From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 23 Nov 2012 18:39:42 +0000 (-0500)
Subject: Move the partition function out of Integration.Trapezoid and into Misc.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=92d61dc6ab8dc3e8c9e5b4c869134f1e8079013f;p=numerical-analysis.git

Move the partition function out of Integration.Trapezoid and into Misc.
Fix some trapezoid doctests.
---

diff --git a/src/Integration/Trapezoid.hs b/src/Integration/Trapezoid.hs
index 9598001..8d4b769 100644
--- 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)
diff --git a/src/Misc.hs b/src/Misc.hs
new file mode 100644
index 0000000..4d8f3e7
--- /dev/null
+++ b/src/Misc.hs
@@ -0,0 +1,31 @@
+-- | Stuff for which I'm too lazy to come up with a decent name.
+module Misc
+where
+
+-- | Partition the interval [@a@, @b@] into @n@ subintervals, which we
+--   then return as a list of pairs.
+--
+--   Examples:
+--
+--   >>> partition 1 (-1) 1
+--   [(-1.0,1.0)]
+--
+--   >>> partition 4 (-1) 1
+--   [(-1.0,-0.5),(-0.5,0.0),(0.0,0.5),(0.5,1.0)]
+--
+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)