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

[numerical-analysis.git] / src / Misc.hs

diff --git a/src/Misc.hs b/src/Misc.hs
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+++ b/src/Misc.hs
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+-- | 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)