src/Misc.hs

   1 {-# LANGUAGE RebindableSyntax #-}
   2
   3 -- | Stuff for which I'm too lazy to come up with a decent name.
   4 module Misc
   5 where
   6
   7 import NumericPrelude
   8 import Algebra.Field
   9 import Algebra.ToInteger
  10
  11 -- | Partition the interval [@a@, @b@] into @n@ subintervals, which we
  12 --   then return as a list of pairs.
  13 --
  14 --   Examples:
  15 --
  16 --   >>> partition 1 (-1) 1
  17 --   [(-1.0,1.0)]
  18 --
  19 --   >>> partition 4 (-1) 1
  20 --   [(-1.0,-0.5),(-0.5,0.0),(0.0,0.5),(0.5,1.0)]
  21 --
  22 partition :: (Algebra.Field.C a, Algebra.ToInteger.C b, Enum b)
  23           => b -- ^ The number of subintervals to use, @n@
  24           -> a -- ^ The \"left\" endpoint of the interval, @a@
  25           -> a -- ^ The \"right\" endpoint of the interval, @b@
  26           -> [(a,a)]
  27  -- Somebody asked for zero subintervals? Ok.
  28 partition 0 _ _ = []
  29 partition n a b
  30   | n < 0 = error "partition: asked for a negative number of subintervals"
  31   | otherwise =
  32     [ (xi, xj) | k <- [0..n-1],
  33                  let k' = fromIntegral k,
  34                  let xi = a + k'*h,
  35                  let xj = a + (k'+1)*h ]
  36     where
  37       h = (b-a)/(fromIntegral $ toInteger n)