X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FIntegration%2FSimpson.hs;h=f0f57f29245db1a7db7bd10bd05a39a87c2347df;hb=ae914d13235a4582077a5cb2b1edd630d9c6ad62;hp=c9ad414b4fa7cc85705af2604d2295524ceeb01e;hpb=2f54e89d36e835c58efcc281741632d457859b20;p=numerical-analysis.git diff --git a/src/Integration/Simpson.hs b/src/Integration/Simpson.hs index c9ad414..f0f57f2 100644 --- a/src/Integration/Simpson.hs +++ b/src/Integration/Simpson.hs @@ -1,14 +1,17 @@ +{-# LANGUAGE NoImplicitPrelude #-} {-# LANGUAGE RebindableSyntax #-} -module Integration.Simpson +module Integration.Simpson ( + simpson, + simpson_1 ) where -import Misc (partition) +import Misc ( partition ) -import NumericPrelude hiding (abs) -import qualified Algebra.RealField as RealField -import qualified Algebra.ToInteger as ToInteger -import qualified Algebra.ToRational as ToRational +import NumericPrelude hiding ( abs ) +import qualified Algebra.RealField as RealField ( C ) +import qualified Algebra.ToInteger as ToInteger ( C ) +import qualified Algebra.ToRational as ToRational ( C ) -- | Use the Simpson's rule to numerically integrate @f@ over the -- interval [@a@, @b@]. @@ -45,7 +48,7 @@ simpson_1 :: (RealField.C a, ToRational.C a, RealField.C b) simpson_1 f a b = coefficient * ((f a) + 4*(f midpoint) + (f b)) where - coefficient = (fromRational' $ toRational (b - a)) / 6 + coefficient = fromRational' $ (toRational (b - a)) / 6 midpoint = (a + b) / 2