{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
module Numeric.AD.Rank1.Newton.Double
(
findZero
, inverse
, fixedPoint
, extremum
) where
import Prelude hiding (all, mapM)
import Numeric.AD.Mode
import Numeric.AD.Rank1.Forward (Forward)
import qualified Numeric.AD.Rank1.Forward as Forward
import Numeric.AD.Rank1.Forward.Double (ForwardDouble, diff')
import Numeric.AD.Internal.On
import Numeric.AD.Internal.Combinators (takeWhileDifferent)
findZero :: (ForwardDouble -> ForwardDouble) -> Double -> [Double]
findZero :: (ForwardDouble -> ForwardDouble) -> Double -> [Double]
findZero ForwardDouble -> ForwardDouble
f = forall a. Eq a => [a] -> [a]
takeWhileDifferent forall b c a. (b -> c) -> (a -> b) -> a -> c
. (ForwardDouble -> ForwardDouble) -> Double -> [Double]
findZeroNoEq ForwardDouble -> ForwardDouble
f
{-# INLINE findZero #-}
findZeroNoEq :: (ForwardDouble -> ForwardDouble) -> Double -> [Double]
findZeroNoEq :: (ForwardDouble -> ForwardDouble) -> Double -> [Double]
findZeroNoEq ForwardDouble -> ForwardDouble
f = forall a. Eq a => [a] -> [a]
takeWhileDifferent forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. (a -> a) -> a -> [a]
iterate Double -> Double
go where
go :: Double -> Double
go Double
x = Double
xn where
(Double
y,Double
y') = (ForwardDouble -> ForwardDouble) -> Double -> (Double, Double)
diff' ForwardDouble -> ForwardDouble
f Double
x
xn :: Double
xn = Double
x forall a. Num a => a -> a -> a
- Double
yforall a. Fractional a => a -> a -> a
/Double
y'
{-# INLINE findZeroNoEq #-}
inverse :: (ForwardDouble -> ForwardDouble) -> Double -> Double -> [Double]
inverse :: (ForwardDouble -> ForwardDouble) -> Double -> Double -> [Double]
inverse ForwardDouble -> ForwardDouble
f Double
x0 = forall a. Eq a => [a] -> [a]
takeWhileDifferent forall b c a. (b -> c) -> (a -> b) -> a -> c
. (ForwardDouble -> ForwardDouble) -> Double -> Double -> [Double]
inverseNoEq ForwardDouble -> ForwardDouble
f Double
x0
{-# INLINE inverse #-}
inverseNoEq :: (ForwardDouble -> ForwardDouble) -> Double -> Double -> [Double]
inverseNoEq :: (ForwardDouble -> ForwardDouble) -> Double -> Double -> [Double]
inverseNoEq ForwardDouble -> ForwardDouble
f Double
x0 Double
y = (ForwardDouble -> ForwardDouble) -> Double -> [Double]
findZeroNoEq (\ForwardDouble
x -> ForwardDouble -> ForwardDouble
f ForwardDouble
x forall a. Num a => a -> a -> a
- forall t. Mode t => Scalar t -> t
auto Double
y) Double
x0
{-# INLINE inverseNoEq #-}
fixedPoint :: (ForwardDouble -> ForwardDouble) -> Double -> [Double]
fixedPoint :: (ForwardDouble -> ForwardDouble) -> Double -> [Double]
fixedPoint ForwardDouble -> ForwardDouble
f = forall a. Eq a => [a] -> [a]
takeWhileDifferent forall b c a. (b -> c) -> (a -> b) -> a -> c
. (ForwardDouble -> ForwardDouble) -> Double -> [Double]
fixedPointNoEq ForwardDouble -> ForwardDouble
f
{-# INLINE fixedPoint #-}
fixedPointNoEq :: (ForwardDouble -> ForwardDouble) -> Double -> [Double]
fixedPointNoEq :: (ForwardDouble -> ForwardDouble) -> Double -> [Double]
fixedPointNoEq ForwardDouble -> ForwardDouble
f = (ForwardDouble -> ForwardDouble) -> Double -> [Double]
findZeroNoEq (\ForwardDouble
x -> ForwardDouble -> ForwardDouble
f ForwardDouble
x forall a. Num a => a -> a -> a
- ForwardDouble
x)
{-# INLINE fixedPointNoEq #-}
extremum :: (On (Forward ForwardDouble) -> On (Forward ForwardDouble)) -> Double -> [Double]
extremum :: (On (Forward ForwardDouble) -> On (Forward ForwardDouble))
-> Double -> [Double]
extremum On (Forward ForwardDouble) -> On (Forward ForwardDouble)
f = forall a. Eq a => [a] -> [a]
takeWhileDifferent forall b c a. (b -> c) -> (a -> b) -> a -> c
. (On (Forward ForwardDouble) -> On (Forward ForwardDouble))
-> Double -> [Double]
extremumNoEq On (Forward ForwardDouble) -> On (Forward ForwardDouble)
f
{-# INLINE extremum #-}
extremumNoEq :: (On (Forward ForwardDouble) -> On (Forward ForwardDouble)) -> Double -> [Double]
extremumNoEq :: (On (Forward ForwardDouble) -> On (Forward ForwardDouble))
-> Double -> [Double]
extremumNoEq On (Forward ForwardDouble) -> On (Forward ForwardDouble)
f = (ForwardDouble -> ForwardDouble) -> Double -> [Double]
findZeroNoEq (forall a. Num a => (Forward a -> Forward a) -> a -> a
Forward.diff (forall t. On t -> t
off forall b c a. (b -> c) -> (a -> b) -> a -> c
. On (Forward ForwardDouble) -> On (Forward ForwardDouble)
f forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall t. t -> On t
On))
{-# INLINE extremumNoEq #-}