src/Misc.hs

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