[Haskell-cafe] Application of iterate

[Henning Thielemann]

On Fri, 23 Mar 2007, Neil Mitchell wrote:

> Hi Longesh
>
> > But I've found learning Haskell so tough (this is my 4th try in the last
> > two years) that I feel I have to bore everyone with my first non-trivial
> > program.
>
> Well done on getting something going!
>
> > my_sqrt t = last (take 20 (iterate (\n -> n/2 + t/(2 * n)) t))

http://darcs.haskell.org/htam/src/Numerics/ZeroFinder/Newton.hs

with
  inverse t (\x->(x^2,2*x)) t

> > It is a bit crude though.  20 iterations is a bit arbitrary. I don't suppose
> > there is a easy way to iterate until the results stop changing.
>
> close (x:y:xs) | abs (x - y) < 0.1 = y
> close (x:xs) = close xs
>
> I don't know how to add it into the one liner though - although I
> suspect someone here will :)


http://darcs.haskell.org/htam/src/Numerics/Sequence.hs

limitDifference :: (Real a) => a -> [a] -> a
limitDifference tol xs =
   case dropWhile ((> tol) . abs . uncurry (-)) $ zip xs (tail xs) of
      ((_,x):_) -> x
      [] -> error "limitDifference: Finite sequence, but no element satisfies abort criterion."