Rodrigo Queiro overdrigzed at gmail.com
Thu Sep 6 10:34:25 EDT 2007

```When you get to more than two arguments, it will probably be nicer to
do something like this:
fibs = map (\(a,b) -> a) \$ iterate (\(a,b) -> (b, a+b)) (0,1)
or
fibs = unfoldr (\(a,b) -> Just (a, (b, a+b))) (0,1) -- this uses
unfoldr to get rid of the map

This is essentially a translation of the imperative algorithm - the
state is stored in the tuple, which is repeatedly transformed by the
function \(a,b) -> (b, a+b), and then you extract the values to be
yielded from the state with \(a,b) -> a.

On 06/09/07, Axel Gerstenberger <axel.gerstenberger at gmx.de> wrote:
> Thanks to all of you. The suggestions work like a charm. Very nice.
>
> I still need to digest the advices, but have already one further
> question: How would I compute the new value based on the 2 (or even
> more) last values instead of only the last one?
>
> [ 2, 3 , f 3 2, f((f 3 2) 3), f ( f((f 3 2) 3)  f 3 2)), ...]
>
> (background: I am doing explicit time stepping for some physical
> problem, where higher order time integration schemes are interesting.
> You advance in time by extrapolating based on the old time step values.)
>
> I guess I just wrote the definition and define iterate2 as
>
> iterate2 history =
>       case history of
>           []   -> error "no start values"
>           x1:x2:xs   -> iterate2 ([f x1 x2] ++ xs)
> or
>
> iterate2 :: [Double] -> [Double]
> iterate2 history =
>       case history of
>           []   -> error "two start values needed"
>           x1:[]   -> error "one more start values"
>           x1:x2:xs   -> iterate2 (history ++ ([f a b]))
>              where [a,b] = take 2 \$ reverse history
>
> however,I don't get it this to work. Is it possible to see the
> definition of the iterate function? The online help just shows it's usage...
>
> Again thanks a lot for your ideas and the links. I knew there was a
> one-liner for my problem, but I couldn't find it for days.
>
> Axel
>
> Dougal Stanton wrote:
> > On 06/09/07, Axel Gerstenberger <axel.gerstenberger at gmx.de> wrote:
> >
> >> module Main where
> >>
> >> import System.IO
> >> import Text.Printf
> >>
> >> main :: IO ()
> >> main = do
> >>      let all_results1 = take 20000 \$ step [1]
> >>      --print \$ length all_results1 -- BTW: if not commented out,
> >>                                    --      all values of all_results
> >>                                    --      calculated here
> >>      loop [1..50] \$ \i -> do
> >>          let x = all_results1!!i
> >>          putStrLn \$ show i ++ "  " ++ show x
> >>
> >> -- create an infinite list with values u_{n+1} ++ [u_n,u_{n-1},...,u_1]
> >> -- where u_{n+1} = f (u_n)
> >> step history =
> >>      case history of
> >>          []   -> error "no start values"
> >>          xs   -> xs ++ (step [ f (head \$ reverse (xs) )])
> >
> > To create an infinite list where each f(u) depends on the previous u,
> > with a single seed value, use 'iterate':
> >
> > Prelude> let us = iterate f 3
> >
> > That produces your infinite list of values, starting with [f 3, f(f3),
> > f(f(f 3)), ...]. Pretty neat.
> >
> > Then all you really need is
> >
> > main = mapM_ (uncurry (printf "%d %f\n")) (zip [1..50] (iterate f 3))
> >
> > You can probably shorten this a bit more with arrows but I've got a
> > cold at the moment and not really thinking straight.
> >
> > Cheers,
> >
> > D.
> >
> _______________________________________________