Haskellで自動微分

autoDiff.hs

-- 参考: http://www.mathgram.xyz/entry/rust/ad/forward

data Dual = Dual { x :: Double
                 , dx :: Double
                 } deriving Show

instance Num Dual where
  (Dual x1 dx1) + (Dual x2 dx2) = Dual { x = x1 + x2, dx = dx1 + dx2 }
  (Dual x1 dx1) * (Dual x2 dx2) = Dual { x = x1 * x2, dx = dx1 * x2 + x1 * dx2 }

instance Fractional Dual

instance Floating Dual where
  sin (Dual x dx) = Dual { x = sin x, dx = dx * cos x }
  cos (Dual x dx) = Dual { x = cos x, dx = - dx * sin x }
  exp (Dual x dx) = Dual { x = exp x, dx = dx * exp x }

f :: Dual -> Dual
f x = x * x + x

g :: Dual -> Dual
g x = sin x + x * exp x

main :: IO ()
main = do
  let a = Dual { x = 2, dx = 1 } -- Dual {x = 6.0, dx = 5.0}
  print $ f a
  let b = Dual { x = 0, dx = 1 } -- Dual {x = 0.0, dx = 2.0}
  print $ g b