Numeric.AD.Rank1.Forward.Double

Documentation

data ForwardDouble

Instances

Enum ForwardDouble

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]

Eq ForwardDouble

Methods

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

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

Floating ForwardDouble

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

Fractional ForwardDouble

Methods

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

recip :: ForwardDouble -> ForwardDouble

fromRational :: Rational -> ForwardDouble

Num ForwardDouble

Methods

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

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

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

negate :: ForwardDouble -> ForwardDouble

abs :: ForwardDouble -> ForwardDouble

signum :: ForwardDouble -> ForwardDouble

fromInteger :: Integer -> ForwardDouble

Ord ForwardDouble

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

Read ForwardDouble

Methods

readsPrec :: Int -> ReadS ForwardDouble

readList :: ReadS [ForwardDouble]

readPrec :: ReadPrec ForwardDouble

readListPrec :: ReadPrec [ForwardDouble]

Real ForwardDouble

Methods

toRational :: ForwardDouble -> Rational

RealFloat ForwardDouble

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

RealFrac ForwardDouble

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

Methods

showsPrec :: Int -> ForwardDouble -> ShowS

show :: ForwardDouble -> String

showList :: [ForwardDouble] -> ShowS

Erf ForwardDouble

Methods

erf :: ForwardDouble -> ForwardDouble

erfc :: ForwardDouble -> ForwardDouble

erfcx :: ForwardDouble -> ForwardDouble

normcdf :: ForwardDouble -> ForwardDouble

InvErf ForwardDouble

Methods

inverf :: ForwardDouble -> ForwardDouble

inverfc :: ForwardDouble -> ForwardDouble

invnormcdf :: ForwardDouble -> ForwardDouble

Mode ForwardDouble

Associated Types

type Scalar ForwardDouble :: *

Methods

isKnownConstant :: ForwardDouble -> Bool

isKnownZero :: ForwardDouble -> Bool

auto :: Scalar ForwardDouble -> ForwardDouble

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

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

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

zero :: ForwardDouble

Jacobian ForwardDouble

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

type Scalar ForwardDouble

type Scalar ForwardDouble = Double

type D ForwardDouble

type D ForwardDouble = Id Double

Gradient

grad :: Traversable f => (f ForwardDouble -> 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 => (f ForwardDouble -> 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) -> (f ForwardDouble -> 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) -> (f ForwardDouble -> 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) => (f ForwardDouble -> g 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) => (f ForwardDouble -> g 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) -> (f ForwardDouble -> g 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) -> (f ForwardDouble -> g 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) => (f ForwardDouble -> g ForwardDouble) -> f Double -> f (g Double)

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

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