IntegralApproximations.hs

import Prelude
import Control.Applicative

-- These are some sketchy implementations of integral approximations.
-- They work, but are probably in need of refactoring.
-- I repeat: I SUCK at Haskell, so this is really gross.

midApp n a b f = h * (foldl (+) 0 vals) where
  h = (b - a)/n
  vals = [midF i | i <- [1..n]] where
    midF i = let x = (*h) in f $ (x (i - 1) + x i) / 2

simpApp n a b f = h/3 * (foldl (+) 0 vals) where
  h = (b - a)/(fromIntegral n)
  vals = (val <$> [0,n]) ++ (vals' odd 4) ++ (vals' even 2) where
    val i = f $ (fromIntegral i) * h
    vals' p m = (*m) <$> val <$> filter p [1..n-1]

trapApp n a b f = h/2 * (foldl (+) 0 vals) where
  h = (b - a)/(fromIntegral n)
  vals = (val <$> [0,n]) ++ ((*2) <$> val <$> [1..n-1]) where
    val i = f $ (fromIntegral i) * h