Move the partition function out of Integration.Trapezoid and into Misc.

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

diff --git a/src/Integration/Trapezoid.hs b/src/Integration/Trapezoid.hs
index 959800135ea27be2da25aacd8bb3fc4a690139a6..8d4b76903b04603a09ebb748e501582b4026b0c6 100644 (file)
--- a/src/Integration/Trapezoid.hs
+++ b/src/Integration/Trapezoid.hs
@@ -1,26 +1,7 @@
 module Integration.Trapezoid
 where
 
-
--- | 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 Misc (partition)
 
 -- | Use the trapezoid rule to numerically integrate @f@ over the
 --   interval [@a@, @b@].
@@ -52,18 +33,18 @@ trapezoid_1 f a b =
   (((f a) + (f b)) / 2) * (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:
 --
 --   >>> 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
+--   >>> let area = trapezoid 1000 sin 0 pi
+--   >>> abs (area - 2) < 0.0001
 --   True
 --
 trapezoid :: (RealFrac a, Fractional b, Num b, Integral c)