Clean up imports everywhere.

[numerical-analysis.git] / src / Integration / Trapezoid.hs

diff --git a/src/Integration/Trapezoid.hs b/src/Integration/Trapezoid.hs
index 5452a5e8a5fe70195cf3de6711934dadd8cb623d..df4da781b6cea30e7fbe763ee20da9ba85549db7 100644 (file)
--- a/src/Integration/Trapezoid.hs
+++ b/src/Integration/Trapezoid.hs
@@ -1,7 +1,19 @@
-module Integration.Trapezoid
+{-# LANGUAGE NoImplicitPrelude #-}
+{-# LANGUAGE RebindableSyntax #-}
+
+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 )
+
 
 -- | Use the trapezoid rule to numerically integrate @f@ over the
 --   interval [@a@, @b@].
@@ -24,30 +36,37 @@ import Misc (partition)
 --   >>> trapezoid_1 f (-1) 1
 --   2.0
 --
-trapezoid_1 :: (RealFrac a, Fractional b, Num b)
+trapezoid_1 :: (Field.C a, ToRational.C a, Field.C b)
             => (a -> b) -- ^ The function @f@
             -> a       -- ^ The \"left\" endpoint, @a@
             -> a       -- ^ The \"right\" endpoint, @b@
             -> b
 trapezoid_1 f a b =
-  (((f a) + (f b)) / 2) * (realToFrac (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
 --
-trapezoid :: (RealFrac a, Fractional b, Num b, Integral c)
+trapezoid :: (RealField.C a,
+              ToRational.C a,
+              RealField.C b,
+              ToInteger.C c,
+              Enum c)
           => c -- ^ The number of subintervals to use, @n@
           -> (a -> b) -- ^ The function @f@
           -> a       -- ^ The \"left\" endpoint, @a@