[Haskell-cafe] iota

2009-06-01 Thread Paul Keir 
Hi all,

 

I was looking for an APL-style iota function for array indices. I
noticed

range from Data.Ix which, with a zero for the lower bound (here
(0,0)),

gives the values I need:

 

 let (a,b) = (2,3)

 index ((0,0),(a-1,b-1))

 [(0,0),(0,1),(0,2),(1,0),(1,1),(1,2)]

 

However, I need the results as a list of lists rather than a list of
tuples; and

my input is a list of integral values. I ended up writing the following
function

instead. The function isn't long, but longer than I first expected. Did
I miss a

simpler approach?

 

iota :: (Integral a) = [a] - [[a]]

iota is = let count = product is

   tups = zip (tail $ scanr (*) 1 is) is

   buildRepList (r,i) = genericTake count $ cycle $

   [0..i-1]
= genericReplicate r

   lists = map buildRepList tups

 in transpose lists

 

 length $ iota [2,3,4]

 24

 

Thanks,

Paul

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Re: [Haskell-cafe] iota

2009-06-01 Thread Raynor Vliegendhart 
The iota function you're looking for can be a whole lot simpler if you
know about monads (list monad in particular) and sequence. For lists,
sequence has the following behaviour:


sequence [xs1,xs2, ... xsn] =
   [[x1,x2, ... , xn] | x1 - xs1, x2 - xs2, ... , xn - xsn]


Using this, you can reduce your iota function to a powerful one-liner:

iota = sequence . map (enumFromTo 0 . pred)


Kind regards,

Raynor Vliegendhart


On 6/1/09, Paul Keir pk...@dcs.gla.ac.uk wrote:



 Hi all,



 I was looking for an APL-style “iota” function for array indices. I noticed

 “range” from Data.Ix which, with a zero for the lower bound (here (0,0)),

 gives the values I need:



  let (a,b) = (2,3)

  index ((0,0),(a-1,b-1))

  [(0,0),(0,1),(0,2),(1,0),(1,1),(1,2)]



 However, I need the results as a list of lists rather than a list of tuples;
 and

 my input is a list of integral values. I ended up writing the following
 function

 instead. The function isn’t long, but longer than I first expected. Did I
 miss a

 simpler approach?



 iota :: (Integral a) = [a] - [[a]]

 iota is = let count = product is

tups = zip (tail $ scanr (*) 1 is) is

buildRepList (r,i) = genericTake count $ cycle $


[0..i-1] = genericReplicate r

lists = map buildRepList tups

  in transpose lists



  length $ iota [2,3,4]

  24



 Thanks,

 Paul
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