{-# LANGUAGE NoImplicitPrelude #-}
+{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE RebindableSyntax #-}
module Integration.Simpson (
-- >>> simpson_1 f 0 1
-- 0.25
--
-simpson_1 :: (RealField.C a, ToRational.C a, RealField.C b)
+simpson_1 :: forall a b. (RealField.C a, ToRational.C a, RealField.C b)
=> (a -> b) -- ^ The function @f@
-> a -- ^ The \"left\" endpoint, @a@
-> a -- ^ The \"right\" endpoint, @b@
-> b
-simpson_1 f a b =
- coefficient * ((f a) + 4*(f midpoint) + (f b))
+simpson_1 f x y =
+ coefficient * ((f x) + 4*(f midpoint) + (f y))
where
- coefficient = fromRational' $ (toRational (b - a)) / 6
- midpoint = (a + b) / 2
+ coefficient = fromRational' $ (toRational (y - x)) / 6 :: b
+ midpoint = (x + y) / 2
-- | Use the composite Simpson's rule to numerically integrate @f@