+{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE RebindableSyntax #-}
-module Integration.Trapezoid
+module Integration.Trapezoid (
+ trapezoid,
+ trapezoid_1 )
where
-import Misc (partition)
+import Misc ( partition )
+
+import NumericPrelude hiding ( abs )
+import qualified Algebra.Field as Field ( C )
+import qualified Algebra.RealField as RealField ( C )
+import qualified Algebra.ToInteger as ToInteger ( C )
+import qualified Algebra.ToRational as ToRational ( C )
-import NumericPrelude hiding (abs)
-import Algebra.Absolute (abs)
-import qualified Algebra.Field as Field
-import qualified Algebra.RealField as RealField
-import qualified Algebra.RealRing as RealRing
-import qualified Algebra.ToInteger as ToInteger
-import qualified Algebra.ToRational as ToRational
-- | Use the trapezoid rule to numerically integrate @f@ over the
-- interval [@a@, @b@].
-> a -- ^ The \"right\" endpoint, @b@
-> b
trapezoid_1 f a b =
- (((f a) + (f b)) / 2) * (fromRational' $ toRational (b - a))
-
+ (((f a) + (f b)) / 2) * coerced_interval_length
+ where
+ coerced_interval_length = fromRational' $ toRational (b - a)
-- | Use the composite trapezoid rule to numerically integrate @f@
-- over @n@ subintervals of [@a@, @b@].
--
-- Examples:
--
+-- >>> import Algebra.Absolute (abs)
-- >>> let f x = x^2
-- >>> let area = trapezoid 1000 f (-1) 1
-- >>> abs (area - (2/3)) < 0.00001
-- True
--
+-- >>> import Algebra.Absolute (abs)
-- >>> let area = trapezoid 1000 sin 0 pi
-- >>> abs (area - 2) < 0.0001
-- True