On 06/26/2011 04:16 PM, michael rice wrote:
MathWorks has the function seqperiod(x) to return the period of sequence x. Is there an equivalent function in Haskell?
Could you specify what exactly the function is supposed to do? I am pretty sure that a function like seqPeriod :: (Eq a) => [a] -> Maybe Integer -- Nothing iff non-periodic cannot be written. If "sequences" are represented by the terms that define them (or this information is at least accessible), chances might be better, but I would still be interested how such a function works. The problem seems undecidable to me in general. On finite lists (which may be produced from infinite ones via 'take'), a naive implementation could be this:
import Data.List (inits, cycle, isPrefixOf) import Debug.Trace
-- Given a finite list, calculate its period. -- The first parameter controls what is accepted as a generator. See
below.
-- Set it to False when looking at chunks from an infinite sequence. listPeriod :: (Eq a) => Bool -> [a] -> Int listPeriod precisely xs = case filter (generates precisely xs) (inits xs) of -- as (last $ init xs) == xs, this will always suffice. (g:_) -> length g -- length of the *shortest* generator
-- @generates prec xs g@ iff @g@ generates @xs@ by repitition. If @prec@, the -- lengths have to match, too. Consider -- -- >>> generates True [1,2,3,1,2,1,2] [1,2,3,1,2] -- False -- -- >>> generates False [1,2,3,1,2,1,2] [1,2,3,1,2] -- True generates :: (Eq a) => Bool -> [a] -> [a] -> Bool generates precisely xs g = if null g then null xs else (not precisely || length xs `mod` length g == 0) && xs `isPrefixOf` cycle g
-- Steffen