractional ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

(/) :: ForwardDouble -> ForwardDouble -> ForwardDouble

recip :: ForwardDouble -> ForwardDouble

fromRational :: Rational -> ForwardDouble

Real ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

toRational :: ForwardDouble -> Rational

RealFrac ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

properFraction :: Integral b => ForwardDouble -> (b, ForwardDouble)

truncate :: Integral b => ForwardDouble -> b

round :: Integral b => ForwardDouble -> b

ceiling :: Integral b => ForwardDouble -> b

floor :: Integral b => ForwardDouble -> b

Show ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

showsPrec :: Int -> ForwardDouble -> ShowS

show :: ForwardDouble -> String

showList :: [ForwardDouble] -> ShowS

Erf ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

erf :: ForwardDouble -> ForwardDouble

erfc :: ForwardDouble -> ForwardDouble

erfcx :: ForwardDouble -> ForwardDouble

normcdf :: ForwardDouble -> ForwardDouble

InvErf ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

inverf :: ForwardDouble -> ForwardDouble

inverfc :: ForwardDouble -> ForwardDouble

invnormcdf :: ForwardDouble -> ForwardDouble

Eq ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

(==) :: ForwardDouble -> ForwardDouble -> Bool

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

Ord ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

Methods

compare :: ForwardDouble -> ForwardDouble -> Ordering

(<) :: ForwardDouble -> ForwardDouble -> Bool

(<=) :: ForwardDouble -> ForwardDouble -> Bool

(>) :: ForwardDouble -> ForwardDouble -> Bool

(>=) :: ForwardDouble -> ForwardDouble -> Bool

max :: ForwardDouble -> ForwardDouble -> ForwardDouble

min :: ForwardDouble -> ForwardDouble -> ForwardDouble

type D ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

type D ForwardDouble = Id Double

type Scalar ForwardDouble

Defined in Numeric.AD.Internal.Forward.Double

type Scalar ForwardDouble = Double

Gradient

grad :: Traversable f => (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f Double -> f Double

Compute the gradient of a function using forward mode AD.

Note, this performs O(n) worse than grad for n inputs, in exchange for better space utilization.

grad' :: Traversable f => (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f Double -> (Double, f Double)

Compute the gradient and answer to a function using forward mode AD.

Note, this performs O(n) worse than grad' for n inputs, in exchange for better space utilization.

gradWith :: Traversable f => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f Double -> f b

Compute the gradient of a function using forward mode AD and combine the result with the input using a user-specified function.

Note, this performs O(n) worse than gradWith for n inputs, in exchange for better space utilization.

gradWith' :: Traversable f => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f Double -> (Double, f b)

Compute the gradient of a function using forward mode AD and the answer, and combine the result with the input using a user-specified function.

Note, this performs O(n) worse than gradWith' for n inputs, in exchange for better space utilization.

>>> gradWith' (,) sum [0..4]
(10.0,[(0.0,1.0),(1.0,1.0),(2.0,1.0),(3.0,1.0),(4.0,1.0)])

Jacobian

jacobian :: (Traversable f, Traversable g) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> g (f Double)

Compute the Jacobian using Forward mode AD. This must transpose the result, so jacobianT is faster and allows more result types.

>>> jacobian (\[x,y] -> [y,x,x+y,x*y,exp x * sin y]) [pi,1]
[[0.0,1.0],[1.0,0.0],[1.0,1.0],[1.0,3.141592653589793],[19.472221418841606,12.502969588876512]]

jacobian' :: (Traversable f, Traversable g) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> g (Double, f Double)

Compute the Jacobian using Forward mode AD along with the actual answer.

jacobianWith :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> g (f b)

Compute the Jacobian using Forward mode AD and combine the output with the input. This must transpose the result, so jacobianWithT is faster, and allows more result types.

jacobianWith' :: (Traversable f, Traversable g) => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> g (Double, f b)

Compute the Jacobian using Forward mode AD combined with the input using a user specified function, along with the actual answer.

Transposed Jacobian

jacobianT :: (Traversable f, Functor g) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> f (g Double)

A fast, simple, transposed Jacobian computed with forward-mode AD.

jacobianWithT :: (Traversable f, Functor g) => (Double -> Double -> b) -> (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f Double -> f (g b)

A fast, simple, transposed Jacobian computed with Forward mode AD that combines the output with the input.

Derivatives

diff :: (forall s. AD s ForwardDouble -> AD s ForwardDouble) -> Double -> Double

The diff function calculates the first derivative of a scalar-to-scalar function by forward-mode AD

>>> diff sin 0
1.0

diff' :: (forall s. AD s ForwardDouble -> AD s ForwardDouble) -> Double -> (Double, Double)

The diff' function calculates the result and first derivative of scalar-to-scalar function by Forward mode AD

diff' sin == sin &&& cos
diff' f = f &&& d f

>>> diff' sin 0
(0.0,1.0)

>>> diff' exp 0
(1.0,1.0)

diffF :: Functor f => (forall s. AD s ForwardDouble -> f (AD s ForwardDouble)) -> Double -> f Double

The diffF function calculates the first derivatives of scalar-to-nonscalar function by Forward mode AD

>>> diffF (\a -> [sin a, cos a]) 0
[1.0,-0.0]

diffF' :: Functor f => (forall s. AD s ForwardDouble -> f (AD s ForwardDouble)) -> Double -> f (Double, Double)

The diffF' function calculates the result and first derivatives of a scalar-to-non-scalar function by Forward mode AD

>>> diffF' (\a -> [sin a, cos a]) 0
[(0.0,1.0),(1.0,-0.0)]

Directional Derivatives

du :: Functor f => (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f (Double, Double) -> Double

Compute the directional derivative of a function given a zipped up Functor of the input values and their derivatives

du' :: Functor f => (forall s. f (AD s ForwardDouble) -> AD s ForwardDouble) -> f (Double, Double) -> (Double, Double)

Compute the answer and directional derivative of a function given a zipped up Functor of the input values and their derivatives

duF :: (Functor f, Functor g) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f (Double, Double) -> g Double

Compute a vector of directional derivatives for a function given a zipped up Functor of the input values and their derivatives.

duF' :: (Functor f, Functor g) => (forall s. f (AD s ForwardDouble) -> g (AD s ForwardDouble)) -> f (Double, Double) -> g (Double, Double)

Compute a vector of answers and directional derivatives for a function given a zipped up Functor of the input values and their derivatives.