Safe Haskell	None
Language	Haskell2010

Numeric.AD.Rank1.Forward.Double

Contents

Gradient
Jacobian
Transposed Jacobian
Derivatives
Directional Derivatives

Synopsis

Documentation

data ForwardDouble Source #

Instances

Enum ForwardDouble Source #
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 Source #
Methods (==) :: ForwardDouble -> ForwardDouble -> Bool # (/=) :: ForwardDouble -> ForwardDouble -> Bool #
Floating ForwardDouble Source #
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 Source #
Methods (/) :: ForwardDouble -> ForwardDouble -> ForwardDouble # recip :: ForwardDouble -> ForwardDouble # fromRational :: Rational -> ForwardDouble #
Num ForwardDouble Source #
Methods (+) :: ForwardDouble -> ForwardDouble -> ForwardDouble # (-) :: ForwardDouble -> ForwardDouble -> ForwardDouble # (*) :: ForwardDouble -> ForwardDouble -> ForwardDouble # negate :: ForwardDouble -> ForwardDouble # abs :: ForwardDouble -> ForwardDouble # signum :: ForwardDouble -> ForwardDouble # fromInteger :: Integer -> ForwardDouble #
Ord ForwardDouble Source #
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 Source #
Methods readsPrec :: Int -> ReadS ForwardDouble # readList :: ReadS [ForwardDouble] # readPrec :: ReadPrec ForwardDouble # readListPrec :: ReadPrec [ForwardDouble] #
Real ForwardDouble Source #
Methods toRational :: ForwardDouble -> Rational #
RealFloat ForwardDouble Source #
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 Source #
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 Source #
Methods showsPrec :: Int -> ForwardDouble -> ShowS # show :: ForwardDouble -> String # showList :: [ForwardDouble] -> ShowS #
Erf ForwardDouble Source #
Methods erf :: ForwardDouble -> ForwardDouble # erfc :: ForwardDouble -> ForwardDouble # erfcx :: ForwardDouble -> ForwardDouble # normcdf :: ForwardDouble -> ForwardDouble #
InvErf ForwardDouble Source #
Methods inverf :: ForwardDouble -> ForwardDouble # inverfc :: ForwardDouble -> ForwardDouble # invnormcdf :: ForwardDouble -> ForwardDouble #
Mode ForwardDouble Source #
Associated Types type Scalar ForwardDouble :: * Source # Methods isKnownConstant :: ForwardDouble -> Bool Source # isKnownZero :: ForwardDouble -> Bool Source # auto :: Scalar ForwardDouble -> ForwardDouble Source # (^) :: Scalar ForwardDouble -> ForwardDouble -> ForwardDouble Source # (^) :: ForwardDouble -> Scalar ForwardDouble -> ForwardDouble Source # (^/) :: ForwardDouble -> Scalar ForwardDouble -> ForwardDouble Source # zero :: ForwardDouble Source #
Jacobian ForwardDouble Source #
Associated Types type D ForwardDouble :: * Source # Methods unary :: (Scalar ForwardDouble -> Scalar ForwardDouble) -> D ForwardDouble -> ForwardDouble -> ForwardDouble Source # lift1 :: (Scalar ForwardDouble -> Scalar ForwardDouble) -> (D ForwardDouble -> D ForwardDouble) -> ForwardDouble -> ForwardDouble Source # lift1_ :: (Scalar ForwardDouble -> Scalar ForwardDouble) -> (D ForwardDouble -> D ForwardDouble -> D ForwardDouble) -> ForwardDouble -> ForwardDouble Source # binary :: (Scalar ForwardDouble -> Scalar ForwardDouble -> Scalar ForwardDouble) -> D ForwardDouble -> D ForwardDouble -> ForwardDouble -> ForwardDouble -> ForwardDouble Source # lift2 :: (Scalar ForwardDouble -> Scalar ForwardDouble -> Scalar ForwardDouble) -> (D ForwardDouble -> D ForwardDouble -> (D ForwardDouble, D ForwardDouble)) -> ForwardDouble -> ForwardDouble -> ForwardDouble Source # lift2_ :: (Scalar ForwardDouble -> Scalar ForwardDouble -> Scalar ForwardDouble) -> (D ForwardDouble -> D ForwardDouble -> D ForwardDouble -> (D ForwardDouble, D ForwardDouble)) -> ForwardDouble -> ForwardDouble -> ForwardDouble Source #
type Scalar ForwardDouble Source #
type Scalar ForwardDouble = Double
type D ForwardDouble Source #
type D ForwardDouble = Id Double

Gradient

grad :: Traversable f => (f ForwardDouble -> ForwardDouble) -> f Double -> f Double Source #

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) Source #

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 Source #

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) Source #

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) Source #

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) Source #

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) Source #

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) Source #

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) Source #

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) Source #

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

Derivatives

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

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) Source #

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 Source #

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) Source #

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 Source #

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) Source #

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 Source #

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) Source #

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