X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FIntegration%2FTrapezoid.hs;h=df4da781b6cea30e7fbe763ee20da9ba85549db7;hb=ae914d13235a4582077a5cb2b1edd630d9c6ad62;hp=959800135ea27be2da25aacd8bb3fc4a690139a6;hpb=57a982c464095201f7635977aac937ad6a08c0b0;p=numerical-analysis.git

diff --git a/src/Integration/Trapezoid.hs b/src/Integration/Trapezoid.hs
index 9598001..df4da78 100644
--- a/src/Integration/Trapezoid.hs
+++ b/src/Integration/Trapezoid.hs
@@ -1,25 +1,18 @@
-module Integration.Trapezoid
+{-# LANGUAGE NoImplicitPrelude #-}
+{-# LANGUAGE RebindableSyntax #-}
+
+module Integration.Trapezoid (
+  trapezoid,
+  trapezoid_1 )
 where
 
+import Misc ( partition )
 
--- | Partition the interval [@a@, @b@] into @n@ subintervals, which we
---   then return as a list of pairs.
-partition :: (RealFrac a, Integral b)
-          => b -- ^ The number of subintervals to use, @n@
-          -> a -- ^ The \"left\" endpoint of the interval, @a@
-          -> a -- ^ The \"right\" endpoint of the interval, @b@
-          -> [(a,a)]
- -- Somebody asked for zero subintervals? Ok.
-partition 0 _ _ = []
-partition n a b
-  | n < 0 = error "partition: asked for a negative number of subintervals"
-  | otherwise =
-    [ (xi, xj) | k <- [0..n-1],
-                 let k' = fromIntegral k,
-                 let xi = a + k'*h,
-                 let xj = a + (k'+1)*h ]
-    where
-      h = fromRational $ (toRational (b-a))/(toRational n)
+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
@@ -43,30 +36,37 @@ partition n a b
 --   >>> 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) * (fromRational $ toRational (b - a))
-
+  (((f a) + (f b)) / 2) * coerced_interval_length
+  where
+    coerced_interval_length = fromRational' $ toRational (b - a)
 
--- | Use the composite trapezoid tule to numerically integrate @f@
+-- | 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
+--   >>> abs (area - (2/3)) < 0.00001
 --   True
 --
---   >>> let area = trapezoid 1000 sin (-1) 1
---   >>> abs (area - 2) < 0.00001
+--   >>> 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@